A Platform for Studying Locomotion Systems: 

Modular Reconfigurable Robots 

Ying Zhang, Craig Eldershaw, Mark Yim, Kimon Roufas, Dave Duff 

System and Practice Lab, Palo Alto Research Center 

Palo Alto, CA 94304 

Email: yzhang,celdersh,yim,kroufas,dduff@parc.com

ABSTRACT 

There are many fundamentally different mechanical motions that a 

system can use to achieve locomotion. Two standard examples are 

the wheels on a car or the legs of an artificial ant, but many others 

exist as well. As with all systems, there is an obvious desire to 

quantify how "well" each locomotion method performs. 

Unfortunately, as with many metrics, this is far from being a welldefined problem. Apart from the usual difficulty of deciding 

exactly what is the most important measure (peak speed, efficiency, 

etc), there is the question of divorcing the underlying locomotive 

concept from the particular implementation (just like a universal 

machine such as Turing Machine divorces hardware 

implementations from algorithms). 

This paper proposes a particular platform which the authors 

believe can be used as part of a standard system for evaluating 

many different means of locomotion. Since one of the 

fundamentally different aspects of each of these locomotive 

methods is the underlying mechanism, then any standard platform 

must be capable of changing its shape and fashion of moving so as 

to be able to faithfully perform the locomotion to be tested. The 

PolyBot system, developed at PARC, is capable of just this.

KEYWORDS: locomotion systems, locomotion gaits, 

modular self-reconfigurable robots, experimental platforms, 

performance measures

1. MOTIVATION 

Locomotion is an important attribute for many intelligent 

systems. All known intelligent species of life are capable of 

locomotion by some means or other. The focus of this paper 

will be a little narrower, focusing only on locomotion on 

solid surfaces (thus excluding swimming or flying). Over the 

last century human beings have invented various kinds of 

locomotion systems for motion over ground, mostly for fast 

and efficient transportation. Probably the two most 

widespread of these are as cars and trains. Most cars or trains 

cannot be considered intelligent systems, because (1) they 

are not autonomous to any significant degree, (2) despite a 

large internal sensor network, their perception of the outside 

world is very limited, (3) they are intended for use in very 

specialized artificial environments -- (cars on highways and 

trains on railways). 

The world is being constantly changed through the 

increasing availability of progressively cheaper and more 

powerful computation. Predictions have been made 

suggesting that in twenty years time, cars and trains will 

become intelligent robotic systems. Like animals, these 

vehicles will not only have a brain (central control) but also 

nervous systems (networking) connecting all sensing and 

actuation components. 

The majority of existing man-made locomotion systems is 

wheeled, since that is simple and efficient in a conveniently 

engineered environment (flat surfaces or rails). However 

natural locomotive systems (such as used by animals) have 

almost exclusively favored employing legs. The use of 

wheeled vehicles is largely limited to flat environments. 

Tracked vehicles tend to handle a wider variety of terrain but 

suffer in efficiency. Legged machines tend to be less efficient 

and harder to control but have the potential of traversing an 

even wider variety of terrains. While much research has 

been done on legged locomotion, little has been usefully 

commercialized. Even though legged locomotion is 

generally recognized to be more flexible, and has the 

potential to effectively traverse natural environments, as yet 

more knowledge and understanding of how to engineer such 

systems is needed. 

It is hard to compare two locomotion systems with 

radically different design, or two systems engineered for use 

in different environments. This paper proposes the use of 

modular self-reconfigurable robots as a standard platform for 

studying various types of locomotion and developing 

concrete performance metrics. By using this one platform 

for testing all locomotive ideas, the fundamental locomotive 

principle being tested is somewhat divorced from the specific 

physical implementation. 

A modular self-reconfigurable robot, named PolyBot, has 

been developed over the last three years at the Palo Alto 

Research Center (http://www.parc.com/modrobots). 

PolyBot consists of many component modules (possibly 

hundreds), each of which has sensing, actuation and 

computation. These modules can be configured into many 

different shapes, such as wheels/loops, snakes and 

centipedes. It is due to this versatility that PolyBot is able to 

implement a wide variety of different locomotive systems, 

allowing concrete performance metrics to be calculated and 

clear comparisons to be performed. 
With PolyBot, it is possible to develop various types of 

locomotion gaits for different types of configurations, and 

study the effectiveness of various control strategies. The 

results can be used to develop the performance metrics, 

which in turn allows quantitative improvements to be made 

in the quality of locomotion systems. 

