Time-optimal control of a visco-elastic joint

We address the time-optimal, rest-to-rest motion problem under bounded control for a two-mass system interconnected by a visco-elastic joint. A complete geometric solution has recently been found in [1] for the purely elastic case, exploiting symmetries that are lost with the introduction of viscous damping. A semi-analytic solution is presented here by decoupling the fourth-order problem into its rigid body and visco-elastic second-order subproblems and imposing then motion coordination of the two subsystems. The presented numerical results confirm the optimality of the obtained bang-bang solutions, all having three control switchings.