# Prototype of the Arm-Z Modular Solar Tracker

Ela Zawidzka, Jacek Szklarski, Wojciech Kiński, Machi Zawidzki

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Ela Zawidzka, Jacek Szklarski, Wojciech Kiński, Machi Zawidzki. Prototype of the Arm-Z Modular Solar Tracker. Automation 2022: New Solutions and Technologies for Automation, Robotics and Measurement Techniques, Łukasiewicz Research Network - Industrial Research Institute for Automation and Measurements PIAP, May 2022, Warsaw, France. pp.273-282, 10.1007/978-3-031-03502-9_28.hal-04969412

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# Prototype of the Arm-Z modular solar tracker

Ela Zawidzka¹ Jacek Szklarski¹, Wojciech Kiński², and Machi Zawidzki¹

¹ Institute of Fundamental Technological Research, Polish Academy of Sciences, zawidzka@ippt.pan.pl

² Industrial Research Institute for Automation and Measurements PIAP

**Abstract.** Arm-Z is a hyper-redundant manipulator based on a sequence of linearly joined identical modules. Each module has only one degree of freedom - a twist relative to the previous module. Arm-Z can be potentially economical, as the modules can be mass-produced. Arm-Z is also robust, as the malfunctioning module can be replaced. Moreover - if some modules malfunction the device can still execute tasks with certain accuracy. However, the disadvantage of Arm-Z is a non-intuitive and difficult control. This paper presents the prototype of a modular Sun-tracking device comprised of four identical modules. The possible application: solar energy harvesting or Sun-shading.

**Keywords:** Extremely Modular System, Arm-Z, Hyper-redundant manipulator, Rapid prototyping, Low-tech

## 1 Introduction

Snakes are supremely adapted for various habitats. This is due to the redundancy of the snake mechanism. In some cases of non-regular environments the biology-inspired trunk-like robot can outperform conventional robot mobility (e.g. legged, tracked or wheeled). The research on snake-like robots commenced already several decades ago. The locomotion of snakes was systematically studied as early as 1940s ([1]). A half of a century later the mathematical model was introduced. In 1993 trunk-like manipulators and locomotors were proposed in [2]. This type of manipulators have distinct characteristics of motion. This gives them particular advantage in conditions where conventional robotic manipulators are impractical. Snake/trunk-like manipulator can place working head in a complicated space which is inaccessible by other methods. The range of reach of such manipulators is relatively large (tens of meters). Most importantly, such manipulators can operate in unsafe environments. Depending on the working head installed at the tip of such manipulator - it can weld, clean, serve for visual inspection etc. There are only a few enterprises offering this type of manipulator, the available solutions are scarce and mostly experimental (for examples see Fig. 1).
<figure><img src="image_2.png" /><figcaption>Fig. 1: Two examples of robotic trunk-like manipulators offered by Oliver Crispin Robotics Ltd. (http://www.ocrobotics.com).</figcaption></figure>

In addition, snake/trunk-like robotic arms can have considerably larger num-
bers of degrees-of-freedom (DOFs). This contrasts with conventional industrial
manipulators which have low number of DOF. In the case of Arm-Z manipulator,
its DOF number equals to the number of linearly assembled units -1. Redundant
number of DOFs allows not only the ability of executing complex movements,
but also substantially improves the robustness and fault tolerance. This is in
alignment with the idea of so-called hyper-redundant-manipulators (HRM for
short, [3]). Due to the high non-linear characteristics of the HRM, its advantage
comes at the cost of very difficult and counter-intuitive controlling. For example,
the control of a *bionic trunk* requires quite intensive application of AI (artifi-
cial intelligence) techniques [4], [5], [6], while the control of a typical industrial
manipulator is straightforward, as its inverse kinematic problem can be solved
easily ([7]). For more details on hyper-redundant robotic arms see [8]. The idea
of extreme modularisation is novel and still fairly unexplored. The research on
structural optimisation of modular constructions is also comparatively scarce.
As an example - Ref.[9] presents a multi-objective optimisation of a set of a
number of vehicle structures at the level of common beam parts. Another exam-
ple - of a layout optimisation of a modular bridge, where the design variables are
effectively discrete and encode the choice from a predefined set of local module
topologies has been presented in [10].

