# Mechatronic Design of Mobile Robots for Stable Obstacle Crossing at Low and High Speeds

Jean-Christophe Fauroux, Frédéric Chapelle, Belhassen-Chedli Bouzgarrou,

Philippe Vaslin, Mohamed Krid, Marc Davis

► To cite this version:

Jean-Christophe Fauroux, Frédéric Chapelle, Belhassen-Chedli Bouzgarrou, Philippe Vaslin, Mohamed Krid, et al.. Mechatronic Design of Mobile Robots for Stable Obstacle Crossing at Low and High Speeds. Maki K. Habib. Handbook of Research on Advancements in Robotics and Mechatronics, IGI Global, pp.567-630, 2015, 9781466673878. 10.4018/978-1-4666-7387-8 . hal-05008291

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# Mechatronic Design of Mobile Robots for Stable Obstacle Crossing at Low and High Speeds

Jean-Christophe FAUROUX<fnref n="1" />

Frédéric CHAPELLE<fnref n="1" />

Belhassen-Chedli BOUZGARROU<fnref n="1" />

Philippe VASLIN<fnref n="2" />

Mohamed KRID<fnref n="1" />

Marc DAVIS<fnref n="2" />

## ABSTRACT

This chapter presents recent mechatronics developments to create original terrestrial mobile robots capable to cross obstacles and maintain their stability on irregular grounds. Obstacle crossing is both considered at low and high speeds. The developed robots use wheeled propulsion, efficient on smooth grounds, and improve performance on irregular grounds with additional mobilities, bringing them closer to legged locomotion (hybrid locomotion).

Two sections are dedicated to low speed obstacle crossing. Section 2 presents an original mobile robot combining four actuated wheels with an articulated frame to improve obstacle climbing. Section 3 extends this work to a new concept of modular poly-robot for agile transport of long payloads.

The last two sections deal with high speed motion. Section 4 describes new suspensions with four mobilities that maintain pitch stability of vehicles crossing obstacles at high speed. After the shock, Section 5 demonstrates stable pitch control during ballistic phase by accelerating-braking the wheels in flight.

## KEYWORDS

Agile mobile robots, All-terrain vehicles, Obstacle crossing, Hybrid leg-wheel locomotion, Stability criterion, Low actuation, Collaborative robots, Suspension, Parallel mechanism, Ballistic pitch stabilization, OpenWHEEL i3R, C³Bots AT/VLP, miniFAST, Susp4D, RobCAT.

## 1 MECHATRONIC DESIGN OF MOBILE ROBOTS FOR OBSTACLE CROSSING

We are currently seeing a strong expansion of flying drones (UAVs, Unmanned Aerial Vehicles) of every sizes for professional activities and leisure. Although some of them are strong enough to carry a small payload, most of them are inexpensive light robots only equipped with vision sensors for tasks related to aerial inspection.

However, the majority of human activities are located on the ground and terrestrial mobile robots have a higher potential for helping humans in a convincing way, with a longer autonomy. Many tasks are becoming possible, such as transport on unstructured grounds or fast inspection by fleets of small agile robots. Civil and military service applications can be imagined for agriculture, forestry, transport, disabled people, industry, defence and crisis management during natural catastrophes.

<footnote n="1">¹ Clermont University, French Institute for Advanced Mechanics (IFMA), Institut Pascal, UMR 6602 UBP/CNRS/IFMA, B.P.10448, F-63000 Clermont-Ferrand, France</footnote>

<footnote n="2">² Clermont University, Blaise Pascal University, Laboratory of Computer Sciences, Modelling and System Optimization (LIMOS – UMR 6158 CNRS), B.P. 10448, F-63000 Clermont-Ferrand, France.</footnote>
One difficulty that prevents the extension of terrestrial mobile robots, compared to flying robots, is the varied nature of ground environments. For example, they can be structured or non structured, flat or irregular, with cohesive or granular materials. Mobile robots are already well known in industry, where they move easily on structured flat cohesive grounds, guided by referenced landmarks. For example, Automatic Guided Vehicles (AGVs) are commonly used for transporting large parts for aeronautics and performing logistics tasks. However, as soon as the environment is natural, with irregular surfaces and granular grounds, without regular roadways and reference points, terrestrial mobile robots have difficulties to move and to perform their task.

## 1.1 Mechatronics for mobile robotics

Mechatronics can be seen as a unifying transversal discipline touching many sectors, from automotive to robotics (Habib, 2007). The particular domain of mobile robotics requires suitable mechatronic architectures for robots that evolve in varied environments (Siegwart, Nourbakhsh, & Scaramuzza, 2011). A semantic map of some useful concepts connected with mechatronics for mobile robotics can be seen in Figure 1. Moreover, many general terms useful for this paper are regrouped in a glossary at the end of this work in the section *Key terms and definitions*.

<caption>Figure 1: Semantic map of a selection of concepts connected with mechatronics for locomotion.</caption>

Defining a mobile robot architecture generally starts by choosing its kinematics, propulsion devices and locomotion modes. Although the majority of vehicles use one of the three main types of propulsion devices that are wheel / track / leg, reviews show that many new kinematics and ways to combine propulsion devices appear each year, so this research sector can be considered very active (Bruzzone & Quaglia, 2012). Some architectures claim to be efficient on several types of terrains such as rocky and sandy areas, inclined planes or stairs (A. K. Gupta & V. K. Gupta, 2013). Kinematic redundancy and modularity can be another way to enhance mobility on rough terrain (Labenda, Sadek, & Heckes, 2010).

Mobile robots use varied types of sensors to provide information about the environment. Distance sensors such as odometers and ultrasound sensors allow localizing the robot with respect to obstacles (Izumi, Habib, Watanabe, & Sato, 2008). Attitude sensors such as accelerometers, gyrometers, gyroscopes and IMUs (Inertial Measurement Units) can evaluate angles, angular speeds and accelerations. Global sensors such as cameras (De Croon, De Weerdt, De Wagter, & Remes, 2010) or LIDARs (Light Detection And Ranging) help to construct maps of the environment, either during locomotion or by using preliminary observation (Ohki, Nagatani, & Yoshida, 2013). Force sensors can be used to detect contacts and even be included into the wheels for ground characterization (Park, Kim, & Lee, 2012). Whatever the precision of the sensors, fusion is often required between data coming from varied sensors in order to improve reliability of the information about the environment (Shih, Chen, & Chou, 2012).

Most of the time, control of mobile robot uses path planning in structured environments based on obstacle avoidance. A virtual force-field between mobile robots and the obstacles to keep them away at a desired distance can be used for control (Wen, Zheng, Zhu, Li, & Chen, 2012), combined with fuzzy adaptive control to compensate the uncertainties in the dynamic model, also used for unicycle Khepera robots (Samsudin, Ahmad, & Mashohor, 2011). Neural networks can also be used to guide mobile robots through a maze with arbitrary obstacles (Chi & Lee, 2011). Frontiers of the navigation map are other types of obstacles that require specific control methods for border patrolling (Matveev, Teimoori, & Savkin, 2011). Recent developments also aim to safely control robots in crowded environment, where humans are a sort of obstacle, either by statistical training based on human patterns (Chung & Huang, 2011) or by a hybrid control approach (roaming trails) combining a map of the environment and local perception (Sgorbissa & Zaccaria, 2012). Most of these approaches rely on quasi-static locomotion but
some works integrate high dynamics (Semini et al., 2011) and real time obstacle avoidance using impenetrability of multiple convex shaped objects (Khansari-Zadeh & Billard, 2012).

However, other works consider mobile robots on rough terrain, where the robot has to be stabilized on ground irregularities.

Some works deal with wheeled locomotion and optimal approaches are developed to minimise contact force variations and maximise draw bar pull of off-road vehicles on different types of grounds (Isher, Xu, & Long, 2012). The interaction of the wheel with the ground (terramechanics) can also be optimized for minimal slippage and maximal traction of wheeled vehicles in a dry sandy terrain (Ani, Xu, Liu, & Isher, 2012).

Very numerous works are dedicated to control legged mobile robots in rough terrain. An efficient walking gait can be obtained by active tilting (Kamikawa, Takubo, Mae, Inoue, & Arai, 2012), active compliance and dynamical balancing (Ugurlu, Kotaka, & Narikiyo, 2013), force-control (Irawan & Nonami, 2011) or passive dynamics (Aoyama, Sekiyama, Hasegawa, & Fukuda, 2012). For quadrupeds evolving on unperceived rough terrain, modular controllers can be used based on a biomimetic central pattern generator (Ajallooeeian, Gay, Tuleu, Spröwitz, & Ijspeert, 2013). Optimisation is generally extensively applied to find both structural and articular parameters that improve the posture and stability on rough terrain (Zhang, Liu, Zhao, Chen, & Yan, 2014; Zucker et al., 2011). Locomotion can also benefit from learning of foothold choices from expert demonstration, combined with optimal ZMP stability criterion and force control (Kalakrishnan, Buchli, Pastor, Mistry, & Schaal, 2011). Multiple modes of locomotion are also considered for a given robot, such as biped walking, quadruped walking, vertical climbing and even brachiation, a form of arboreal locomotion in which a primate swings its body like a pendulum to transfer from a tree limb to another using its arms (Lu, Aoyama, Sekiyama, Hasegawa, & Fukuda, 2014).

All these works show the profuseness and inventiveness that characterize the domain of locomotion of mobile robots. Most of current mobile robots are controlled to avoid obstacles. Some of them are given moderate crossing-capacities allowing them to cross only irregularities of the ground and not real obstacles. It also appears clearly that obstacle crossing is not often treated.

## 1.2 Why obstacle crossing is a challenge for wheeled vehicles

The notion of obstacle is very general. It can be used to refer to any part of the environment that cannot be reached by the robot, or that prevents that the robot runs along its planned trajectory. In this chapter, the considered robot will be defined with a local reference frame at its centre of mass $G_R$ with $X_R$ in the direction of longitudinal motion, $Z_R$ in the direction opposite to gravity and $Y_R$ oriented laterally so that $(X_R, Y_R, Z_R)$ is direct. Generally, obstacles for terrestrial mobile robots have a strong component of their normal vector against the horizontal motion of the robot (i.e. along $-X_R$) and a great height $h_0$ with respect to the robot height $h_R$ (Fig. 2). The pitch angle is the angle between the horizontal ground axis $X_G$ and the longitudinal robot axis $X_R$ around lateral axis $Y_R$.

<caption>Figure 2: A mobile robot, its local frame $(X_R, Y_R, Z_R)$ and different local shapes of the ground ranging from an easy to cross irregularity up to a challenging obstacle.</caption>

Although wheels are the more common propulsion system, this chapter will also introduce other propulsion systems such as legs and tracks, and also try to hybridize wheels with legs, so that the resulting hybrid robot can take advantages of both systems. Wheels are notably known for their good efficiency on smooth grounds, whereas legs are efficient on irregular grounds (Bekker, 1969). Obstacle crossing can be considered as a challenge for terrestrial robots. Although some military and spatial exploration robots have interesting obstacle crossing capacities, a lot of work remains to be done for creating simple architectures capable to cross high obstacles with low energy, few actuators and a guaranteed stability during the whole process.
As shown in Table 1, this chapter is divided into four sections. Here is a summary of section contents:

- Section 2 deals with obstacle crossing at low speed. In this part is introduced *OpenWHEEL i3R*, an agile mobile robot designed by the authors, with articulated chassis and four motorized wheels (Fauroux, Chapelle, & Bouzgarrou, 2006, 2008, 2009, 2010; Fauroux & Vaslin, 2011). Chassis mobilities are used to maintain the wheel contacts on ground surface and lift off the wheels during cross-over manoeuvres of obstacles. This sequence of manoeuvres can be seen as a climbing mode which uses both wheels and inter-axle actuation, thus pertaining to the category of hybrid leg-wheel locomotion. After giving a geometric model and the minimal equations for its design and control, some experimental results are provided, based on the three prototypes created both at small scale (30cm) and high scale (2m).

- Section 3 is also focused on low speed but the payload is here explicitly considered. An original patented concept of poly-robot assembled from several collaborative modular mono-robots is presented (Fauroux, Bouzgarrou, & Krid, 2014). In this case, the payload is also used as a part of the frame, which helps to simplify the mono-robot structure. The poly-robot with its payload can cross obstacles and maintain its stability thanks to suitable internal mobilities and a control strategy derived from OpenWHEEL i3R. The corresponding robot is named here *C³Bots*, which means Collaborative Cross and Carry mobile roBots. This version is named *AT/VLP* (All Terrain / Ventral Long Payload) (Krid, Fauroux, & Bouzgarrou, 2014).

- Section 4 presents obstacle crossing at high speed. Most of wheeled vehicles meeting an obstacle at high speed tend to tip-over and destroy their suspension. This section shows how a suspension with four mobilities, including a longitudinal translation allowing the wheel to go rearwards with respect to the frame, could provide better dynamic performance. Structural synthesis was used to create nine solutions. The best solution is named *Susp4D* and integrated in the *miniFAST* rover. It was patented (Fauroux & Cousturier, 2011, 2012) and first introduced in (Fauroux, 2012).

- Section 5 concludes the chapter with an original active pitch stabilizing strategy suitable for high speed rovers in ballistic phase. This work is based on the experimental analysis of motorbike jumping (Vaslin, Pouzols, Gouinaud, Fauroux, Deleplanque, & Davis, 2011) and presents a dynamic model for correcting the pitch angle in flight by accelerating / braking the wheels. The equations are successfully tested on a simulator and can be used to stabilize a wheeled rover in flight (Davis, Vaslin, Fauroux, Gouinaud, & Ju, 2012). The corresponding prototype rover is named *RobCAT*, the rover that jumps and always lands on its wheels.

<table><caption>Table 1: Topic dispatching of the different chapter sections.</caption><thead><tr><th>Section #</th><th>Scientific topic</th><th>Device / Robot name</th><th>High speed</th><th>Obstacle crossing</th><th>Active stabilization</th><th>Co-mani-pulation robot-robot</th></tr></thead><tbody><tr><td>2</td><td>Agile robots for obstacle-crossing at low speed Modular cooperative mobile robots for ventral long payload transport and obstacle crossing</td><td>OpenWHEEL i3R</td><td></td><td>X</td><td>X</td><td></td></tr><tr><td>3</td><td>Synthesis of spatial parallel mechanisms for a vertical and longitudinal all-terrain suspension</td><td>C³Bots AT/VLP</td><td></td><td>X</td><td>X</td><td>X</td></tr><tr><td>4</td><td></td><td>Susp4D suspension MiniFAST rover</td><td>X</td><td>X</td><td></td><td></td></tr><tr><td>5</td><td>Dynamic pitch control of a mobile robot in ballistic phase</td><td>RobCAT</td><td>X</td><td></td><td>X</td><td></td></tr></tbody></table>
The scientific topics can be classified according to four criteria (Table 1):

- The first criterion is **speed**: at low speed (typically a few centimetres per second for a robot of one metre dimension), the robot and its payload are considered as a quasi-static system; high speeds require to apply the theorems of dynamics and to consider dynamic forces and inertial effects.