This paper is organized as follows. Section 2 characterizes 

some initial concepts on locomotion systems and gaits, 

Section 3 discusses terrain evaluations, Section 4 presents 

locomotion performance metrics; Section 5 describes more 

completely PolyBot, the modular reconfigurable robot. 

Finally, there are possible directions for future research using 

PolyBot as a platform for studying locomotion systems. 

2. LOCOMOTION SYSTEMS AND GAITS 

A locomotion system is a powered system being able to move 

from one position/orientation to another. There is a 

considerable body of knowledge on animal locomotion [1] 

and vehicle locomotion [2]. The most typical classification of 

land locomotion divides locomotion into four types: 

wheeled, tracked, legged, and other. From authors’ point of 

view, this is unsatisfactory for several reasons. First, the last 

area is a catchall, and would include such dissimilar means 

of locomotion as snake-like sidewinding, concertina, screw 

locomotion, etc. Second, there are too many instances of 

ambiguity. For example, a child cartwheeling may be 

considered legged locomotion since the child has legs. 

Would a spoked wheel with no rim or partial rims also be 

considered legged locomotion? Tracked locomotion is 

defined as traveling on endless belts. Is a belt around a tire 

then tracked locomotion? What about a slightly flat tire? 

Yim [3] in his PhD thesis in 1994 studied various locomotion 

systems and first characterized locomotion gaits 

systematically. 

A locomotion gait is defined as one cycle of a pattern of 

motion that is used to achieve locomotion. There are simple 

gaits and compound gaits; compound gaits are combinations 

of two or more simple gaits. There are maybe finite classes 

of simple gaits, but combination of these can generate 

infinite number of compound gaits. For example as wheeled 

locomotion is one type of locomotion and bipedal walking 

clearly is another, the two can be combined as with a person 

wearing roller skates. 

A large portion of ground-based locomotion gaits can be 

characterized as statically stable gaits. To achieve statically 

stable locomotion in general, one has to repeatedly do three 

things in any order: 

1. remove ground contact points from the rear, 

2. place ground contact points in front, 

3. shift weight forward. 

Throughout all of these steps, maintain static equilibrium 

throughout all motions. A statically stable gait defines a 

cyclical pattern that achieves these steps. 

The simple ground-based statically stable locomotion gaits 

are characterized by three categories [3]: (R)oll/(S)wing, 

(D)iscrete/(C)ontinuous, (B)ig/(L)ittle Footed. For 

examples, a 4-wheel passenger car is RCL, a treaded tank is 

RCB, a cockroach is SDL, an earthworm is SCB, human is 

SDB, etc. 

Yim [3] also characterized three fundamental ways that a 

simple gait may be combined: articulated, hierarchical and 

morphological. Articulated combination is to unite more 

than one locomotion systems, e.g., track and trailer. 

Hierarchical combination is to add one locomotion system on 

the top of another, e.g., roller skating. Morphological 

combination is to merge locomotion systems with different 

axis, e.g., a rolling sphere. 

When deciding which gait would be most appropriate for a 

given situation, it would be useful to know the characteristics 

of each type of classification. For simple gaits, rolling 

systems tend to be simpler and more efficient. Continuous 

motion can be smoother over hard flat terrains. The larger the 

footprint, the better the performance in terms of speed, 

efficiency and mobility, etc. For compound gaits, single 

chain articulated gaits have several desirable features: the 

ability to travel in highly constrained areas, to fit between or 

cross large obstacles, with a large payload. Hierarchical gaits 

can achieve higher speeds than individual gaits, e.g., walking 

on a moving track belt is faster than walking on a ground. 

Morphological gaits add degrees of freedom to locomotion, 

which make the system more flexible. 

3. TERRAIN EVALUATIONS 

Simply comparing the locomotion capabilities of a horse to a 

wheeled car is meaningless, just like comparing apples and 

oranges. In nature, each form of locomotion exists in the 

environment that fits it best. Locomotion performance 

metrics will not be complete without terrain evaluations. Yim 

[3] defined the taxonomy of terrain effects (Figure 1). 

