Control/structure optimization approach for minimum-time reconfiguration of tensegrity systems

For a new class of tendon-driven robotic systems that is generalized to include tensegrity structures. this paper focuses on a method to jointly optimize the control law and the structural complexity for a given point-to-point maneuvering task. By fixing external geometry, the number of identical stages within the domain is varied until a minimal mass design is achieved. For the deployment phase, a new method is introduced which determines the tendon force inputs from a set of admissible. non-saturating inputs, that will reconfigure each kinematically invertible unit along its own path in minimum time. The approach utilizes the existence conditions and solution of a linear algebra problem that describe how the set of admissible tendon forces is mapped onto the set of path-dependent torques. Since this mapping is not one-to-one, free parameters in the control law always exist. An infinity-norm minimization with respect to these free parameters is responsible for saturation avoidance. In addition to the required time to deploy the expended control energy during the post-movement phase is also minimized with respect to the total number of stages. Conditions under which these independent minimizations yield the same robot illustrate the importance of considering control/structure interaction within this new robotics paradigm.