- A second criterion is the **obstacle crossing capacity** of the robot. The three first robots can cross obstacles whereas the fourth can compensate the dynamic effects of a violent obstacle crossing leading to a ballistic phase.

- A third criterion is **active stabilization** performed by suitable control of the mobilities of the robot. All the robots provide a stabilization during obstacle crossing. The Susp4D suspension is a passive system (simple control) but could be equipped with actuators in future works.

- The last criterion is related to **co-manipulation between several robots**. Of the four projects, only C³Bots AT/VLP is designed in this way. This concept allows to adjust the number of elementary robots to the task, thus providing some sort of modularity.

The four sections widely cover the problems of obstacle crossing with wheeled and hybrid leg-wheel mobile robots at low and high speeds. They aim to show how new mechatronic architectures can lead to agile terrestrial mobile robots.

## 2 AGILE ROBOTS FOR OBSTACLE CROSSING AT LOW SPEED – THE OpenWHEEL i3R ROBOT

This section presents the elaboration of an innovative principle for crossing and / or climbing obstacles within the framework of an open architecture dedicated to wheeled robots, keeping the efficiency of the wheels while improving mobility and static stability by a good compromise between climbing performance, stiffness, complexity and technological pragmatism. This last point includes a reasonable number of wheels and actuators. The application field of the climbing robot and associated control methods described here could be commercial all-terrain wheeled vehicles as well as mobile robots with original kinematics dedicated to exploration.

The section is based on several previous works of the authors. The original obstacle crossing principle of the OpenWHEEL i3R mobile robot was first published in (Fauroux, Chapelle, & Bouzgarrou, 2006) and tested at a small scale in (Fauroux, Bouzgarrou, & Chapelle, 2008). A preliminary analysis of the mobility, kinematics and dynamics was made in (Bouzgarrou, Chapelle, & Fauroux, 2009). The analyses of front-rear non-symmetry and dimensional sensitivity of several geometric parameters were provided in (Fauroux, Bouzgarrou, & Chapelle, 2009). Finally, a model for steering-warping coupling was provided and a full scale model was constructed (Fauroux, Chapelle, & Bouzgarrou, 2010). Additional works such as an alternative architecture based on actuated trailing arms can be found in (Fauroux, Forlorou, Bouzgarrou, & Chapelle, 2007) as well as considerations on bio-inspiration of hybrid leg-wheel robots and similarities with balancing of legged creatures (Fauroux & Vaslin, 2011).

### 2.1 Agile mobile robots with hybrid leg-wheel architecture

Vehicles are considered as systems driven by their own propulsion device, most of the time controlled by a human operator, and intended to move people and payloads in their environment. Usual applications may be transport, agriculture or leisure. Mobile robots have a higher degree of autonomy than vehicles and are more specially designed to perform complex reproducible tasks. For this aim, they usually have a reactive behaviour with the help of sensors for internal and external perception, actuators, control laws and strategies for interpretation of sensory data and decision (Devy, Chatila, Fillatreau, Lacroix, & Nashashibi, 1995; Siegwart, Nourbakhsh, & Scaramuzza, 2011). They are usually intended to exploration or inspection tasks, often at low speed. The mechatronic architecture can allow one single or several
modes of locomotion. Mobile robots differ in chassis internal mobilities, that can be passive (without actuators) or include some actuated mobilities (active robots). Additional sensors allow adaptation to unknown factors and ground changes (reactive robots).

The wheeled terrestrial propulsion is known to be a very energy-efficient way of moving, because energy is mainly used for propulsion and not lift (Bekker, 1969). Wheels are particularly fast on flat grounds, with low power consumption, reliability and adaptability to the ground thanks to tires. Their main drawback is difficulties to deal with obstacles and terrain discontinuities. Climbing obstacles remains a challenge for wheeled robots and good locomotion is no more guaranteed. In that case, legged propulsion, that provides discrete discontinuous ground contacts, regains some interest. However, it needs complex control and requires high energy for moving at high speed. Tracked propulsion (Bakhsh, Hasnan, & Ahmed, 2013) is another solution that provides good traction capacity with respect to wheeled locomotion, at the price of high dissipative energy, particularly during steering.

Many robots offer a hybrid architecture by combining several propulsion devices such as wheels, tracks and legs, for a better adaptability to varied terrains. Some examples of recent hybrid mobile robots can be seen in Table 2. An analysis of the various types of locomotion can be found in (Bruzzone & Quaglia, 2012) and a history of hybrid robots is presented in (Conduraru Slătineanu, Doroftei, & Conduraru, 2014).

Some hybrid robots use additional legs with a 4-wheel architecture (Table 2a, Bruzzone & Fanghella, 2014; Table 2b, Kasprzyczak, Trenczek, & Cader, 2012). An important class regroups hybrid robots that use wheels on articulated legs, either on leg articulation (Table 2c, Ding, Li, & Xu, 2012) or at the end of the leg (Hirose & Takeuchi, 1996; Halme, Leppänen, Suomela, Ylönen, & Kettunen, 2003; Grand, BenAmar, Plumet, Bidaud, 2004; Table 2d, Wen et al., 2013). An interesting sub-group of wheel-leg hybrid robots use a passive deformable frame, either with a rocker-bogie suspension (Bickler, 1998), coupled passive parallelograms (Table 2e, Strupler, Pradalier, & Siegwart, 2014) or several wheels fixed on four-bar mechanisms (Siegwart, Lamon, Estier, Lauria, & Piguet, 2002). In this sub-group, only the wheels are actuated, although the passive deformable frame provides a substantial improvement in crossing capacity.

Another class of hybrid robots uses orientable tracks as legs (Michaud et al., 2003; Nagatani, Kinoshita, Yoshida, Tadakuma, & Koyanagi, 2011; Table 2g, Brunner, Brüggemann, & Schulz, 2012). Some propelling elements can be re-designed for obstacle crossing, such as tracks with deformable frame (Table 2h, Luo, Shang, & Zhang, 2013), legs that rotate like wheels (Table 2i, Ordonez, Shill, Johnson, Clark, & Collins, 2013), deformable wheels with claws that can grip the obstacle edges (Table 2j, Chou & Yang, 2013) or planetary wheels in groups of three (Table 2k, Fang, Lu, He, & Yuan, 2012; Table 2l, Quaglia, Orderio, Bruzzone, & Razzoli, 2013). Obstacle crossing can be also obtained by hopping (Kikuchi et al., 2008). Some robots also present original articulated frames (Rollins, Luntz, Foessel, Shamah, & Whittaker, 1998; Apostolopoulos, 2001; Lacroix et al., 2002) in order to locate and orientate wheels for specific purposes.

Those hybrid mobile robots generally focus on improving mobility, stability or climbing capabilities. However, this improvement is often obtained at the price of higher complexity, great number of actuated joints, low stiffness and great number of contact points with the ground. The additional degrees of freedom are often actuated in a specific way, allowing several distinct locomotion modes.

All the previous considerations prove that there is enough room for generic and modular mechatronic architectures, possibly usable into commercial vehicles, developed for obstacle crossing with very slightly actuated frame. Focus is particularly set on new locomotion modes for climbing over obstacles and terrain discontinuities while ensuring static stability, as wheeled locomotion, a mode scarcely present in nature, should be developed even more towards all-terrain locomotion.
<table><caption>Table 2: A selection of recent developments in 2012-2014 on hybrid mobile robots using wheels, legs and tracks.</caption><thead><tr><th>Robot Name</th><th>Mantis</th><th>PIAP GMRI</th><th>NOROS-II</th></tr></thead><tbody><tr><th>Picture</th><td></td><td></td><td></td></tr><tr><th>Functional scope of the reference</th><td>a) Surveillance and inspection robot.<br>Combination of 4 wheels and 2 front legs.</td><td>b) Four wheel robot with two central legs for hazardous environment.</td><td>c) Wheel-legged robot with large height variations.</td></tr><tr><th>Reference</th><td>(Bruzzone & Fanghella, 2014)</td><td>(Kasprzyczak, Trenczek, & Cader, 2012)</td><td>(Ding, Li, & Xu, 2012)</td></tr></tbody></table>
<table><thead><tr><th>FWRA</th><th>Crabli</th><th>Kenaf</th></tr></thead><tbody><tr><td>d) Four-wheel rhombus-arranged rover with articulated frame for lunar exploration.<br>(Wen et al., 2013)</td><td>e) Perception and control of a rover with passive suspension.<br>(Strupler, Pradalier, & Siegwart, 2014)</td><td>f) Perception for a mobile rescue robot.<br>(Nagatani, Otake, & Yoshida, 2014)</td></tr></tbody></table>

<table><thead><tr><th>Telemax</th><th>RTMBot</th><th>RHex light</th></tr></thead><tbody><tr><td>g) Adjustable tracked chassis.<br>(Brunner, Brüggemann, & Schulz, 2012)</td><td>h) Reconfigurable tracked robot. Modular design.<br>(Luo, Shang, & Zhang, 2013)</td><td>i) Deformable rotative leg with terrain identification.<br>(Ordonez, Shill, Johnson, Clark, & Collins, 2013)</td></tr></tbody></table>

<table><thead><tr><th>Prototype Robot-II</th><th>iBot like</th><th>Epi.q</th></tr></thead><tbody><tr><td>j) Transformable robot. Claw-wheel.<br>(Chou & Yang, 2013)</td><td>k) Stair-climbing wheelchair with planetary wheels. Stability analysis.<br>(Fang, Lu, He, & Yuan, 2012)</td><td>l) Modular ground robot with wheels in triangular setting.<br>(Quaglia, Orderio, Bruzzone, & Razzoli, 2013)</td></tr></tbody></table>
The section introduces a modular architecture for mobile robots and the associated crossing mode
making possible to obtain high crossing capacities, with low actuation and good stiffness. The concepts
remain sufficiently generic to be easily transposable on existing wheeled vehicles systems (e.g. All
Terrain Vehicles (ATV) or quad bikes). The global motorization is chosen to be distributed on the wheels,
with one electric motor attached to each wheel, for compactness and genericness. Only one internal
supplemental motor will be located at the centre of the frame as described in the following subsections,
presenting the paradigm (§2.2) and kinematics (§2.3) of our OpenWHEEL i3R robot. Then are introduced
the climbing strategy (§2.4), reduced models (§2.5), full-scale demonstrator (§2.6) and the geometric
model used to control and improve the obstacle climbing strategy (§2.7).

## 2.2 OpenWHEEL paradigm

*Figure 3: Kinematic structure of OpenWHEEL i3R (Fauroux, Bouzgarrou, & Chapelle, 2009).*

OpenWHEEL is the name given to a family of rovers with articulated frame and/or innovative suspensions. The name “i3R” defines its kinematics: “i” for inter-axle, highlighting the central mechanism joining the axles; “3R” for describing its serial kinematics using three revolute joints: one passive steering rotation per axle and one central active warping joint. This kinematics combines the speed of wheeled propulsion with the agility offered by an articulated chassis for good all-terrain performance. Kinematics of OpenWHEEL i3R was first defined in (Fauroux, Chapelle, & Bouzgarrou, 2006). It features an articulated frame allowing the rover to climb on obstacles with only four wheels. This number can be considered as a *minimum*, three wheels being used for stability and the fourth one as an exploring wheel.

A sequential motion strategy was jointly developed to cross an obstacle with a step-profile. The kinematics and strategy are crafted to be "kept as simple as possible", while remaining within the limits of static stability. They were designed to be easy to transfer to a commercial vehicle such as a quad bike or ATV, for transporting tasks or semi-autonomous inspection in a spirit of robustness and reliability, notably for the possibility of supporting a payload on the field. OpenWHEEL is likely to meet a variety of obstacles. The steepest possible obstacle to find in the external environment is a step-like obstacle. The motion strategy is built with the assumption that the horizontal length of this step is sufficient to permit the robot to stand on top of it on its four wheels. Staircase climbing (Gonzales, 2009) is not considered here but the robot is capable to cross a hurdle (i.e. a thin and high obstacle) using modified movements.

## 2.3 OpenWHEEL kinematics

The kinematic structure of OpenWHEEL i3R is shown in Fig. 3. The robot is made of two axles named ($A_a$) with $a$ the axle number (1 for front, 2 for rear). Wheels are numbered ($W_{a1}$) with $s$ the side number (1 for right, 2 for left). The axles are linked by a serial inter-axle mechanism using two frames ($F_1$) and ($F_2$) and three revolute joints $R_k$ and thus named i3R ('i' standing for "inter-axle").

The central joint $R_0$ is actuated for the warping of the structure. The $R_1$ and $R_2$ joints are passive and are used for dual Ackermann steering. They also give a longitudinal mobility that allows to bring the exploring wheel towards the obstacle (i.e. wheel $W_{12}$ on Fig. 3). Analysis showed that the robot has a mobility of 3 while rolling and 4 while climbing (Bouzgarrou et al., 2009). Stability is ensured when the projected centre of mass $G'$ lays inside the lifting triangle ($P_{11}P_{21}P_{22}$ in Fig. 3). Distance $HG'$ gives a geometric representation of the stability margin.

Each link (L) of the robot has a local reference frame $R_L$ ($O_L$, $x_L$, $y_L$, $z_L$). The origins $O_{F1}$ and $O_{F2}$ of the links ($F_1$) and ($F_2$) are defined confounded in the middle of the robot and $R_{F1}$ represent the reference frame of the whole robot. The angles $\alpha, \beta, \gamma$ represent respectively the yaw, pitch and roll of frame $R_{F1}$ with respect to ground reference $R_0$. Angles $\theta_0, \theta_1, \theta_2$ measure respectively the frame warping and axle steering of ($A_1$) / ($A_2$). They are defined by: $\theta_0=(\bar{y}_{F1}, \bar{y}_{F2})=(\bar{z}_{F1}, \bar{z}_{F2})$, $\theta_1=(\bar{x}_{F1}, \bar{x}_{A1})=(\bar{y}_{F1}, \bar{y}_{A1})$ and $\theta_2=(\bar{x}_{F2}, \bar{x}_{A2})=(\bar{y}_{F2}, \bar{y}_{A2})$. Only $\theta_0$ is actuated. The steering angles $\theta_a$ are indirectly controlled via the
self-rotation $\theta_{as}$ of the actuated wheels, with $\theta_{as}=(\overline{x_{Was}}, \overline{x_{Aa}})=(\overline{z_{Was}}, \overline{z_{Aa}})$. The centre of mass of axle ($A_a$) is denoted $G_a$ and supposed located on line ($O_{Aa}, z_{Aa}$), at the middle of the axle, as the axles are laterally equilibrated.