Figure 1: Taxonomy of Terrain Features 

Terrain Effects 

Static 

Quasidynamic 

Dynamic 

Elevation

Map 

Full 3D 

Slope 

Ditch 

Hangup 

Barrier 

Height 

Width 

Curvature 

Elasticity 

Plasticity 

Penetrability 
Static 2.5D terrain features include slopes, gradual 

elevation with height, ditches, holes in the ground, hang-ups, 

bumps in the ground, and barriers, a vertical object to cross 

like a wall. Full 3D terrain features include height

constraints, obstacles on the top, width constraint, obstacles 

on the sides, and curvature constraint, the radius to turn. 

Quasi-dynamic terrain features include elasticity, plasticity

and penetrability of ground surface, for example, a 

locomotion system will perform differently on soft mud 

terrain and hard wood floors. Dynamic terrain features 

include moving wind/current, moving terrain and obstacles, 

etc. 

4. LOCOMOTION PERFORMANCE 

METRICS 

The complexity inherent in intelligent systems means that it 

is rare for a useful metric to measure just one aspect of 

performance. In general, the evaluation function which 

serves as the metric will have multiple objectives which must 

be appropriately scaled and weighted. There are two main 

types of measurements for locomotion systems: system 

centric and environment centric. 

In system-centric measurements, the type of environment 

is fixed (e.g. a dirt road) and other aspects (e.g. speed, 

acceleration, efficiency, stability, payload) are compared. In 

an environment-centric measurement, the value is some 

measure of the terrain which can be traversed (e.g. how steep 

the environment can be, or how rough) in terms of metrics of 

slopes, ditches, hang-ups, barriers, height, width and 

curvature constraints etc. 

In addition to mechanical capabilities, computational 

capabilities can also be measured, such as adaptability, 

robustness, self-repair-ability, as well as the underlying 

computational components such as CPU speed, memory, 

communication rate, etc. 

In addition to these "hard" measurements of locomotion 

systems, there are also "soft" measurements reflecting quality 

of system design (both hardware and software); these include 

maintainability, modularity, scalability and reusability. 

Some of these attributes are not directly related to 

performance, but are relevant to the total cost of ownership. 

Others are even less of interest to an end-user, but are still of 

importance for decision-making by the developer. 

The authors do not claim to have yet developed a complete 

metric which satisfies all the conditions discussed above–this 

is work in progress. However they do put forward the idea 

of employing a uniform platform for locomotion testing. 

This, they argue, will simplify the measurement and 

comparison process, allowing effort to be directed towards 

refining the base metric. This universal platform is described 

in the next section. 

5. MODULAR ROBOTICS PLATFORM 

A modular reconfigurable robot is one that consists largely 

(or entirely) of identical components which can be assembled 

into many topological configurations. These different 

configurations generally equate to different physical shapes – 

each with different abilities and limitations. In this way the 

platform can be used to test many fundamentally different 

forms of locomotion. The platform proposed here is a 

modular self re-configurable robot: one that can change from 

one configuration to another autonomously. While this 

capability is not actually essential for its use as a universal 

platform as proposed here, the sensing, distributed 

computation, communications and control middleware 

required to support self reconfiguration will prove useful in 

carrying out the measurements for the performance metric. 

There are a growing number of modular self-reconfigurable 

robotic [4][5][6][7][8][9]. This paper focuses on one 

particular modular self-reconfigurable robot, named PolyBot 

[10]. 

PolyBot, is a modular reconfigurable robot system 

composed of two types of modules, one called a segment and 

the other called a node. The segment module has two 

connection ports and one degree of freedom (DOF) motion. 

The node module is a rigid cube with six connection ports 

but no internal DOF. PolyBot has been designed for 

applications including planetary exploration, undersea 

mining, search and rescue and other tasks in unstructured, 

unknown environments. PolyBot has been developed through 

its third generation at the Palo Alto Research Center. The 

latest design features smaller module size (5cm), more 

sensors (IR range, touch, force) and multiple actuators for 

locomotion, manipulation and reconfiguration, as well as 

bridged networks using CAN (Controller Area Networks). 

Each PolyBot module has a Motorola PowerPC MPC555

embedded processor with 448K internal flash ROM and 1M 

of external RAM. Software architecture has been developed 

for PolyBot, with a higher layer CAN protocol MDCN 

(Massively Distributed Control Nets) [11][12] and an 

Attribute/Service Model [11][13] for coordination of 

multiple tasks in multiple processes. 

