  Robots built from cable-driven tensegrity (`tension-integrity') structures
have many of the advantages of soft robots, such as flexibility and robustness,
while still obeying simple statics and dynamics models. However, existing
tensegrity modeling approaches cannot natively describe robots with arbitrary
rigid bodies in their tension network. This work presents a method to calculate
the cable tensions in static equilibrium for such tensegrity robots, here
defined as compound tensegrity. 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 proposed 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 proposed methodology.
