Theoretical and experimental analysis of a soft and miniature quadruped

Abstract

Multi-body dynamic modeling of non-rigid and legged robots is an active research area with the goal of investigating the interaction of a robot with its environment and its resulting locomotion. The results of such studies can be used to build a simulation that will be used for the iterative process of the mechanical design of the robot, and the algorithm design of its high- and low-level controllers. The dynamics of soft robots is more challenging comparing to rigid robots because of the partial derivatives and the shape integrals existing in the dynamic models, and the literature is open to improvement. The subject of this study is S-Quad, a soft and miniature quadruped with c-shaped legs. To analyze the effect of the compliance of its body and legs to its locomotion, a soft-body dynamic model has been developed. The development process starts with the rigid-body dynamic analysis, which will be a base for the soft-body dynamic analysis and used to examine the rigid body - rigid legs (RBRL) version of the robot. The Newton-Euler method has been used to develop this model, in which the contact forces are estimated with the viscoelasticity theory. Scenarios of different model parameters were simulated to estimate the motion of the robot. With the obtained results the effects of the model parameters were discussed, and then appropriate parameters have been selected. The contact analysis of a curved leg inside of the robot dynamics, in which any intersection algorithm is not used, is an advantageous aspect of this study. The compliance of the legs has been incorporated into this dynamic analysis with a non-linear viscoelastic model. The dependency of the leg compliance to the roll angle of the leg was derived from Castigliano’s theorem. Then, the motion of the rigid body - soft leg (RBSL) robot was estimated accordingly. The comparison of the RBRL and the RBSL results was utilized to interpret the effect of the leg compliance. The modeling and the integration with robot dynamics of this compliant leg model is a novel aspect of this model. An offline Finite Element Analysis has been conducted to estimate the deflections of the soft body under the contact forces, which were exported from the RBRL simulation. The estimated deflections were put back into this simulation to obtain the simulation of soft body - rigid legs (SBRL) robot. Thus, the capability of the developed model to include body deflections has been proven. Finally, the RBRL and the RBSL robot simulations have been verified with the experiments conducted with a motion capture system. These experimental results were also used to interpret the advantages and disadvantages of using a soft body in the robot.