Inverse Statics Optimization for Compound Tensegrity Robots

Robots built from cable-driven tensegrity (`tension-integrity') structures have many of the advantages of soft robots, such as flexibility and robustness, yet still obey simple statics and dynamics models. However, existing approaches cannot natively model tensegrity robots with arbitrary rigid bodies in their tension network. This work presents a method to calculate the cable tensions in static equilibrium for such robots, here defined as compound tensegrities. First, a static equilibrium model for compound tensegrity robots is reformulated from the standard force density method used with other tensegrity structures. Next, we pose the problem of calculating tension forces in the robot's cables under our model. A solution is proposed as a quadratic optimization problem with practical constraints. Simulations illustrate how this inverse statics optimization problem can be used for both the design and control of two different compound tensegrity applications: a spine robot and a quadruped robot built from that spine. Finally, we verify the accuracy of the inverse statics model through a hardware experiment, demonstrating the feasibility of low-error open-loop control using our methodology.