## 2 The idea of Arm-Z

Complicated 3D tubular shapes may be constructed with comparatively uncom-
plicated identical modules ([11]). Ref. [12] introduced a parametric design system
composed of congruent units. The idea of Arm-Z robotic manipulator is based
on assembly of congruent units. Each unit has one degree-of-freedom (1-DOF)
- namely a twist relative to the previous unit ([13]). The emerging behaviour of
Arm-Z manifested by complex movements in 3D results from simple alterations
of these relative twists, which can be discrete or continuous.

The modules of Arm-Z are geometric entities analogue to sectors of circular
tori. All modules are defined by the following parameters: size *r*, offset *d*, number
of sides $k$, and $\zeta$, that is the angle between upper (T) and lower (B) planes of the module. These parameters are illustrated in Fig. 2.

<figure><img src="image_3.png" /><figcaption>Fig. 2: On the left: visualisation of Arm-Z module which is defined by the following parameters: $r$, $d$, $\zeta$ and $k = 6$ (hexagon) and its isometric view. On the right: examples of simple assembly of modules with various combinations of their geometrical parameters.</figcaption></figure>

The shape of entire Arm-Z structure depends on: the number of units, their geometric parameters, and the relative rotations among the modules. As an example, two Arm-Z units at 6 successive discrete rotations from 0 to $\pi$ are shown in Fig. 3.

<figure><img src="image_4.png" /><figcaption>Fig. 3: The relative rotations of Arm-Z unit. The bottom module is fixed and shown in grey. Red line indicated the axis of rotation for the next module in the sequence.</figcaption></figure>

## 3 The Sun-tracking task

As an example of a steady movement of the manipulator following given direction we propose a sun-tracking device with possible application e.g. for solar energy harvesting. Fig. 4 shows the position of the Arm-Z in the coordinate system and explains the tracking parameters. is the normal vector to the surface of the last module, in other words, it is a vector pointing from the tip of the manipulator. stands for the desired direction of the normal vector (in this case, the sunlight direction). ($\phi, \theta$) is defined by the azimuth $\phi$ and altitude $\theta$. In this task, must follow, in other words the angle between these two vectors is minimized. is the
position of the tip of the manipulator. is the number of degrees of freedom of
the system, it is equal to the number of modules - 1.

<figure><img src="image_5.png" /><figcaption>Fig. 4: The coordinate system, notation and the control parameters.</figcaption></figure>

In this task the intention is to follow the Sun direction during summertime
(from summer solstice to September equinox) between 10 a.m. and 6 p.m., as
illustrated in Fig. 5.

<figure><img src="image_6.png" /><figcaption>Fig. 5: Possible sun location during a year and for the given periods during summertime (indicated in red).</figcaption></figure>
The angular errors for manipulators of various numbers of degrees of freedom: 1,2,3,4,6 and 7 are shown in Fig. 6. White line indicates there is no horizontal plane. Black indicates very small errors. Already a 4-module manipulator can cover almost all desired directions. The last figure shows that 7 degrees of freedom allow to cover almost all directions in 3D space (including the space below the manipulator).