## 2.4 OpenWHEEL climbing strategy

The climbing process is a sequence of stages that connect successive characteristic poses of the robot. All the poses are statically stable, i.e. when a wheel is lifted, the projection of the centre of gravity is kept within the support triangle formed by the three other wheels. A sequence of 19 stages was first presented in (Fauroux, Chapelle, & Bouzgarrou, 2006) and interpolated to obtain a complete climbing process with quasi-static stability.

In order to climb the obstacle, each wheel has to become successively the “exploring wheel”, being lifted over the obstacle while the robot lays only on three contact points $P_{as}$. Before lifting the exploring wheel ($W_{as}$), the robot must be controlled in such a way that the wheel ($W_{a's}$) of the same side s but of the other axle $a'$ is brought as close as possible to ($W_{as}$). This allows to maintain $G$ strictly above the triangular lifting polygon and to guarantee stability. The robot motion during climbing is described qualitatively in Fig. 4 and the stability margin $HG'$ of Fig. 3 is approximated here in 2D in the top view.

**Figure 4: Reference description of the climbing process of OpenWHEEL i3R in 7 phases and 19 stages.**

The process is divided into 7 phases and 19 stages. Phase A brings the vehicle against the obstacle. Phase B is for ($W_{11}$) climbing. It is decomposed into 4 stages: stage 2 where the robot reconfigures the rear axle ($A_2$) to bring ($W_{21}$) close to the exploring wheel ($W_{11}$); stage 3 where ($W_{11}$) is lifted via $\theta_0$ warping; stage 4 where ($W_{11}$) is pushed forward by the rear axle ($A_2$); stage 5 where ($W_{11}$) lands on top of the obstacle via $\theta_0$ unwarping. Phase C unrolls the same process for ($W_{12}$). Phase D brings the second axle in contact with the obstacle. Similarly, phase E and F are for ($W_{21}$) and ($W_{22}$) respectively. The final F phase serves only to unsteer $\theta_1$ and $\theta_2$.

It should be noted that the robot can climb and also go down from the obstacle in a very similar way, wheel after wheel. The only requirement is that the areas before and after the obstacles are wide enough for the robot. This means that mountains can be crossed (climbing, then going down) as well as valleys (going down, then climbing). Narrow mountains (i.e. hurdles) can be crossed provided they are lower than the axle and that, with one wheel before the hurdle, the other wheel of the same axle can be brought after the hurdle by axle steering. Narrow valleys (i.e. ditches) can be crossed if one wheel can lay on one side of the ditch and the other wheel of the same axle can reach the other side by axle steering.

The whole climbing procedure was validated first by an Adams 3D multibody model (Fig. 5, Fauroux, Chapelle, & Bouzgarrou, 2006) and by several demonstrators, presented in the following subsections.
Figure 5: 3D multibody model of obstacle crossing with OpenWHEEL i3R simulated with Adams software. This model used initially only 17 stages (Fauroux, Chapelle, & Bouzgarrou, 2006), but the decomposition in 19 stages presented in Fig. 4 is the recommended one.
## 2.5 Small-scale demonstrators

Built from Lego Mindstorms RCX elements with a rough open-loop control, the first model, denoted V1 (Fig. 6) permitted to highlight a number of critical points on certain stages of the crossing (Fauroux, Bouzgarrou, & Chapelle, 2008).

The most critical point is that the tilting of the model may compromise obstacle crossing (Fig. 7). Tilting a vehicle of angle $\beta$ with a high centre of gravity $G$ shifts backward the position of the projected centre of gravity $G'$ and induces instability in stages 12 and 16 during climbing of the rear axle. Distance $P_2G'$ is given by equation (1) with $b$ being the wheelbase length and $h_l$ the leg length.

$$P_2G' = b \cos(\beta)/2 - h_l \sin(\beta) \quad (1)$$

Figure 6: (a) Small scale version of OpenWHEEL i3R V1 with RCX kit. (b) Experimenting the climbing process of Fig. 4.

Figure 7: Obstacle crossing is compromised by tilting angle $\beta$ and restored by a new mass repartition.

The robot seems temporarily heavier from the rear. This phenomenon was analysed in (Fauroux, Bouzgarrou, & Chapelle, 2009) and required the installation of a frontal counterweight CW (Fig. 7c). A qualitative analysis showed that a counterweight of 144g with a robot mass of 1530g, located 90mm forward of $G_1$ allowed to bring $G$ forward of 16mm (9% of the wheelbase length $b = 175mm$) and cured the instability.

This remark made for climbing can be extended to descent. When climbing the obstacle, the robot noses-up, and the projected centre of gravity $G'$ goes rearwards with respect to the lifting polygon. This could be corrected by a payload translation towards the front of the vehicle. When descending the obstacle, the robot noses-down and $G'$ goes forward with respect to the lifting polygon. This could be corrected by a payload translation towards the rear of the vehicle.

The second noticeable phenomenon is named steering-warping coupling. It was solved by a corrective modification of control and requires a formalized model that will be presented in §2.7. The last phenomenon is the loss of contact adherence when the normal force decreases or where the obstacle blocks the advance of a wheel, and can be avoided by control adjustments or supplemental force sensors.

Model V1 climbs obstacles of 55mm (Fig. 6b), which seems to be close to the maximum performance for this particular implementation of the robot. The maximum obstacle height does not depend on the wheel diameter and represents 66% of the height of its centre of gravity, which is the metrics we recommend to quantify crossing performance.

A second small scale model, named V2, was based on the Mindstorms NXT next generation kit (Fig. 8). With actuators that include a coder, V2 allowed to test some control laws with closed loops using the NXC programming language, a C like language including a complete NXT API (Hansen, 2010). The V2 model has stronger actuators and smaller reduction ratios than V1, which ensures higher dynamics, but still lacks of rigidity. Several sensors where added in V2, such as steering rotation sensors to measure $\theta_1$ and $\theta_2$, distance ultrasound sensors to measure horizontal distance and height of the obstacle, contact sensors on the front to start the climbing process and a 3D accelerometer used as an inclinometer to measure the tilt angle. The NXT control program was designed for V2 and to be directly implanted on the full-scale demonstrator with simple adjustments of scale constants.

Figure 8: Small scale version of OpenWHEEL i3R V2 with NXT kit and closed loop control.
Figure 9: Full-scale OpenWHEEL i3R V3 crossing an obstacle in lateral (a) and top view (b).

## 2.6 Full-scale demonstrator

The full scale OpenWHEEL i3R V3 robot is around 1.85m long, 1.38m wide, 0.98m high with a total weight approaching 200kg (Fig. 9). The robot frame is made of modular aluminium profile. The five identical 24V DC actuators include a coder and have a power of 330W each, a nominal torque of 30Nm that can exceed 100Nm for short periods. With a reduction ratio of 10.9 and torque exceeding 1100Nm, the central mechanism is capable to warp the robot of 45° in only one second, which is fifteen times faster than the small-scale version V1 and may even generate an unexpected dynamic loss of equilibrium. This problem can be avoided by adjusting acceleration ramps in the Curtis 1228 DC controllers, that modulate intensities up to 70A. Two or four 12V 48Ah on-board batteries store the energy. V3 is also equipped with a central electric clutch that allows to decouple the warping mechanism when rolling and to guarantee contact for the four wheels on irregular ground (no over-constraint).

## 2.7 Control and Sequential geometric model

OpenWHEEL i3R can be teleoperated on smooth terrain. However, the step-climbing process is complex and is supposed to be left completely automatic. The pilot has only to choose when to trigger climbing. An approximate control in open loop of the robot was made for OpenWHEEL V1 based on the sequence presented in Fig. 4. OpenWHEEL V2 and 3 are controlled in closed loop and use a more detailed sequential geometric model. This requires writing a 3D geometric model for each of the 19 stages. This allows adjusting the model according to the scale of the considered robot and tuning the control strategy to the dimensions of the obstacle. Doing so, smaller obstacles will be crossed with smaller motions, which means a faster, more energy efficient and more stable climbing process.
<table><caption>Table 3: List of geometric parameters for the different versions of robots.</caption><thead><tr><th>Name</th><th>Definition</th><th>OW V1</th><th>OW V2</th><th>OW V3</th></tr></thead><tbody><tr><td>b</td><td>Wheelbase length T<sub>1</sub>T<sub>2</sub></td><td>175 mm</td><td>260 mm</td><td>1210 mm</td></tr><tr><td>t</td><td>Track width O<sub>a1</sub>O<sub>a2</sub></td><td>190 mm</td><td>151 mm</td><td>1250 mm</td></tr><tr><td>r<sub>w</sub></td><td>Wheel radius</td><td>25 mm</td><td>25 mm</td><td>190 mm</td></tr><tr><td>h<sub>l</sub></td><td>Leg height</td><td>72 mm</td><td>105 mm</td><td>500 mm</td></tr><tr><td>m</td><td>Mass</td><td>1530 g</td><td>2330 g</td><td>&lt; 200kg</td></tr><tr><td>k<sub>0</sub></td><td>Reduction ratio for central joint</td><td>560</td><td>35</td><td>10,9</td></tr><tr><td>k<sub>w</sub></td><td>Reduction ratio for the wheels</td><td>15</td><td>3</td><td>1,3</td></tr></tbody></table>

<caption>Figure 10: Model for steering reconfiguration between stages 01 and 02.</caption>

**Design parameters:** the considered design parameters characterizing geometry and scale of the different versions are summarised in Table 3.

**Steering reconfiguration for stability:** before lifting the exploring wheel, the stability margin must be increased by steering the other axle. This is done at stages 2, 6, 11 and 15, that is to say the first stage of the climbing phase of each wheel. For instance for stage 2 (Fig. 10), the required steering angle of axle 2 is denoted $\theta_2^{S2}$ and must be smaller than $\theta_{a max}$, which is defined at $\pi/4$ for design reasons and to avoid the singular configuration where all contact points $P_{as}$ are aligned. The kinematics equation (2) based on rolling without slipping of wheels ($W_{a2}$) gives the opposite rotations $\theta_{21}^{S2}$ and $\theta_{22}^{S2}$ of the wheels required to generate the steering angle $\theta_2^{S2}$ for stage 2. It is also written in actuator configuration space.

$$ \theta_{21}^{S2} = -\theta_{22}^{S2} = t \frac{\theta_2^{S2}}{2} r_w \quad \Leftrightarrow \quad \theta_{act 21}^{S2} = -\theta_{act 22}^{S2} = k_w t \frac{\theta_2^{S2}}{2} r_w \quad (2) $$

However, it is not safe to rely on the non-slipping hypothesis. Using the additional steering rotation sensor, a much more robust solution is to increase $\theta_{21}^{S2}$ and decrease $\theta_{22}^{S2}$ at the same rate until the steering angle $\theta_2^{S2}$ reaches the expected value $\theta_{a max}$.

**Steering-warping coupling:** steering-warping coupling is a phenomenon that concerns stages 6, 11 and 15, where the robot is no more horizontal. In order to anticipate the lifting of the exploring wheel ($W_{as}$), the other axle ($A_a$) has to be steered. When the robot is not horizontal anymore (i.e. the steering axis $z_{Aa'}$ is no more normal to the ground plane), the wheels of axle ($A_a$) cannot stay in the plane of the ground after steering, and one contact is lost. This can be solved by a corrective warping of $R_0$.

For example at stage 6 (Fig. 11), if the front frame ($F_1$) is supposed fixed to the ground and submitted to a roll angle $\alpha$ and a pitch angle $\beta$ with respect to the fixed frame ($T_1, x_0, y_0, z_0$), the wheel-centre point $O_{21}$ is calculated by the product

$$ O_{21} = R_y(\beta) \cdot R_x(\alpha) \cdot T_x(-b/2) \cdot R_x(\theta_0) \cdot T_x(-b/2) \cdot R_z(\theta_2) \cdot T_z(-h_1) \cdot T_y(-t/2) \cdot T_1 \quad (3) $$

with $R$ and $T$ being homogeneous matrices for rotation / translation and $T_1$ being the point defined in Fig. 3. The vertical coordinate of $O_{21}$ in the ground frame ($T_1, x_0, y_0, z_0$) is given by (4).

$$ z_{O21} = \cos(\beta)[\cos(\alpha)(-\frac{t}{2}\sin(\theta_0)\cos(\theta_2) - h_1\cos(\theta_0)) + \sin(\alpha)(-\frac{t}{2}\cos(\theta_0)\cos(\theta_2) - h_1\sin(\theta_0))] - \sin(\beta)[\frac{t}{2}\sin(\theta_2) - b] \quad (4) $$

$z_{O22}$ can be deduced from (4) by replacing parameter $t$ by $-t$. The difference of altitude between $O_{21}$ and $O_{22}$ does not depend on $b$ and $h_1$ and can be simplified into (5).

$$ z_{O22} - z_{O21} = t[\cos(\beta)\cos(\theta_2)\sin(\alpha + \theta_0) + \sin(\beta)\sin(\theta_2)] \quad (5) $$

As the track width $t$ is positive, the condition to keep $O_{21}$ and $O_{22}$ at the same altitude is given by (6).
$$ \sin(\alpha + \theta_0) = -\tan(\beta)\tan(\theta_2) \qquad (6) $$

As angles $\alpha$ and $\beta$ can be measured with a 3D accelerometer fixed to the front frame ($F_2$) and used as an inclinometer, equation (6) allows to extract the corrective warping $\theta_0$ for a given steering $\theta_2$.

**Lifting the exploring wheel:** an exploring wheel is lifted at stages 3, 7, 12 and 16, which represent the 2nd stage of each climbing phase. Lifting is controlled by $\theta_0$ and calculated in (7) for stage 3 (Fig. 12a).

$$ \theta_0^{S3} \approx \sin(h_s/t) \qquad (7) $$

<caption>Figure 11: Model for steering-warping coupling at stages 5 and 6.</caption>

Figure 12: Model for: (a) lifting the exploring wheel; (b) pushing the wheel over the obstacle.

**Pushing the exploring wheel over the obstacle:** an exploring wheel is pushed over the obstacle at stages 4, 8, 13 and 17, which are the third stage of each climbing phase. For stage 4 (Fig. 12b), the exploring wheel ($W_{11}$) is pushed forward by axle ($A_2$) until it lays completely over the step in top view, which leads to a limit on the front steering angle $\theta_1$ given by equation (5).

$$ \theta_1^{S4} \approx atan(2r_w/t) \qquad (8) $$

**Landing the exploring wheel on the obstacle:** an exploring wheel lands on top of the obstacle at stages 5, 9, 14 and 18, that are the fourth and last stage of the climbing phase of each wheel. Landing is controlled by $\theta_0$ in a similar way as lifting with equation (7).

