Time-energy optimal control of hyper-actuated mechanical systems with geometric path constraints

For a general class of Hyper-Actuated Mechanical Systems (HAMS) that is generalized to include robotic manipulators and tendon-driven tensegrity structures, this paper determines the tendon force inputs from a set of admissible, non-saturating inputs, that will move the rigid-body system from point A to point B along a prescribed path with minimum time and control energy. The approach herein utilizes the existence conditions and solution of a linear algebra problem that describes 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. This paper determines the best time-invariant free parameters. This yields a novel control law for HAMS that tracks the center of the admissible set and reduces the number of states in the optimal control problem to two. The prevalence of HAMS in nature is discussed. Numerical examples illustrate the method and demonstrate tensegrity’s superior maneuvering and saturation avoidance capabilities.