<figure><img src="image_7.png" /><figcaption>Fig. 6: Visualization of the angular errors for Arm-Z manipulators of various numbers of degrees of freedom: 1,2,3,4,6 and 7. The outline indicating the tracking period from Fig. 5 is superimposed as the white dashed line for the case of 3 DOF.</figcaption></figure>
## 3.1 The optimisation of the tracking action

In order to perform realistic simulations, the manipulator has been implemented in Bullet Physics SDK [14]. It is a widely used tool for real-time collision detection and multi-physics simulation for virtual reality (VR), robotics, machine learning etc. In order to control the manipulator, the inverse dynamics has been solved by two numerical methods: the classical recursive Newton Euler algorithm (RNEA), [15] and by means of dual annealing [16, 17]. As it turned out, the latter method performed better (in terms of average errors) than RNEA. This can be attributed to the fact, that the system is highly nonlinear and even small changes in position of modules at the bottom can profoundly influence the tip position.

In order to continuously control the manipulator, the twist velocities and spins of three modules have been optimised with the dual annealing method in a way in which significant deviations from the current state have been penalized. This made possible to achieve a quite smooth movement of the manipulator. The results (angular velocities of the individual modules) are shown in Fig. 7.

<figure><img src="image_8.png" /><figcaption>Fig. 7: Joint states $x_1, x_2, x_3$ for a four-module structure which follows the sun on July 1st between 8 a.m. and 8 p.m. local time.</figcaption></figure>

Fig. 8 shows the angular errors throughout the tracking period.
<figure><img src="image_9.png" /><figcaption>Fig. 8: Error (angle between and ) for globally optimal states and for the continuous control scenario (some peaks can be noticed for the latter). From Fig. 6, it follows that the tips normal vector can not follow the sun for low latitudes, especially during sunrise/sunset. Hence the growing error from approximately 6 p.m.</figcaption></figure>

# 4 The prototype

The prototype of Arm-Z solar tracker is equipped with advanced gears which allow for: switching the spin of given module (right/left) about its axis and transferring of the motion to the subsequent module. The cogwheels with involute outline has been used for the gear train. In order to avoid slipping, they are embedded on the rods with square section. Moreover, in order to minimize the rolling resistance, 608ZZ bearings have been used. The gear train has been equipped with so called "reverse switch". A dedicated left/right lever switch has been placed in the side of the casing of each module as shown in Fig. 9.

<figure><img src="image_10.png" /><figcaption>Fig. 9: The switch for changing the spin of the rotation of the module.</figcaption></figure>
This corresponds to along/counter spin of the previous module. Each module
is equipped with toothed ring as show in Fig. 10.

<figure><img src="image_11.png" /><figcaption>Fig. 10: The drive cogwheel (on the bottom) an corresponding tooth wheel (on the top).</figcaption></figure>

In each module there is a sleeve which forms a continuous pipe through
entire Arm-Z device. Its main purpose is for the wiring. In order to form a
firm and smooth connections of the entire Arm-Z, the modules are attached
to each other with special bracing equipped with bearings. The gear train can
be freely modified inside each module. The gear ratio of each module can be
adjusted by alteration of the number of teeth of the cogwheels of gear trains.
The cogwheel sets are also modular and can be easily replaced. In this project,
the design principle was to use as many elements as possible off-the-shelf, in other
words, not designed or made to order but taken from existing stock or supplies,
e.g.: commercially available bearings, standard rods, etc. Certain elements have
been 3D-printed using FDM/FFF (Fused Deposition Modeling/Fused Filament
Fabrication) technology and enhanced materials, e.g. with increased abrasion
resistance by use of polyamide (PA) filaments with carbon fiber. The cogwheels
have been fabricated in two versions: 3D printed and laser-cut from aluminum
sheet. The CAD visualization of the prototype of a four-unit Arm-Z solar tracker
is shown in Fig. 11.
<figure><img src="image_12.png" /><figcaption>Fig. 11: The CAD visualization of the prototype of a 4-module Arm-Z solar tracker.</figcaption></figure>

## Acknowledgements

This research is a part of the project titled *Arm-Z: an extremely modular hyper-redundant low-cost manipulator – development of control methods and efficiency analysis* and funded by OPUS 17 research grant No. 2019/33/B/ST8/02791 supported by the National Science Center, Poland.

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