## 2.8 Conclusion on agile obstacle crossing at low speed

This section presented the OpenWHEEL i3R mobile robot, a rover capable to roll on regular ground and to climb step-obstacles as high as two-thirds of its centre of gravity. This one has been the object of work of design and modelling for several years by Fauroux, Bouzgarrou and Chapelle (2006, 2007, 2008, 2009, 2010) and Fauroux and Vaslin (2011). The original architecture of OpenWHEEL i3R and the associated crossing modes published since 2006 have been re-used by Nakajima for his robot RT-Mover (Nakajima, 2008, 2014).

OpenWHEEL i3R is interesting as it combines the rolling efficiency of the wheeled propulsion to the agility of the legged locomotion, with a simple control based on minimal actuation of the four wheels and only one central warping actuator. Three demonstrators were built to demonstrate the concept: two at small scale and one at full scale, comparable to a commercial vehicle such as an ATV. A sequential geometric model was built, based on a 3D geometric model for each stage. Control is based on the position of the joints and the main required equations are given here for lifting, pushing and landing the exploring wheel over the obstacle. Parasite phenomena and their associated equations are also identified, such as the negative effect of pitch angle, cured by a proper mass repartition, and steering-warping coupling, cured by an adjustment in warping control. The tests on the demonstrators are very encouraging and typically allow OpenWHEEL i3R to cross obstacles as high as two-third of the height of its centre of mass. This robot opens perspectives on designing new highly efficient wheeled robots and vehicles for agile mobility on all-terrain and clearance performance, even with only four wheels and a few actuators.

# 3 MODULAR COOPERATIVE MOBILE ROBOTS FOR VENTRAL LONG PAYLOAD TRANSPORT AND OBSTACLE CROSSING – THE C³BOTS AT/VLP ROBOTS

The OpenWHEEL i3R project allowed proving that a mobile wheeled robot with additional mobilities in its articulated frame could cross obstacles that cannot be crossed by a standard wheeled vehicle. For this subsequent work named the C³Bots project (Collaborative Cross and Carry mobile roBots), it was decided to focus on the transporting tasks from a general point of view. The payload is here considered as a part of
the robotic system. As payloads can have varied shapes and masses, it was decided to provide a modular
architecture where a variable number of robotic units can self-attach to the payload at suitable locations.
Two payload positions are considered in the C³Bots project :

* Payload on top of the robots: dorsal transport is suitable to very general payloads but requires energy and a specific device to put the payload on the robot top platforms. This concept is currently under exploration with the C³Bots DGP (Dorsal General Payload) part of the project. An overview of the concept can be found in (Hichri, Fauroux, Adouane, Mezouar, & Doroftei, 2013), with a proposition for a lifting mechanism (Hichri, Fauroux, Adouane, Doroftei, & Mezouar, 2014) and a suitable control strategy (Hichri, Adouane, Fauroux, Mezouar, & Doroftei, 2014).

* Payload under the robots: ventral transport may have some advantages, as a low payload permits to keep a low centre of mass of the complete system. The payload can be directly caught on the ground and elevated under the robot without having to pass on the side, minimizing risks of instability. A study of existing devices showed that very few robotic systems use this principle. An example can be found in (Holland, Marmaras, & Oulman, 2008), where a remote controlled transport system uses a ventral platform elevated by winches. However, the system does not seem to be capable to directly catch a payload from the ground and requires a preliminary loading operation. Another problem with ventral transport is that the bottom part of the robots is generally used by locomotion organs, such as wheels, legs or tracks. These organs must also be oriented for proper steering of the robot, so a reduced workspace remains available for the ventral payload. However, the stability advantage seemed to be a sufficient argument to investigate deeper the possibility of ventral transport, and the limited workspace can be suitable for long objects transported between left and right wheels/legs/tracks. This concept is currently evaluated within the C³Bots AT/VLP name (All-Terrain/Ventral Long Payload) part of the project. An overview of the concept was given in (Krid, Fauroux, & Bouzgarrou, 2014) and is extended below in this section. Several kinematics were patented in (Fauroux, Bouzgarrou, & Krid, 2014).

More generally, agile transporting mobile robots may prove very helpful where human operators
cannot go, such as in hostile environments (contaminated or radioactive areas), and to transport heavy,
wide or delicate payloads (ranging over big structural parts, fragile objects, explosives or even injured
people on stretchers). In this case, the robot must be able to manipulate and transport objects of varied
shapes, to manoeuvre on irregular grounds and to cross obstacles. Many types of agile all-terrain mobile
robots have been developed for planetary or dangerous area exploration. They have different architectures
(Bay, 1995; Trebi-Ollennu et al., 2002; Saranli, Buehler, & Koditschek, 2001; Kim, D., Hong, H., Kim,
H.S., & Kim, J., 2012; Fauroux, 2012) and locomotion modes (Michaud et al. 2003; Fauroux, 2013) but
the same purposes: they must be able to evolve on irregular or unstructured environment and to guarantee
a minimum stability during a mission.

As presented before, C³Bots differs from OpenWHEEL i3R by its modularity: several single
robots (called “mono-robots”) connect to the payload in a modular way in order to perform the
transporting task. The fleet of connected robots and the payload will be named “poly-robot”. In the
literature, cooperative mobile robots for transport are often complex (Aiyama, Hara, Yabuki, Ota, & Arai,
1999; Ben-Tzvi, Goldenberg, & Zu, 2001). They use many actuated joints and a sophisticated control
system (Hashimoto, Oba, & Eguchi, 1993; Kosuge & Oosumi, 1996; Kurabayashi, Sasaki, & Aiyama,
1996). The simpler ones suffer from limitations on payload manipulation and adaptation to the
environment, such as Army Ant cooperative transporting robots (Bay, 1995).

In this section, we present the synthesis of the cooperative C³Bots AT/VLP mobile robot.
Subsection 3.1 describes the resulting poly-robot, associating two or more identical mono-robots that
connect directly to the payload for transporting it. Subsection 3.2 describes the kinematics of the mono-
robot, particularly the required degrees of freedom for the ventral manipulator. In subsection 3.3, the
mobilities are combined to present two obstacle crossing locomotion modes: one with only two mono-
robots, inspiring from OpenWHEEL i3R; and a second mode with three mono-robots (or more) following
a plane motion.

## 3.1 C³ Bots AT/VLP general architecture

The concept presented in this work is based on the *OpenWHEEL i3R* platform (Fauroux, Chapelle, & Bouzgarrou, 2006) presented in section 2. *OpenWHEEL i3R* contains two axles linked with a serial inter-axle mechanism using three simple revolute joints (one active central joint for warping and two passive joints for steering). Each axle contains two actuated wheels.

*OpenWHEEL i3R* has an original climbing process based on a serpentine movement and divided into nineteen stages. Each stage is related to a joint motion or a wheel contact being removed or regained. For the new *C³Bots AT/VLP* robot, it was decided to design a new platform suitable for the ventral transport of long payloads and partially inspiring from *OpenWHEEL i3R* for stable obstacle crossing. *C³Bots* is original by the concept of combining several identical mono-robots with simple kinematics that make a poly-robot system using the payload as a connecting frame. *C³Bots AT/VLP* focuses particularly on the ventral transport of long payloads. The stability of the platform is a necessary condition to perform the climbing process.

<caption>Figure 13: (a) Unstable configuration due to the centre of mass on the edge of the lifting triangle of support. (b) Stability improvement by translating the rear mono-robot along the payload axis.</caption>

Previous works (Chebab, 2013; Fauroux, Bouzgarrou, & Chapelle, 2009) showed that decreasing the wheelbase with respect to the track width increased the stability on three wheels during steps 4, 8, 13, 17 of the climbing process. It was also noticed that increasing the wheelbase reduced pitch variation when crossing an obstacle of a given height. From these two remarks came the idea to have a *variable wheelbase* for the new robot (idea I1). Another important result was that crossing a high obstacle required to bring frontward the centre of mass with respect to the contact points in order to equilibrate the crossing capacities of front and rear axles (Fauroux, Chapelle, & Bouzgarrou, 2010). This result directly led to the idea of *moving longitudinally the payload* with respect to the wheels (idea I2). These two ideas I1 and I2 can be satisfied simultaneously if *each axle is given a longitudinal translational mobility along the payload axis* (requirement R1). Fig. 13 shows how the additional translational mobility required by R1 can improve the stability margin of the poly-robot. A second requirement concerns modularity. The concept of collaborative robots led us to separate the initial *OpenWHEEL i3R* robot into two single axle mono-robots. So *each mono-robot will have to integrate an axle for locomotion, and a positioning mechanism ending with gripper* to catch the payload (requirement R2).

By combining requirements R1 and R2 was born the *C³Bots AT/VLP* (All-Terrain/Ventral Long Payload) robot concept using several single axle mono-robots able to catch the payload, translate along the payload longitudinal axis to change the wheelbase length and to rotate around their longitudinal axis to warp the poly-robot and elevate one wheel with respect to the others. *C³Bots AT/VLP* must be able to transport long payloads. To overcome the constraints related to the length of the transported payload, two or more cooperative mono-robots are used. The mono-robots are initially independent entities. Then, they connect to the payload, that becomes part of the resulting platform, called poly-robot (Fig. 15). It should be noted that some lorries dedicated to long payload transport also use the payload as a structural part (Wobben, 2008). The mono-robot cannot climb obstacles with its simple kinematic structure. But the poly-robot version can perform such an operation because it has more contact points on the ground and the additional mobilities in the connecting chains can be used to generate relative motions between the mono-robots and the payload. In the next subsection, the mono-robot kinematics and poly-robot architecture will be presented.
## 3.2 Required mobilities and proposed kinematics

The mono-robot includes an axle, a positioning mechanism and a gripping mechanism (Fig. 14). The single-axle mono-robot #a, denoted $MR_a$, includes two wheels $W_{a1}$ and $W_{a2}$ motorized independently with two motors (with first index “a” equal to “1” for front axle and “2” for rear axle, second index equal to “1” for right wheel and “2” for left wheel). To be able to manipulate the object, the robot is equipped with a gripper mounted at the bottom of the chassis. The originality of the concept lies on the kinematic chain of the positioning mechanism. The axle frame ($A_a$) can freely steer around the cylindrical joint $C_a$ with respect to slider ($S1_a$). The remaining vertical motorized translation $T_{za}$ of $C_a$ allows controlling the altitude of the gripper and consequently of the payload. The roll motion $R_{xa}$ between the slider body ($S1_a$) and the support body ($S2_a$) is ensured by the revolute motorized joint ($R_{a3}$) which is compulsory to reproduce warping motion of one axle roughly around the longitudinal axis of the payload, as the original *OpenWHEEL i3R* did. During solo locomotion, the mono-robot can transport small payloads on flat ground. Stability can be obtained by several solutions: dynamic pitch control in the same way as (Segway, 2010) or deployment of a retractable arm with a passive caster wheel.

Figure 14: (a) Kinematic diagram of the mono-robot $MR_a$. (b) Kinematic graph of the mono-robot $MR_a$.

The connection between the mono-robots is ensured by the transported payload as shown in Fig. 15. The co-manipulation of the payload by the two mono-robots allows obstacle crossing. The poly-robot combines the mobilities of the mono-robots. It can control the passive rotation $R_{za}$ of the cylindrical joint ($C_a$) on each mono-robot by the difference of angular velocities of the two wheels of each axle. The redundant revolute joints $R_{13}$ (front) and $R_{23}$ (rear) give two warping degrees of freedom to the poly-robot. When joints $R_{a3}$ are actuated (either $R_{13}$ or $R_{23}$), a warping motion is generated of one mono-robot around the joint $R_{a3}$ axis with respect to the payload. This movement allows lifting the exploration wheel off the ground. The poly-robot changes its support configuration, with only three wheels remaining in contact with the ground. Finally, prismatic joint $P_a$ between gripper $GW_a$ and support $S2_a$ in each mono-robot allows translating the mono-robot along the payload axis. As a conclusion, the implementation shown in Fig. 15 provides the four mobilities required on each mono-robot for stable payload transport and obstacle of the poly-robot:

* a rotation $R_{xa}$ for wheel elevation on obstacles (provided by joint $R_{a3}$),

* a rotation $R_{za}$ for steering and stabilization on 3 wheels configuration ($C_a$),

* a translation $T_{xa}$ for an improved stabilization with a long payload ($P_a$),

* a translation $T_{za}$ for payload elevation ($C_a$).
Figure 15: Relative position of each frame and the associated angles.

Several serial kinematic chains are capable to generate the four required mobilities ($T_{xa}$, $T_{za}$, $R_{xa}$, $R_{za}$) between axle and gripper (Fig. 16) and can be used for a real implementation.

Figure 16: Selection of equivalent joint combinations for producing the four required mobilities ($T_{xa}$, $T_{za}$, $R_{xa}$, $R_{za}$) between axle and gripper.

## 3.3 Locomotion modes for obstacle crossing

In this section, two locomotion modes are described for obstacle crossing with two axles or more. First, the 3D warping mode inspired by *OpenWHEEL i3R* is developed for two axles. Then, a 2D crossing mode with three axles and more is shown.

### 3.3.1 Two axles warping mode inspired by OpenWHEEL i3R

The climbing process of the $C^3Bots$ AT/VLP platform is a process based on a 'serpentine' movement. It is divided into eighteen steps regrouped in six phases (Fig. 17). Each step is performed by the motion of a single joint or by a change in the contacts of wheels on the ground. A phase *P* is a group of steps, considered as a series of manoeuvres *M* that conducts to crossing a wheel $W_{as}$. Thereby, there are four main phases in the process, one per wheel, along with two intermediate phases to bring the axle in contact with the obstacle. The phases and manoeuvres are given representative names according to the wheel to be lifted during each phase. For example, $PW_{12}$-$M_2$ is the second manoeuvre $M_2$ of the phase referring to lifting the front left wheel $W_{12}$.

The climbing process starts by approaching the obstacle (Phase 1). The first axle of the poly-robot is brought parallel to the obstacle and the axle frames ($A_1$) and ($A_2$) are set perpendicular to the payload axis. The mono-robots are at the extremity of the payload before starting the climbing process.

