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On the Locomotion of Spherical Tensegrity Robots

  • Author(s): Kim, Kyunam
  • Advisor(s): Agogino, Alice M
  • et al.

This dissertation studies novel robotic systems based on tensegrity structures, with an emphasis on their locomotion capabilities. Naturally compliant tensegrity structures have several unique properties that are advantageous for co-robotic or soft robotic platforms; they are lightweight, deployable, robust, and safe. By leveraging these distinctive features of tensegrity structures, tensegrity robots are expected to overcome the barriers for today's robots. In this regard, tensegrity robots have been envisioned for a wide range of new applications that have not been explored before, including assistive and rehabilitative healthcare, search and rescue, and planetary space exploration, to name a few. In order to be actually deployed for these applications, tensegrity robots should have mobility in the rst place. For this reason, two modes of locomotion are examined for spherical tensegrity robots in this research: rolling and hopping.

This research begins by presenting four hardware prototypes of spherical tensegrity robots that have been constructed at the Berkeley Emergent Space Tensegrities laboratory. Three of them (named TT-1, TT-2, and TT-3) are based on a six-rod tensegrity structure, and the last one (named T12-R) is based on a twelve-rod tensegrity structure. A six-rod tensegrity structure is the simplest three-dimensional tensegrity structure that has an outer shape similar to a sphere, and for this reason, the structure is chosen as a basis for the rst three robots. However, the rolling speed of the TT-series robots is limited because their outer surfaces consist only of triangles, which forces them to move in a zig-zag way and lose their momentum as they do so. This motivated the development of T12-R whose outer surface consists of mostly rectangles. This geometry enables the robot to move in a straight line, and thus prevents the loss of momentum. The hardware designs of all four prototypes are described in details.

A spherical tensegrity robot rolls by deforming its shape and by shifting its center of mass. The study of tensegrity deformation, however, is not trivial and poses a unique problem because kinematics and statics of tensegrity structures are tightly coupled and need to be considered concurrently. This work develops two systematic ways of obtaining desirable deformations of spherical tensegrity robots for rolling. As a first step to both approaches, a condition on the center of mass of a spherical tensegrity robot that must be satised for the desirable deformations is stated. The first approach relies on a greedy search algorithm, and it quickly finds one deformation satisfying the condition. This algorithm was implemented in the NASA Tensegrity Robotics Toolkit simulator and the outcome of the simulation was tested on TT-1 and TT-2. Our hardware experiments show that the robots can realize a piecewise continuous rolling motion with the deformations found in the simulation. However, it was also observed that the robots occasionally fail to roll because the algorithm did not take reliability of the rolling motion into account when searching for the desired deformations.

To overcome this drawback, the second approach that combines a dynamic relaxation

technique with a multi-generation Monte Carlo is proposed. It is known in the literature

that the dynamic relaxation is well suited for solving for the deformation of tensegrity structures under non-uniform internal tension distributions. This work adapts the technique to nd the deformations of the hardware robots, but with an explicit description of the rod constraint forces such that the convergence property of the technique is improved. The multi-generation Monte Carlo is then used to find a set of good deformations for reliable rolling by sampling and evaluating a number of deformed shapes through the dynamic relaxation. This procedure is simulated by using a custom-written software in MATLAB, and the results of the simulation as well as their validation on TT-2 are discussed in details. Furthermore, this latter approach is not limited to six-rod tensegrity robots only, and its generalization to other spherical tensegrity robots is presented and demonstrated with T12-R.

Hopping is another viable option for the locomotion of tensegrity robots as they can survive from significant impact shocks due to their structural compliance, while protecting the payloads they are carrying. This contrasts to many other rigid robots that are likely to break if they are dropped from a large height. Hopping could be especially useful when tensegrity robots are deployed for planetary exploration missions because it allows the robots to quickly travel long distances and to be less affected by ground conditions that are potentially unknown. To enable hopping, a tensegrity robot with a cold-gas thruster system is studied and its motion is simulated in this work. The simulation study of different hopping profiles on the Moon shows that longer hops are more energy-efficient but are subject to higher impulse at landing, which may lead to damaging the robot. Hence there is a trade-off between energy-efficiency and safety of the robot. This work also presents a path planning algorithm that is based on the A-star search algorithm, and it combines hopping and rolling for economical navigation on the lunar surface. A localization method based on height measurements of surroundings is also discussed.

Another observation from the simulation study is that a thrust vectoring mechanism is

necessary to increase the fuel efficiency of the thruster-based tensegrity robot. This work

introduces four mechanisms that could be used for this purpose, and among them, a system with two reaction wheels is extensively studied. A spin-axis stabilization problem of the reaction wheel system is formally posed, and the controller that orients the thrust to an arbitrary direction is developed. For this, the (z,w)-parameterization is used to describe the rotational kinematics of the thruster system, but this work modifies the parameterization to explicitly include the target orientation. Based on this description of rotational kinematics, the controller is designed by using the Lyapunov's direct method in conjunction with LaSalle's invariance principle. This controller is globally and asymptotically stable and the proof is given. The controller is simulated on an example thruster system and the results are provided.

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