On the Locomotion of Spherical Tensegrity Robots

Abstract

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 relaxationtechnique with a multi-generation Monte Carlo is proposed. It is known in the literaturethat 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 T