The second phase consists in stepping over the obstacle with wheel $W_{11}$. The first manoeuvre $PW_{11}$-$M_1$ is made to find the optimal position of rear axle in order to prepare to lift-off the exploring wheel $W_{11}$ with a maximum stability margin. Two parameters must be found for this manoeuvre: the distance between the mono-robots and the steering angle of the rear axle. Stability analysis and optimization of these parameters will be presented in a future work. Warping the front mono-robot lifts-off the exploring wheel at manoeuvre $PW_{11}$-$M_2$. At manoeuvre $PW_{11}$-$M_3$, the rear wheels are actuated while the wheel $W_{12}$ is locked. The exploring wheel $W_{11}$ passes over the obstacle by an induced steering motion of the front axle. Finally, the first phase is achieved by putting down the exploring wheel $W_{11}$ at manoeuvre $PW_{11}$-$M_4$.

The same is done for $W_{12}$ crossing in the third phase $PW_{12}$, which starts at $PW_{12}$-$M_1$ by finding the optimal position of the rear mono-robot and finishes by putting down the exploring wheel $W_{12}$ on the obstacle at $PW_{12}$-$M_4$. After finishing the three first phases, the front axle of the robot is on the obstacle.

Phase 4 allows bringing the rear axle in contact with the obstacle. The last two phases will bring the exploring wheel (respectively wheel $W_{21}$ and $W_{22}$) on the obstacle. Phase 5 starts with manoeuvre $PW_{21}$-$M_1$, that consists in finding the optimal position of front axle. After warping the rear mono-robot at manoeuvre $PW_{21}$-$M_2$, the front axle moves forward to bring the exploring wheel $W_{21}$ over the obstacle (manoeuvre $PW_{21}$-$M_3$) and puts down the exploring wheel in the last manoeuvre $PW_{21}$-$M_4$.

The sixth and last phase $PW_{22}$ starts by finding the optimal steering position of the front mono-robot at manoeuvre $PW_{22}$-$M_1$ and finishes by putting the exploring wheel $W_{22}$ on the obstacle after manoeuvre $PW_{22}$-$M_4$. Finally, the poly-robot can rearrange the positions of the rear and front axles to find its standard configuration (phase not represented).
It should be noted that the proposed process organization can be modified to generated variants.
One variant could allow shortening the group of steps 9-10-11. As the axles have the same relative
positions in steps 9 and 11, it could be interesting to maintain them also at step 10. Passing from step 9 to
11 would be obtained by a pure longitudinal translation of the payload within the poly-robot, thus
avoiding useless travel of the front axle. Another process variant could be obtained by climbing with left
wheels first.
Figure 17: Climbing sequence of the poly-robot with only two axles, in 18 steps and 6 phases.

### 3.3.2 Three axles and more 2D crossing modes

The climbing process with three axles and more is very simple compared to the two axles configuration, because during the climbing process, the poly-robot has always two axles or more on the ground and one axle only is lifting off to climb obstacle. With three axles $A_1, A_2, A_3$ (Fig. 18), the climbing process starts by approaching the obstacle (step 01) and moving forward $A_2$ to have the centre of mass of the payload between $A_2$ and $A_3$ (step 02-$PA_1_M_1$). After that, axle $A_1$ is raised (03-$PA_1_M_2$). Then $A_2$ and $A_3$ are actuated to bring $A_1$ over the obstacle (04-$PA_1_M_3$). Axle $A_1$ is then put down on the obstacle (05-$PA_1_M_4$). The same is done for axles $A_2$ (steps 06-08) and $A_3$ (steps 09-12). As a conclusion, the three axles (and more) configurations allow an easy 2D obstacle crossing mode at the price of a high number of axles. Using only two mono-robots and the 3D warping mode described in §3.3.1 requires a minimal number of mono-robots, at the price of a more complex control.

Figure 18: Climbing sequences of a poly-robot with 3 axles, 2D crossing mode in 12 steps.

## 3.4 Conclusion on modular collaborative robots and future work

In this work, we proposed a new concept of cooperative mobile robots to deal with the problem of long object transportation in unstructured environment whatever the payload length. The proposed $C^3Bots AT/VLP$ robot (Collaborative Cross and Carry mobile roBots for All-Terrain/Ventral Long Payload) is formed by the association of two or more mono-robots with simple kinematics forming a poly-robot system. Using such a modular poly-robot provides interesting advantages such as easy adaptation to the task, fast maintenance by simple replacement of defective mono-robots and standardization of the mechatronic architecture and associated control. Moreover, the proposed poly-robot has crossing obstacle capabilities and can use one of the two climbing modes inspired from the *OpenWHEEL i3R* mobile robot. As a perspective for this work, the optimization of the process for all the steps will be considered as well as the evaluation of the dynamic stability for critical configurations of the poly-robot. This must be done to ensure a smooth transition between the steps of the process. By ensuring the stability of the payload and its position control, $C^3Bots AT/VLP$ can transport sensitive payloads such as victims and hazardous equipments that must be maintained in a well-defined position.

# 4 SYNTHESIS OF SPATIAL PARALLEL MECHANISMS FOR A VERTICAL AND LONGITUDINAL ALL-TERRAIN SUSPENSION – THE Susp4D SUSPENSION AND THE MiniFAST ROVER

Sections 4 and 5 focus specifically on dynamics of rovers rolling at high speed on irregular grounds and in presence of obstacles. In section 4, a specific suspension is synthesized for improving dynamic stability of a fast rover during obstacle crossing. This section is based on previous works of the authors about mobile robots in all-terrain environments (Fauroux, Bouzgarrou, Bouton, Vaslin, Lenain, & Chapelle, 2012) and more specifically on several innovative suspensions with 4 Degrees of Freedom (4DOF) synthesized in (Fauroux, 2012) and patented in (Fauroux & Cousturier, 2011, 2012).

## 4.1 Limitations of rovers crossing high obstacles at high speed

Wheels are mostly suitable for motion on $C^1$ continuous surfaces (tangency continuity). In unstructured environments, obstacles may provide only $C^0$ continuity (contour continuity), as seen in Fig. 19a. The worst case occurs for obstacles that do not even have $C^0$ continuity. They will be not treated in this work.

Generally, obstacles can be considered as shapes with a front surface being roughly vertical along
Z, i.e. with a strong component of their normal vector along -X (Fig. 19b). Although vehicle stabilization can sometimes be achieved by control, for instance for lateral rollover avoidance (Bouton, Lenain, Fauroux, & Thuilot, 2007; Bouton, Thuilot, Lenain, & Martinet, 2009) or path tracking (Krid & Ben Amar, 2011), this type of steep and dangerous obstacle requires designing new concepts of suspensions allowing also the longitudinal X damping motion for better obstacle crossing.

**Figure 19:** (a) Considered obstacles have a $C^1$ continuity and possibly only $C^0$. (b) Obstacles generally have a front surface whose normal vector *N* may have a strong horizontal component along -X.

A previous work (Fauroux, Dakhlallah, & Bouzgarrou, 2010) allowed building an Adams multibody simulation (MSC Software Inc., 2008) of a simplified 2D vehicle equipped by suspensions with 2DOF: a vertical one along Z, like most of vehicle suspensions, and also a horizontal one along X, suitable to cross high obstacles with a quasi-vertical front surface (Fig. 19b). The wheels and ground were considered rigid with contact and friction and the wheels were actuated by a constant torque. The obstacle was higher than the wheel radius in order to make its crossing difficult. Although a more refined contact model could benefit to realism (Pacejka, 2006), the preliminary results (Fig. 20) were encouraging and the model equipped by a 2DOF suspension could safely cross the obstacle whereas the model with the classic 1DOF suspension systematically crashed by tip-over.

**Figure 20:** Trajectories of a 2D multibody simulation of a vehicle crossing a high obstacle at high speed.
(a) With classical 1DOF suspensions. (b) With 2DOF front and 1DOF rear suspensions. (Fauroux, Dakhlallah, & Bouzgarrou, 2010).

The tip-over risk was confirmed by a subsequent experimental work (Fauroux & Bouzgarrou, 2011) on vehicles with classical 1DOF double-wishbone suspensions (Fig. 21). It showed that it exists a stability limit for obstacle crossing, above which the vehicle tips-over (Fig. 22). The 2DOF XZ suspension is expected to extend the stability domain by allowing to cross higher obstacles at a given speed (or the same obstacles at a higher speed).

**Figure 21:** Experimental obstacle crossing with 1DOF suspension (Fauroux & Bouzgarrou, 2011).

**Figure 22:** Stability front of classical vehicles with 1DOF Z suspensions: impact speed vs obstacle height. 2DOF XZ suspensions should extend the stability limit (Fauroux & Bouzgarrou, 2011).

Existing all-terrain vehicles mostly rely on wheels that are of great diameter with respect to the obstacles to cross. Most of the fast commercial all-terrain vehicles such as cars, military trucks, ATVs or buggies rely on robust rigid axles or more comfortable double wishbone suspensions, (Fig. 23a-d). Some original architectures can be noticed on small scale radio-controlled cars so-called "crawlers", where each axle is guided by a parallel mechanism including generally four bars with double spherical joints, denoted S joints (Fig. 23e). Some research platforms such as RobuROC 6 also have joints between axles but not necessarily suspensions (Fig. 23f). Both crawlers and RobuROC 6 are suitable for high-obstacle crossing but only at slow speed. No commercial vehicle appears to allow a long-travel longitudinal suspension of its wheels.

The analysis of numerous vehicle suspension patents also confirmed that longitudinal suspension is an original concept. All the suspensions that use a trailing arm guide the wheel along a circular trajectory. The wheel centre motion has a minor longitudinal component, but it is coupled with the vertical component. Trailing arms represent the majority of motorbike rear suspensions, but they can also be transposed into leading arms for front suspensions (Fig. 24a, Slater, 1979). Front and rear arms can
also be coupled longitudinally (Fig. 24b, Asteggiano & Silvano, 2004) to obtain a specific global
behaviour of the vehicle. Because trailing arms can transmit a lot of the longitudinal contact force when
the wheels impact against an obstacle, some suspensions use deformable trailing arms that help to absorb
energy during accidental crashes, but absorption can be done only once (Fig. 24c, Astheimer, 1975).

Figure 23: Existing all-terrain vehicles for fast (a-d) or slow (e-f) motion speeds.

Other suspensions are capable to provide 6DOF, including a longitudinal translation of the wheel, by guiding the wheel with a Gough-Stewart parallel mechanism, but at the price of a complex control because of highly coupled motions (Fig. 24d, Goetzen, Hipp, & Suissa, 1999). Several devices such as the Michelin-IFMA Optimized Contact Patch suspension (Fig. 24e, André, Blondelet, & Gogu, 2004) or the Sacli suspension (Fig. 24f, Sacli, 2009) take advantage of the centrifugal force applied to the vehicle towards the outside of the turns to adjust the camber angle of the wheels and improve adherence. These systems allow lateral but no longitudinal translation of the wheel contact-patch with respect to the vehicle frame. Although no suspension seems to allow wide longitudinal mobility of the wheels, most of the existing suspensions allow small motions, because they replace the classical spherical and revolute joints by compliant components made of rubber injected between metallic parts and also known as “bushings”. Bushings improve longitudinal comfort and vibration filtration for high frequencies. However, they only allow very short motion travel.

One of the very few systems capable to provide longitudinal damping is integrated into the wheel
itself. The SoftWheel Ltd. patent (Winshtein, Gross, Brand, & Sardes, 2012) describes a parallel
mechanism connecting the wheel hub to the wheel rim. This device is interesting but the concept of
articulated wheel seems to be incompatible with high rotation frequencies because small deformations
may generate changes in the inertia matrix and violent dynamic effects. The considered applications are
wheelchairs and bikes and probably could not be high speed vehicles.

Figure 24: Selection of patents for suspension mechanisms. a) Leading arm motorbike suspension (Slater, 1979). b) Coupled arm suspension (Asteggiano & Silvano, 2004). c) Deformable suspension for crash absorption (Astheimer, 1975). d) Daimler-Chrysler suspension based on Gough-Stewart parallel mechanism (Goetzen, Hipp, & Suissa, 1999). e) Michelin-IFMA Optimized Contact Patch suspension (André, Blondelet, & Gogu, 2004). f) Sacli suspension (Sacli, 2009). g) Michelin ActiveWHEEL device integrating propulsion, brake and suspension in the wheel (Rexhep & Daniel, 2004). h) Bose active suspension (Brown, 2010)

To our knowledge, it appears that most of the existing suspensions are *passive* ones. Although they are not as efficient as active suspensions, they have the advantage to be inexpensive, energy efficient, reliable and not to require any knowledge of the environment. Another category of devices are *adjustable passive suspension systems*, that is to say that the adjustments are actuated whereas the damping motions remains passive. In (Cheek & Daye, 2009), a novel suspension system is developed for independent wheel control. The main objective of this system is to provide an independent suspension apparatus for an off-road vehicle that is capable of moving each wheel away and towards a frame or body member of such vehicle. Other works are aimed to adjust vehicle suspension height to provide more ground clearance to the body work of the vehicle (McIntyre, 2009). Other patented innovations try to improve the performance of a shock absorber by controlling fluid flow (Cox, Ericksen, & Allinger, 2009).

The last category is for *active suspensions*, with actuators capable to stabilize the vehicle attitude.
The ActiveWHEEL developed by Michelin corporation is a mechanism that integrates into a single wheel
an electric engine for propulsion, a peripheral brake and a vertical suspension with a spring and an electric actuator (Fig. 24g, Rexhep & Daniel, 2004; Michelin 2008). Bose corporation developed also an active suspension based on a traditional McPherson suspension where the damper is replaced by a long throw linear actuator based on the same technology of loudspeakers (Fig. 24h, Brown, 2010; Bose Systems, 2014).

From this overview, it appears that new suspensions should be designed to absorb both vertical and horizontal components of reaction forces generated by contact shocks of the wheel against rough obstacles in all-terrain. The longitudinal and vertical travels should be of the same order of magnitude. For being used both on front and rear axles, this new mechanism should also include steering and transmission capabilities, so the so-called 2DOF-suspension could become a 4DOF mechanism including the considered mobilities. The prospect of a potential active suspension leads to the following constraint: the horizontal (respectively vertical) damper compression should correspond mostly to a horizontal (respectively vertical) motion of the wheel. This means that horizontal and vertical motions of the wheel should be as decoupled as possible, and also decoupled from the steering and transmission motions. Although a passive mechanism should be designed first, an actuated version could be easily derived and controlled.

In the next sub-section are introduced the very first 2D kinematics that were proposed for the required suspension. Sub-section 4.3 focusses on 3D structural synthesis of realistic mechanisms providing good lateral guidance and managing the coupling phenomenon. In the last sub-section, dimensional synthesis allows finalizing the geometric setting and building a demonstrator for the front suspension of an all-terrain car at scale 1:8.