PolyBot is a good platform for studying various forms of 

locomotion. The PolyBot systems have demonstrated 

versatility by showing multiple modes of locomotion with a 

variety of characteristics, distributed manipulation and the 

ability to self-reconfigure. PolyBot can be configured into 

various shapes (see Figure 2,3,4). Each configuration has 

pros and cons in terms of performance. Snakes can traverse 

terrains with narrow entrance, such as pipes, and is the most 

robust among other configurations. Loops or wheels are most 

efficient over flat terrains. With deformed loops 

(conformance to terrains) it can also traverse effectively over 

stairs. Centipedes or spiders are good for avoiding obstacles 

and traverse rough terrains. 
 

 

Figure 2: Snake Configuration 

Figure 3: Loop Configuration 

Figure 4: Spider Configuration 

6. FUTURE WORK 

There will be 100+ PolyBot modules built by the October 

this year. Various locomotion configurations and gaits will 

be tested and compared in the near future. A more complete 

understanding of and development of locomotion 

performance metrics will commence. 

ACKNOWLEDGEMENT 

This work is funded in part by the Defense Advanced 

Research Project Agency (DARPA) contract # MDA972-98-

C-0009. 

REFERENCES 

[1] Gray, J., “Animal Locomotion”, W.W. Norton & Co. 

Inc., New York, 1968 

[2] Bekkar, M. G., “Introduction to Terrain Vechicle 

Systems”, Ann Arbor MI, The University of Michigan Press, 

1969 

[3] Yim, M., “Locomotion with a Unit-Modular 

Reconfigurable Robot”, PhD Thesis, Stanford University, 

1994 

[4] Fukuda, T. and S. Nakagawa, “Dynamically 

Reconfigurable Robotic System,” Proc. of the IEEE Int. 

Conf. on Robotics and Automation, pp. 1581-1586, 1988. 

[5] Kotay, K., D. Rus, M. Vona, C. McGray, “The Selfreconfiguring Robotic Molecule,” Proc. of the IEEE 

International Conf. on Robotics and Automation, pp424-431, 

May 1998. 

[6] Murata, S., H. Kurokawa, S. Kokaji, “Self-Assembling 

Machine,” Proc. of the IEEE International Conf. on Robotics 

and Automation, pp441-448, May 1994. 

[7] Pamecha, A., C. Chiang, D. Stein, G.S. Chirikjian, 

“Design and Implementation of Metamorphic Robots,” Proc. 

of the 1996 ASME Design Engineering Technical Conf. and 

Computers in Engineering Conf., Irvine, California, August 

1996. 

[8] Unsal, C. and P.K. Khosla, “Solutions for 3-D Selfreconfiguration in a Modular Robotic System: 

Implementation and Path Planning,” Proc. of SPIE Sensor 

Fusion and Decentralized Control in Robotic Systems III, 

Vol. 4196. 

[9] Will P., A. Castano, W-M Shen, “Robot modularity for 

self-reconfiguration,” SPIE Intl. Symposium on Intelligent 

Sys. and Advanced Manufacturing, Proceeding Vol. 3839, 

pp. 236-245, Sept. 1999. 

[10] Yim, M., D. Duff, K. Roufas, “PolyBot: a Modular 

Reconfigurable Robot” Proc. of the IEEE Int. Conf. on 

Robotics and Automation, April 2000. 

[11] Zhang, Y., K. Roufas, M. Yim, “Software Architecture 

for Modular Self-Reconfigurable Robots”, IEEE/RSJ 

International Conference on Intelligent Robots and Systems, 

Hawaii, 2001.

[12] Zhang, Y., K. Roufas, M. Yim, “Massively Distributed 

Control Nets for Modular Self-Reconfigurable Ro-bots”, 

AAAI Spring Symposium for Intelligent Distrib-uted and 

Embedded Systems, 2002 

[13] Zhang, Y., M. Yim, K. Roufas, C. Eldershaw, “Attribute/Service Model: Design Patterns for Distributed 

Coordination of Sensors, Actuators and Tasks”, sub-mitted to 

Workshop on Embedded Systems Codesign, 2002.