Title: Inverse Kinematics for Control of Tensegrity Soft Robots: Existence and Optimality of Solutions,
Abstract: Tension-network (`tensegrity') robots encounter many control challenges as
articulated soft robots, due to the structures' high-dimensional nonlinear
dynamics. Control approaches have been developed which use the inverse
kinematics of tensegrity structures, either for open-loop control or as
equilibrium inputs for closed-loop controllers. However, current formulations
of the tensegrity inverse kinematics problem are limited in robotics
applications: first, they can lead to higher than needed cable tensions, and
second, may lack solutions when applied to robots with high node-to-cable
ratios. This work provides progress in both directions. To address the first
limitation, the objective function for the inverse kinematics optimization
problem is modified to produce cable tensions as low or lower than before, thus
reducing the load on the robots' motors. For the second, a reformulation of the
static equilibrium constraint is proposed, which produces solutions independent
of the number of nodes within each rigid body. Simulation results using the
second reformulation on a specific tensegrity spine robot show reasonable
open-loop control results, whereas the previous formulation could not produce
any solution.