## 4.2 2D structural synthesis of a suspension device with four mobilities

In the nine kinematics presented in the following sections, parts will always be designated according to a three-digit naming convention represented by *VSP* patterns, where *V* stands for the kinematics version, *S* for the considered system and *P* for the part in the system. A system *S* can be a linkage or an assembly of components that are fixed together. A *VS0* pattern designates the considered system *S* of a version *V*. Table 4 summarizes some examples of systems and parts pertaining to all the suspension versions.
<table><caption>Table 4: Naming convention for the different parts with three indexes VSP (Version / System / Part), V being the suspension Version number (from 1 to 9).</caption><thead><tr><th>VSP Ref</th><th>S</th><th>System (assembly or linkage)</th><th>P</th><th>Part</th></tr></thead><tbody><tr><td>V00</td><td>0</td><td>Frame</td><td></td><td></td></tr><tr><td>V10</td><td>1</td><td>Wheel assembly</td><td></td><td></td></tr><tr><td>V11</td><td></td><td></td><td>1</td><td>Hub of the wheel</td></tr><tr><td>V20</td><td>2</td><td>Hub-carrier assembly</td><td></td><td></td></tr><tr><td>V30</td><td>3</td><td>Linkage for lateral guidance</td><td></td><td></td></tr><tr><td>V31</td><td></td><td></td><td>1</td><td>First bar</td></tr><tr><td>V32</td><td></td><td></td><td>2</td><td>Second bar</td></tr><tr><td>V40</td><td>4</td><td>Linkage for vertical suspension</td><td></td><td></td></tr><tr><td>V41</td><td></td><td></td><td>1</td><td>Spring vertical suspension</td></tr><tr><td>V42</td><td></td><td></td><td>2</td><td>Damper vertical suspension</td></tr><tr><td>V50</td><td>5</td><td>Linkage for horizontal suspension</td><td></td><td></td></tr><tr><td>V51</td><td></td><td></td><td>1</td><td>Spring horizontal suspension</td></tr><tr><td>V52</td><td></td><td></td><td>2</td><td>Damper horizontal suspension</td></tr><tr><td>V60</td><td>6</td><td>Steering linkage</td><td></td><td></td></tr><tr><td>V61</td><td></td><td></td><td>1</td><td>Rudder bar</td></tr><tr><td>V70</td><td>7</td><td>Transmission linkage</td><td></td><td></td></tr></tbody></table>

The first evident idea is to create a 2DOF suspension by using a serial linkage (Fig. 25):

- first a vertical joint from the hub of the wheel 120 to an intermediate glider 130;

- second a horizontal joint from the glider 130 to the frame 100.

Putting the vertical joint closer to the wheel allows to avoid that lower parts collide with the ground. In Fig. 25, dampers are not represented and sphere 101 is a lumped mass connected to the frame 100.

<caption>Figure 25: Version V1 of a 2DOF XZ suspension mechanism: 2D serial linkage (Fauroux, Dakhlallah, & Bouzgarrou, 2010).</caption>

<caption>Figure 26: V2: (a) 2D parallel linkage; (b) Variant of V2 with cylinders attached to the frame.</caption>

Version V2 of the suspension (Fig. 26) has a 2D parallel architecture and two limbs copying the serial structure of V1. The parallel architecture introduces a redundancy with respect to the serial architecture. For instance, translating the wheel 210 along X requires both the motion of the actuated Cylinder 2 and the passive prismatic joint 254 (Fig. 26a). Although the mobility of wheel 210 is the same in versions V1 and V2, mechanism strength of V2 will be improved in case of shocks. For example in Fig. 26a, horizontal shocks forces will be absorbed mostly by the compression of cylinder 2, instead of generating bending of rod 243. In a variant of suspension V2 (Fig. 26b), only passive joints are used in the limbs and the shock absorber are attached directly to the frame. This allows decreasing the non-suspended mass and provides better shock absorption.

Dual effect cylinders are represented in Fig. 26, showing the possibility to actuate the suspension through hydraulic or pneumatic hoses 245 and 255. One interesting property of this parallel architecture is that it is maximally regular. This means the Jacobian matrix is a unit matrix (Gogu, 2008) and that pure wheel translation of distance *d* along the X or Z direction is achieved by actuating only Cylinder 2 or 1 of distance *d* respectively. On the contrary, the solution presented in Fig. 24d has a coupled behaviour. A
pure translation requires coupled control of several actuators. The cylinders of Fig. 26 can also be
replaced by passive dampers, possibly with adjustable damping coefficient. One should also note that the
hub carrier 220 may be attached to body 252 or 242 with no significant influence.

Version V3 of the suspension (Fig. 27) has also a parallel architecture but with coupled motions. This drawback is compensated by the elimination of the bending moment around Y axis. Parts 342, 343, 352, 353 only bear traction-compression. The prismatic joints 244 and 254 in V2 are replaced by revolute joints 344 and 354 in V3. This allows part downsizing for the same resistance.

Figure 27: V3: 2D coupled 2(RPR) parallel mechanism.

Figure 28: (a) V4: Spatial hybrid implementation (Riesemann, 2009) with four U-U parallel limbs for spherical translational suspension motions, locally uncoupled behaviour and steering capacity. (b) V5: with rhomboid layout of parallel limbs (without representation of steering device).

4.3 3D structural synthesis of a suspension device with four mobilities

All-terrain suspensions are subject to severe shocks, and the V2 solution is not acceptable because of bending that would damage the gliders 243-244 and 253-254 (Fig. 26). This is why the 2D solution V3 (Fig. 27) will serve as the basis for improved 3D suspensions V4 using a parallel architecture (Fig. 28a, Riesemann, 2009). V3 suffers from several problems that find a solution in V4:

- *Lack of lateral stiffness*, which is critical during turns. Four parallel *U-U* limbs 431-434 were attached to guide the travelling platform 421 in a spherical translation. *U* joints are universal joints (two consecutive revolute joints with perpendicular crossing axes).

- *No steering capacity*. The hub-carrier 420 is now capable to steer thanks to a revolute joint around Z2 direction between 420 and 421. The steering actuation-linkage is not represented.

- *Coupled motions*. The main axes of the cylinders 440 and 450 were rotated -45° around Y to become parallel to Z and X respectively. This setting allows a maximally regular behaviour *only* in the central point of the workspace, where the links 431-434 are parallel to Y axis. Far from this position, extra-diagonal terms appear in the Jacobian matrix.

- *Variation of pitch angle* of the wheel hub 320 was important during suspension compression in V3. It was nullified in V4 by the use of *U* joints that resist to torsion around Y, contrary to *S* joints.

If a cross-section of suspension V4 is made in a plane normal to Y and cutting the four parallel
bars 431-434, the four sections of the bars are located in a square layout. The attachments for the vertical
and horizontal damping linkages 440 and 450 can be made directly to the travelling plate 421. However,
most cars have deep recessed tyre-rims that prevent direct attachment to 421, unless curved bars are used,
that would be submitted to intense bending during shocks.

Version V5 of the suspension is represented in Fig. 28b, without any steering device, to extrapolate from V4. In the same cross-sectional view as previously, bars 531-534 are located in a rhomboid layout, resulting from a 45° rotation applied to bars 431-434 around Y axis. This brings bar 533 on top and bar 534 on the rear of the suspension, providing convenient attachment points for the vertical and horizontal damping linkages 540 and 550, even though the hub-carrier is hidden inside the wheel-rim.

Versions V4 and V5 use a lateral guidance linkage using four identical *U-U* limbs that allow a spherical translation of the wheel. Kinematically, any configuration of *N* parallel limbs with *N* >= 3 may be used, although simplicity dictates to choose *N*=3 for solutions V6 to V9.
**Figure 29:** (a) V6: Parallel mechanism with 3DOF integrating the steering. (b) V7: The attachment points of the vertical and horizontal linkages 740 and 750 avoid any collision. Steering is made around axis Z2 that passes through the tyre contact patch. A transmission line is also included.

Solution V6 (Fig. 29a) offers a better integration of the steering linkage as it re-uses bars from the lateral guidance linkage. The two lower bars 631 and 632 are connected by *U* joints to a rudder-bar 661 on one side and to the hub-carrier 620 on the other side. Rotating 661 around *Z1* axis generates differential traction in 631 and 632 and makes 620 rotate around *Z2* axis of the same angle if bars 631-632-633 are parallel and of the same length.

Solution V7 (Fig. 29b) is an evolution of V6 where the attachment points for vertical and horizontal damping linkages 740 and 750 are located somewhere around the middle of bars 733 and 732 respectively. This layout avoids any collision between the tyre and the horizontal damper. Solution V7 also features a transmission line 770 with several shafts connected by *U* joints. The last important feature is about the steering axis *Z2* of wheel 710, that was designed to pass through the centre of the wheel contact patch with the ground in order to minimize the steering friction momentum. As *Z2* has to pass through *E*<sub>733</sub>, end-point of bar 733, and also through the middle of *E*<sub>731</sub> and *E*<sub>732</sub>, the positioning constraint on *Z2* propagates to the positioning of bars 731-733.

Although V6 and V7 provide an interesting integrated steering system, they must deal with a
disadvantage: a slight coupling remains between steering and horizontal damping motion.

*Figure 30: V8: Steering becomes decoupled from horizontal damping motion thanks to a change in the attachment point of 850 to the top bar 833.*

*Figure 31: V9: Variation on V8. Steering is actuated by a single arm and two bars are directly connected to the frame. This structure is very close the double triangle architecture.*

In solution V8 (Fig. 30), this coupling completely disappears as the attachment point of the longitudinal damping linkage 850 has been moved to a point that is not affected by steering: around the middle of the top bar 833, one of the few attainable points laying in the steering-invariant plane, which contains *Z1* and *Z2* axes. As the *S* joints that connect 840 and 850 to 833 cannot be easily merged, it was chosen to dissociate them enough to avoid any collision.

In solutions V6-V7-V8, the lower bar was eliminated among the four lateral guidance bars, mostly to clear out the space under the suspension. Solution V9 (Fig. 31) shows a variation on V8 where the rear bar was suppressed (it could be the front bar as well). The rudder-bar 961 now pulls only bar 931 to apply steering to the hub-carrier 920, whereas bars 932 and 933 are in charge of lateral guidance.

This choice is interesting as it is compatible with existing vehicles with double-wishbone
suspension. Their frame already has upper and lower attachment points for the triangles that can be re-
used here for V9 suspension.

**4.4 Dimensional synthesis**

In solutions V8 and V9, the top bar 833 or 933 has a critical role, as it transmits both the horizontal and vertical components of impact forces on the obstacle. Consequently, this bar is submitted to combined bending momentums around Z and X and should be reinforced compared to 831-931 and 832-932, that undergo only pure traction and could be downsized.
Figure 32: CAD model of V8 integrating real parts and double-damper sub-assemblies (Cousturier, 2010; Dejeante & Vendrôme, 2011).

Figure 33: Mechanical implementation (Cousturier, 2010; Dejeante & Vendrôme, 2011) of suspension V8 as the front suspension of a Traxxas E-Maxx 1:8 scale model.

Some dimensions result from a compromise in order to avoid interference between parts in different positions of the suspension. The distance between bars 831 and 832 should be as large as possible for better steering stiffness but is limited by the non-interference between the bars and the tyre-rim, particularly at extreme steering position and horizontal compression. It must also be large enough to let enough space for the transmission line 870, whatever the position. Another interference may occur between the internal part of the tyre and the damping linkage 850, mostly at maximum steering. This is why 850 is attached to 833 at point slightly translated in Y direction.

Bars 831-833 should also be taken as long as possible for getting a larger spherical translation radius and for allowing an approximate planar motion of the wheel in plane XZ.

In the real implementation of suspension V8, a Traxxas E-Maxx radio-controlled all-terrain car of scale 1:8 was chosen. Re-using the double cylinder dampers required to refine the 850 linkage (Fig. 32). Cylinders 852 and 852' were rigidly paired thanks to the intermediate part 853, that was connected by a U joint (part 854) to car-body 800. At the other end, the damping assembly was connected to 833 by an S joint. The real implementation (Fig. 33) required some adjustments in the steering mechanism and also a stronger servomotor. The car was successfully tested.

## 4.5 New suspensions of the Susp4D family

This section presented the structural and dimensional synthesis of nine suspension mechanisms designed to provide vertical and longitudinal all-terrain suspension. Eight solutions have parallel kinematics and six of them are spatial mechanisms. Most of them were patented in (Fauroux & Cousturier, 2011, 2012). Solutions V8 & V9 integrate all the constraints and are capable to provide longitudinal & vertical motions of the wheel, with an uncoupled behaviour in the centre of the workspace. They also allow steering and power transmission. They were given the name Susp4D as a reminder of the four mobilities. During the ANR FAST national research project, the Susp4D suspension was integrated on the MiniFAST four-wheel rover. A recent campaign of dynamic obstacle crossing experiments with a non actuated Susp4D mechanism has revealed that the new suspension is more stable and robust than classical 1DOF vertical suspensions. Future work will have to maximize stability by adjusting the horizontal and vertical stiffness and damping parameters. Actuated mechanisms for predictive control and improved obstacle crossing can also be derived.

# 5 DYNAMIC PITCH CONTROL OF A MOBILE ROBOT IN BALLISTIC PHASE – THE RobCAT ROBOT

Whereas Section 4 aimed at designing corrective suspensions capable to absorb the shocks against obstacles on the ground, Section 5 presents a control strategy during the jump, when the vehicle has lost contact with the ground to start an aerial or ballistic phase. This work is adapted from a previous paper initially published in French (Vaslin, Pouzols, Gouinaud, Fauroux, Deleplanque, & Davis, 2011).
## 5.1 Adjusting the pitch of a rolling vehicle during ballistic phases

The pitch motion control during the ballistic phase of a vehicle is empirically well known by pilots of motocross or car models: it consists in accelerating or braking the wheels whether the pilot wishes to nose-up or to nose-down the vehicle. Mechanical parameters of this phenomenon have been identified by measures performed during real jumps, and have then been implemented into a Java 2D simulation software designed for studying the influence of the initial conditions of the jump and of the vehicle characteristics on the control of its pitch motion.

Motocross pilots state that they are able to shorten or to lengthen their trajectories by braking or accelerating theirs wheels respectively, during the ballistic phase of a jump. As this subjective feeling seemed to defy Newton's laws of classical mechanics, we searched to identify its causes using an experimental approach based on measurements performed on the field and in the laboratory. Then, a mechanical model was built and its equations implemented into a simulation software written in Java and designed to reproduce the behaviour of the {Pilot + Motorcycle} system in the three conditions studied during actual experiments:

* when the pilot did not apply any action on the controls (throttle or brakes) during the ballistic phase of the jump ("normal" jump);

* when he accelerated the motorcycle rear wheel ("accelerated" jump);

* and when he braked the wheels ("braked" jump).

