On Time-Optimal Control of Elastic Joints under Input Constraints
We highlight the equivalence between the motion of an elastic joint and the two-body problem in classical mechanics. Based on this observation, a change of coordinates is introduced that reduces the two-body problem to a pair of decoupled one-body problems. This allows to treat the rest-to-rest motion problem with bounded actuator torque in an elegant geometric fashion. Instead of dealing directly with the fourth-order dynamics, we consider two equivalent masses whose motions have to be synchronized in separate phase spaces.