The methods used and the results obtained by these two approaches are presented below, as well as their potential outcomes in the aim of controlling the pitch motion of a mobile wheeled robot during the ballistic phase of a jump caused by an uneven ground.

## 5.2 Experimental approach

Two young pilots engaged in the French Junior Championship performed several jumps with the same motorcycle and on the same bump of the racetrack of the Moto-Club Vicomtois (Puy-de-Dôme, France). Each pilot had to try to arrive on the bump with a constant reference velocity and to perform three types of jumps according to his actions on the motorcycle controls during the ballistic phase: no action ("normal" jump), acceleration of the rear wheel ("accelerated" jump), braking of the rear wheel ("braked" jump). All the jumps were recorded at 25 frames per second (fps) by a numeric video camera (720 x 576 pixels) fixed on a tripod placed at around 20 meters from the trajectory plane (Fig. 34). The optical axis of the camera was oriented perpendicularly to this plane, in which were also recorded the dimensions of a reference scale in order to convert image measurements in actual dimensions.

Figure 34: General view of the different phases of a "normal" jump (camera 720x576 at 25 fps).

Three characteristic jumps ("normal", "accelerated", "braked") performed by a same pilot have been selected and used for a kinematic analysis (Pouzols, 2006). This analysis consisted in splitting each jump recording in individual frames on which the 2D coordinates of characteristic points of the pilot (ankle, knee, hip, shoulder, elbow and wrist joints, foot tip) and of the motorcycle (front and rear wheel axes, footrest, handlebar tip) were digitized.

Masses and positions of the centres of mass of the motorcycle, and of the pilot's helmet and boots were determined in the laboratory with the double-suspension method. Helmet and boots values have been used to weight masses and positions of the centres of mass of the pilot's head, shank and foot segments in the computation of his centre of mass ($G_P$) (Winter, 1990; Duboy, Junqua, & Lacouture, 1994; Junqua, Lacouture, Duboy, Marecot, & Bonneau, 2001). Then, the motorcycle mass and position of its centre of mass ($G_M$) have been used to compute the position of the centre of mass ($G_S$) of the whole system {Pilot + Motorcycle}. The moments of inertia of front ($J_{G1y}$) and rear ($J_{G2y}$) wheels and of the whole motorcycle ($J_{GMy}$) have also been computed using the pendulum method from oscillations measured
on numeric video recordings at 25 fps. These values have been then used in the Java simulation software to compute the total moment of inertia of the system ($J_{GSy}$) and the changes in the chassis orientation induced by the pilot's actions on the controls.

## 5.3 Mechanical model

In parallel with the experimental process, we formulated the hypothesis that the pilot's feelings following his actions on the controls were caused by the changes of motorcycle orientation in the air (pitch rotation). Accounting for the translation velocities observed on the field, aerodynamic resistance was assumed to be null during the jump. In these conditions, the only external force acting on the {Pilot + Motorcycle} system is its weight applied at the system centre of mass ($G_s$), and its moment with respect to this point is null. Therefore, the total angular momentum of the system is equal to the barycentric angular momentum ($\vec{\sigma}^*$) and it remains constant all along the ballistic phase. On the opposite, the angular momenta of front ($\vec{\sigma}_1 = J_{G1y} \vec{\omega}_1$) and rear ($\vec{\sigma}_2 = J_{G2y} \vec{\omega}_2$) wheels may vary according to the pilot's actions on the controls. These angular momenta can be expressed at the centre of mass ($G_s$) of the {Pilot + Motorcycle} system using Koenig's First Theorem (Grossetête & Olive, 1999):

$$ \vec{\sigma}_1^* = \overrightarrow{G_S G_1} \wedge m_1 \vec{v}_1^* + \vec{\sigma}_1 \quad (9) $$

and

$$ \vec{\sigma}_2^* = \overrightarrow{G_S G_2} \wedge m_2 \vec{v}_2^* + \vec{\sigma}_2 \quad (10) $$

where: $\vec{v}_1^* = \vec{v} (G_1 / R^*)$ and $\vec{v}_2^* = \vec{v} (G_2 / R^*)$, are the relative linear velocities of front ($G_1$) and rear ($G_2$) wheels axles in the barycentric reference frame ($R^*$) of the {Pilot + Motorcycle} system.

Similarly, the angular momenta of the pilot ($G_p$) and his motorcycle ($G_M$) centres of mass in ($R^*$) can be written:

$$ \vec{\sigma}_p^* = \overrightarrow{G_S G_p} \wedge m_p \vec{v}_p^* \quad (11) $$

and

$$ \vec{\sigma}_M^* = \overrightarrow{G_S G_M} \wedge m_M \vec{v}_M^* \quad (12) $$

where $\vec{v}_p^* = \vec{v} (G_p / R^*)$ and $\vec{v}_M^* = \vec{v} (G_M / R^*)$ are the relative linear velocities of the pilot's and his motorcycle centres of mass in ($R^*$), respectively.

The total barycentric angular momentum ($\vec{\sigma}^*$) of the {Pilot + Motorcycle} system thus becomes:

$$ \vec{\sigma}^* = \vec{\sigma}_p^* + \vec{\sigma}_M^* + \vec{\sigma}_1^* + \vec{\sigma}_2^* \quad (13) $$

or

$$ \vec{\sigma}^* = \vec{\sigma}_S^* + \vec{\sigma}_1^* + \vec{\sigma}_2^* \quad (14) $$

with

$$ \vec{\sigma}_S^* = \overrightarrow{G_S G_p} \wedge m_p \vec{v}_p^* + \overrightarrow{G_S G_M} \wedge m_M \vec{v}_M^* + \overrightarrow{G_S G_1} \wedge m_1 \vec{v}_1^* + \overrightarrow{G_S G_2} \wedge m_2 \vec{v}_2^* \quad (15) $$

It is worthwhile to notice that the relative linear velocities ($\vec{v}_1^*, \vec{v}_2^*, \vec{v}_M^*, \vec{v}_p^*$) are generally not null because the barycentric reference frame ($R^*$) is, by definition, only in translation with respect to the absolute terrestrial reference frame, and the angular – or pitching – velocity ($\vec{\omega}_S$) of the {Pilot + Motorcycle} system at take-off is also not zero. For instance, in the jumps studied here, ($\vec{\omega}_S$) was negative because the system tipped forward just after take-off.

From equation (13), it is possible to write:

$$ \vec{\sigma}^* = J_{GSy} \vec{\omega}_S + J_{G1y} \vec{\omega}_1 + J_{G2y} \vec{\omega}_2 \quad (16) $$

with

$$ J_{GSy} = m_p (G_S G_p)^2 + m_M (G_S G_M)^2 + m_1 (G_S G_1)^2 + m_2 (G_S G_2)^2, \quad (17) $$
as a first approximation.

Finally, equation (16) allows expressing the system pitching velocity ($\vec{\omega}_s$) as a function of the barycentric angular momentum ($\vec{\sigma}^*$) and the angular velocities of the front ($\vec{\omega}_1$) and rear ($\vec{\omega}_2$) wheels:

$$ \vec{\omega}_s = (\vec{\sigma}^* - J_{G1y} \vec{\omega}_1 - J_{G2y} \vec{\omega}_2) / J_{GSy} \quad (18) $$

As the total angular momentum of the {Pilot + Motorcycle} system ($\vec{\sigma}^*$) must remain constant during the ballistic phase, whatever the type of jump performed, equation (18) allows analysing and explaining the pitch motions observed during the three characteristic jumps studied here.

## 5.4 Experimental results

The main results of the kinematic analysis of the three studied jumps concern the orientation of the {Pilot + Motorcycle} system during aerial phases (Fig. 35): they clearly show that the motorcycle chassis slightly nosed-up during the “accelerated” jump ($\omega_s \approx -6^\circ/s$), whereas it nosed-down during the “braked” jump ($\omega_s \approx +73^\circ/s$), when compared to the “normal” jump ($\omega_s \approx +43^\circ/s$). It can thus be assumed that this pitching movement of the system (positive backwards and negative forwards) is the cause of the pilot's feelings about the jump length:

* The motorcycle nose-up during the “accelerated” jump allowed him to land on the rear wheel and then to tip forwards after landing on the ground. This movement could be the cause of the pilot's feeling of “lengthening” his jump when he accelerates the rear wheel during the ballistic phase;

* Conversely, the motorcycle nose-down during the “braked” jump resulted in landing on the front wheel, followed by a backward tip of the system after landing on the ground. This movement could be the cause of the pilot's feeling of “shortening” his jump when he brakes the rear wheel during the ballistic phase.

Without measurements of the angular velocities of the motorcycle wheels during actual jumps, the other quantitative results of the kinematic analysis did not provide valuable arguments to the question treated here. Nevertheless, real dimensions and inertial parameters of the components of the {Pilot + Motorcycle} system (Table 5) have been implemented with the equations of the mechanical model into the Java software designed to simulate the pitching movement of the system during different jumps performed with identical initial conditions.

<table><caption>Table 5: Inertial parameters of the components of the {Pilot + Motorcycle} system.</caption><thead><tr><td>System component</td><td>Mass</td><td>Moment of inertia</td></tr></thead><tbody><tr><td>Front wheel (diameter = 21 inches)</td><td>m<sub>1</sub> = 8 kg</td><td>J<sub>G1y</sub> = 0.52 kg.m<sup>2</sup></td></tr><tr><td>Rear wheel (diameter = 18 inches)</td><td>m<sub>2</sub> = 11 kg</td><td>J<sub>G2y</sub> = 0.57 kg.m<sup>2</sup></td></tr><tr><td>Whole motorcycle (with wheels)</td><td>m<sub>M</sub> = 111 kg</td><td>J<sub>GMy</sub> = 29.54 kg.m<sup>2</sup></td></tr><tr><td>Sitting Pilot (height = 1.75 m)</td><td>m<sub>P</sub> = 70 kg</td><td>J<sub>GPy</sub> = 12.68 kg.m<sup>2</sup></td></tr><tr><td>{Pilot + Motorcycle} system</td><td>m<sub>S</sub> = 181 kg</td><td>J<sub>GSy</sub> = 52.08 kg.m<sup>2</sup></td></tr></tbody></table>
Figure 35: Results of the kinematic analysis of the three experimental jumps showing the pitching movement of the {Pilot + Motorcycle} system. a) "Normal". b) "Accelerated". c) "Braked".

## 5.5 Simulated jumps

This software has been used for simulating four jumps (Fig. 36) whose identical initial conditions (initial linear velocity: 50 km/h; take-off angle: 30°; initial angular velocity: $\omega_s = +26°/s$) allowed to analyse pitching movements of the {Pilot + Motorcycle} system observed in the following cases:

* "Normal" jump: as $(\vec{\sigma}^*)$ remains constant and as the pilot does not accelerate nor brake the wheels, the angular velocity of the {Pilot + Motorcycle} system remains constant during the ballistic phase ($\omega_s = +26°/s$);

* "Accelerated" jump: $\omega_2$, which is positive at take-off, increases at acceleration. Thus, the subtracted term $-J_{G2y}\omega_2$ also increases in absolute value. This action results in a decrease of $\omega_s$, that can even change of sign. In the simulated case, the rotation speed of the system was reversed (nose-up speed, $\omega_s = -34°/s$);

* "Braked" jump: $\omega_2$ decreases down to zero when the rear wheel is locked. Thus, the term $-J_{G2y}\omega_2$, which was initially negative, disappears, which results in an increase of $\omega_s$ (+56°/s). The result of the braking action is an increase of the forward rotation of the system (nose-down). This effect is more emphasized when both wheels are braked in ballistic phase ($\omega_s = +83°/s$) because the term $-J_{G1v}\omega_1$ also decreases down to zero (Fig. 36d).

## 5.6 Conclusion on active pitch correction and future work

This work was based on experimental measurements on a motorbike and its pilot during the ballistic phase of a jump. Clear trends were identified for the pitching behaviour of the {Pilot + Motorcycle} system. When accelerating the rear wheel, the system noses-up in flight. When braking one or several wheels, the system noses-down in flight. The pitch angular speed variation increases also with the number of actuated wheels, their inertia and the actuation torque.

A mechanical model of the active pitch correction during ballistic phases has been built. It was implemented into a simulation software written in Java in order to study the effects of wheel dynamic actuation on the attitude of the vehicle. The model and the software allowed to reproduce correctly the experimental results. The conclusion on this work can be separated in two parts:

* For vehicles and specifically motorbikes piloted by humans, it is perfectly possible to correct the pitch angle in flight by accelerating or braking rear wheel or braking both wheels. The experimental results and the simulations proved that the laws of classical mechanics were not called into question during these jumps and that the pilot's feelings of "lengthening" or "shortening" his jump, whether he accelerates or brakes the motorcycle rear wheel in the air, could be explained by the pitching movement caused by his actions on the controls and also by the nose-down or nose-up movement of the system after landing on the rear or the front wheel, respectively. Future work can be imagined for the precise identification of the posture of the pilot in flight and its optimization for maximizing the pitching effect.

* For automated vehicles and specifically mobile robots, these results open a wide range of possibilities for correcting phenomena that could not be avoided on the ground during the subsequent aerial phases. The control of this pitching rotation is of main importance for a robotic
terrestrial drone able to move at high speed (10 m/s) in all-terrain and likely to take off the
ground at any time on any type of relief, foreseeable or not. In section 4.1, it was shown that fast
mobile rovers trying to cross high obstacles at high speed generally tip-over (nose-down) and
become uncontrollable. The innovative 4DOF suspension presented in section 4 could be
complemented by the active pitch correction method presented here for in-flight compensation of
the violent nose-down tendency experimented on vehicles crossing high obstacles at high speeds.
Extensions on this work are also considered for active roll correction in ballistic phase (Davis,
Gouinaud, Fauroux, & Vaslin, 2011a). A robotic vehicle owning such qualities could be highly
useful in applications where a light engine able to quickly correct its attitude in a natural
unstructured environment is needed (e.g. exploration, survey, emergency). The RobCAT project,
initiated by the authors, has the ambition to take inspiration from animals (Davis, Gouinaud,
Fauroux, & Vaslin, 2011b) for stabilizing a wheeled-rover so it always lands on its wheels after
ballistic phases (Davis, Vaslin, Fauroux, Gouinaud, & Ju, 2012).

Figure 36: Pitching movement of the {Pilot + Motorcycle} system during four simulated jumps:
(a) “normal” jump; (b) “accelerated” jump; (c) “braked” jump (rear wheel only); (d) “braked” jump
(both rear and front wheels).
# 6 GENERAL CONCLUSION: TOWARDS NEW AGILE VEHICLES

This chapter presented four complementary research works on agile mobile robots capable to cross obstacles in natural environment. The presented advances in term of mechatronic architectures allow improving the capacities of existing mobile robots and vehicles.

Obstacles are one of the major difficulty of unstructured environments and can be found in natural or urban context. We consider an obstacle to be a local irregularity of the ground that cannot be crossed by ordinary wheeled vehicles. The notion of obstacle depends on the vehicle scale and also on the locomotion speed, that is a differentiating criterion for these research works.

In section 2, it was demonstrated that a vehicle with wheels could cross very high obstacles at low speed. An original hybrid architecture was presented, consisting in four actuated wheels mounted on an articulated frame. Only one supplementary central actuator was used to make the four wheels successively cross the obstacle, which illustrates the concept of *minimal actuation* and guarantees both structure stiffness and easy control. A quasi-static climbing process divided into 19 steps was presented and experimented with our OpenWHEEL i3R robot, built in several versions and scales. It allowed climbing obstacles as high as 66% of the altitude of the centre of mass of the robot, independently of the diameter of the wheels. The OpenWHEEL i3R robot demonstrates that a classical four-wheel architecture can be simply upgraded to an agile hybrid architecture, capable to bear heavy loads and keep them in equilibrium over high obstacles. This result is very encouraging and opens wide perspectives in agile vehicle design, with applications for transportation in natural and unstructured environment.

Section 3 demonstrated also low-speed obstacle crossing during transport of long payloads. The crossing mode developed for OpenWHEEL i3R was not sufficient for efficient balancing on a long robot. For this reason, it was proposed an additional longitudinal balancing capacity, for even improved performance. The resulting prototype was named C³Bots AT/VLP (Collaborative Cross and Carry mobile roBots for All-Terrain / Ventral Long Payload) and also introduced an original concept of modularity. According to the payload size, several unitary robots, called mono-robots, catch the payload, using it as a frame for the resulting poly-robot. Longer payloads may use more than two mono-robots. Two locomotion modes where presented: one spatial warping mode derived from OpenWHEEL i3R and suitable for two mono-robots; one planar locomotion mode usable with three mono-robots and more. Several equivalent kinematics were also synthesized for the gripper positioning chain in each mono-robot and patented in (Fauroux, Bouzgarrou, & Krid, 2014).

However, when considering high speeds, even small obstacles can become challenging and can provoke a tip-over of the rover. Section 4 presented the structural and dimensional synthesis of nine suspension mechanisms designed to provide vertical and longitudinal damping in all-terrain. Eight solutions have parallel kinematics and six of them are spatial mechanisms. Most of them were patented in (Fauroux & Cousturier, 2011, 2012). Solutions V8 & V9 integrate all the constraints and are capable to provide longitudinal & vertical motions of the wheel, with an uncoupled behaviour in the centre of the workspace. They also allow steering and power transmission. They were given the name Susp4D as a reminder of the four mobilities. During the ANR FAST national research project, the Susp4D suspension was integrated on the MiniFAST four-wheel rover. A recent campaign of dynamic obstacle crossing experiments with a non actuated Susp4D mechanism has revealed that the new suspension is more stable and robust than classical vertical suspensions. Future work will have to maximize stability by adjusting the horizontal and vertical stiffness and damping coefficients. Actuated mechanisms for predictive control and improved obstacle crossing can also be derived.

Finally, section 5 provides a pitch angle stabilization method during the ballistic phase of rover, after it has taken-off from the obstacle. Accelerating the rover wheels during flight caused a nose-up, whereas braking the wheels made the vehicle nose-down. This inertial corrective method nicely complements the Susp4D suspension and was tested on the RobCAT rover, which integrates a control device to make it land safely on its wheels. It can be adapted to vehicles of varied sizes by adjusting the wheel inertias, number of wheels and accelerating / braking torques.

Sections 2-3-4 show original mechatronic structures of mechanisms suitable for obstacle crossing while section 5 exhibits an original control method suitable to all wheeled vehicles. All these systems
provide active stabilization during obstacle crossing except Susp4D, that is a passive system but could be
updated with actuators for a better anticipation of the obstacle. The work on C³Bots AT/VLP is the only
one to explicitly consider a general payload and its manipulation by a modular poly-robot. Modularity can
be a great advantage because it brings adaptation capacities to payload variation and improves safety and
repair capacity in case of failure of one module.

All these results show that many improvements can be expected for terrestrial mobile robots in
terms of obstacle crossing, payload transport and stabilizing capacities. They open a broad range of new
useful applications for exploration, agriculture, transport and safety so that robots can get used efficiently
in many types of environments, including unstructured ones.

ACKNOWLEDGEMENTS

For the OpenWHEEL i3R agile robot (Section 2), the authors wish to thank the TIMS Federation (Technologies for Innovation, Mobility and Safety) of Clermont-Ferrand University, France, for supporting the OpenWHEEL project. They also thank Region Auvergne & European Union for funding the OW project. Greetings to the following engineering students from 2006: G. Malval, E. Portales, M. Forlorou, S. Marco, Y. Koberle, D. Roux, L. Genevay, M. Tou, F. Bianchini, R. Cartailler, F. Hzag, S. Metais, C. Noellat, Z. Cherni, M. Ayache, H. Hafsia, F. Brelot, J. Gossard, R. Ekobo, S. Hamrat, F. Degezelle, P. Rousseau. Thank you for your dedication & all-terrain help.

For the C³ Bots AT/VLP project (Section 3), the authors acknowledge the funding of the post-doctorate of M. Krid by the laboratory of excellence LabEx IMobS³ Innovative Mobility: Smart and Sustainable Solutions, the French National Centre for Scientific Research (CNRS), Auvergne Regional Council and the European funds of regional development (FEDER). This work has been sponsored by the French government research program "Investissements d'avenir" through the RobotEx Equipment of Excellence (ANR-10-EQPX-44), by the European Union through the program Regional competitiveness and employment 2007 – 2013 (ERDF Auvergne Region), by French Institute for Advanced Mechanics and by the Auvergne Region. The authors also acknowledge the colleagues involved in the C³ Bots DGP (Dorsal General Payload) for structured environment, not presented in this chapter dedicated to unstructured environments and obstacle crossing: L. Adouane, I. Doroftei and Y. Mezouar and also the students B. Hichri, Q. Trebot and M. Lajili.

For MiniFAST and Susp4D (Section 4), the authors wish to thank the French Research National Agency (ANR) for funding this work inside the FAST (FAST Autonomous Rover) project. They also thank the IFMA students that already contributed on the engineering aspects of Section 5: F. Kreit, A. Riesemann, A. Authier, S. Ovazza, R. Cousturier, T. Dejeante and R. Vendrome.

For RobCAT (Section 5), the authors wish to acknowledge Region Auvergne, that funded the PhD
of M. Davis and the post-doctorate of L. Ju. They also want to thank S. Deleplanque, C. Gouinaud, L. Ju
and V. Pouzols for their contribution in the RobCAT project. Last but not least, the young pilots D.
Laroche and T. Steinmetz from Moto-Club Vicomtois (Puy-de-Dôme, France) who kindly accepted to
participate to these measures. More information on RobCAT: https://sites.google.com/site/projetrobcat

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## Section 3 – Modular Cooperative Mobile Robots for Ventral Long Payload Transport and Obstacle Crossing – the C³Bots AT/VLP robots

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## **Section 4 – Synthesis of spatial parallel mechanisms for a vertical and longitudinal all-terrain suspension – The Susp4D suspension and the MiniFAST rover**

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## Section 5 - Dynamic Pitch Control of a Mobile Robot in Ballistic phase – The RobCAT robot

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## ADDITIONAL READING SECTION

Alexander, R. (2006). *Principles of Animal Locomotion*. Princeton University Press.

Behn, C., Zeidis, I., & Zimmermann, K. (2009). *Mechanics of Terrestrial Locomotion: With a Focus on Non-pedal Motion Systems*, Springer-Verlag Berlin Heidelberg.

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Gonzalez de Santos, P., Garcia E., Estremera, J. (2006). *Quadrupedal Locomotion, An Introduction to the Control of Four-legged Robots*. London, Great Britain: Springer.

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Miège, A. J. P., & Cebon, D. (2002). Design and implementation of an active roll control system for heavy vehicles. In *Proceedings of the 6th Int. symposium on Advanced Vehicle Control (AVEC'02)*. Hiroshima, Japan.

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Reimpell, J. (2001). *The Automotive Chassis: Engineering Principles*. Elsevier ISBN 0 7506 5054 0.

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Sardain, P., & Bessonet, G. (2004). Forces acting on a biped robot. Center of pressure - Zero moment point. *IEEE Transactions on systems, man, and cybernetics, 34*(5), 630-637.

Wong, J. Y. (2008). *Theory of ground vehicles (4th ed.)*. Hoboken, New Jersey, USA: John Wiley & Sons.

Wong, J. Y. (2009). *Terramechanics and Off-Road Vehicle Engineering, Terrain Behaviour, Off-Road Vehicle Performance and Design* (2nd ed.). Butterworth-Heinemann.

## KEY TERMS & DEFINITIONS

- **Ackerman steering**: steering manoeuvre obtained with a wheeled vehicle where all the wheels have the same centre of steering-rotation. It can be obtained if all the wheel-axes cross at the same point during steering, which guarantees a null lateral slippage. This condition is also known in France as “épure de Jeantaud”.

- **Agile robot**: robot able to quickly move or change its configuration in order to adapt itself to the environment or to the task requirements.

- **All-terrain**: qualification of a vehicle or a locomotion mode suitable to evolve in every type of environments, including *unstructured environments*.

- **Axle**: a bar or shaft on which a wheel, a pair of wheels, or other rotating members revolve.

- **AGV**: Automated Guided Vehicle. Another name for a *mobile robot*, often used in logistics.

- **Co-manipulation**: task during which several entities (that can be human or robotic) jointly manipulate the same payload. A robot developed to collaborate with humans is named a “cobot”.

- **Cooperative robot**: robot able to cooperate with other robots of similar or different architectures, or even with human operators, to jointly perform a common task. An example of task could be *co-manipulation*.

- **Differential steering**: see Skid-steering.

- **Dimensional synthesis**: the design process that, after *structural synthesis*, enriches kinematics with additional attributes (lengths, materials...) to optimize kinematic properties (trajectories, orientations, workspaces...) and structural properties (strength, stiffness...)

- **Hybrid locomotion**: a general term to describe a type of locomotion using combinations of classical *locomotion modes* and *propulsion devices* such as *wheels, tracks or legs*.

- **Kinematic chain**: system of interconnected links permitting relative motion of any link with respect to the remaining links.

- **Leg**: linkage connecting the body of a walking *mobile robot* to the ground. The last link in contact with the ground is named “foot”.

- **Locomotion mode**: the set of methods, means and media used by a biological or artificial system to generate its displacement in its environment.

- **Mobile robot**: robot with a locomotion capacity. It is an automated *vehicle*. Its functions include exploration (locomotion only), transport of payloads or more complex tasks to perform with onboard systems, such as robotic arms.

- **Obstacle**: object or feature of the environment that blocks locomotion.
- **Parallel mechanism**: a mechanism with a driven link connected to the frame by means of at least two kinematic chains.

- **Payload**: actual weight of the cargo carried by a transport vehicle. Also used in this work to name the manipulated cargo during co-manipulation.

- **Pitch angle**: rotation angle of the vehicle frame around a lateral axis, orthogonal to the longitudinal and vertical directions, generally denoted by Y axis.

- **Pitch stabilisation**: a control method to maintain a vehicle pitch angle in an angular range suitable for proper locomotion on ground or safe landing in case of aerial phases.

- **Propulsion device**: mechanism that is used for vehicle locomotion and includes one or several links in contact with the ground. Classical propulsion devices include wheels, tracks and legs.

- **Robot**: mechanical system under automatic control that performs operations such as handling and locomotion.

- **Rocker-bogie**: suspension arrangement used in the Mars rovers and patented by NASA (Bickler, 1988). Bogies are sub-assemblies of wheels that can have a pitch angle with respect to the frame. This configuration is useful to ensure that all the wheels of the robot (originally six) remain in contact with irregular grounds in unstructured environments.

- **Roll angle**: rotation angle of the vehicle frame around a longitudinal axis, in the locomotion direction, generally denoted by X axis.

- **Serial mechanism**: mechanism with a driven link connected to the frame by means of a serial kinematic chain (series of consecutive links, each being connected to the next neighbour by a single joint).

- **Skid-steering**: steering manoeuvre where vehicle rotation is obtained by a difference in speeds of left and right wheels, but at the price of lateral slippage. It is typical for vehicles with non-orientable wheels.

- **Stability margin**: a numeric indicator to measure the risk of tip-over of a vehicle or mobile robot. It can be calculated for statics or dynamics. Dozens of stability margins exist, according to considered vehicle and locomotion mode (Gonzalez de Santos et al., 2006; Chebab, 2013).

- **Structural synthesis**: the design process that aims at finding mechanical kinematics suitable to given structural parameters (mobility, connectivity, redundancy and overconstraint degrees). This process occurs before dimensional synthesis.

- **Structured environment**: environment that has been modified to remove a sufficient number of obstacles and provide enough localization means to facilitate locomotion and tasks in general.

- **Suspension mechanism**: a mechanism, with one degree of freedom or more, which connects the vehicle frame to one or several wheels (or other propulsion devices). It aims to control the vehicle frame motion during locomotion on irregular grounds by using passive or active devices.

- **Track**: closed band around the wheels of certain vehicles such as tanks, intended to facilitate movement over rough or soft ground. A track can be made of one single deformable band or a chain of articulated links.

- **Tyre**: A rubber covering, typically inflated or surrounding an inflated inner tube, placed round a wheel to form a soft contact with the road.

- **UAV**: Unmanned Aerial Vehicle, commonly known as a flying drone. Not to be confused with AUV (Autonomous Underwater Vehicle).

- **Unstructured environment**: environment that contains many obstacles and where vehicle localization is difficult. Most natural environments are unstructured.

- **Vehicle**: a mobile machine that transports passengers or payload.

- **Wheel**: a circular component, in contact with the ground at its periphery, allowing vehicle locomotion when it rotates around its axis of revolution with respect to a vehicle frame. Wheels facilitate the motion of vehicles and can support a vertical load during transport of heavy objects. They can be rigid of soft, in one part or several. Their shape is variable and can look like a
cylinder or torus. They can include a tyre at their periphery.

- **Yaw angle:** rotation angle of the vehicle frame around the vertical axis, generally denoted by Z axis.

- **ZMP:** Zero Moment Point. A point used for dynamics of legged locomotion, located at the foot-ground contact, and where reaction forces from the ground do not generate any moment around a horizontal axis.