On Time-Optimal Control of Elastic Joints under Input Constraints

M. Keppler and A. De Luca, “On Time-Optimal Control of Elastic Joints under Input Constraints,“ Published in: 2020 59th IEEE Conference on Decision and Control (CDC) DOI: 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. Based on this idea, we derive a complete synthesis method for time-optimal rest-to-rest motions of this elastic system. The solution is a bang-bang control policy with one or three switches. We also introduce the concept of natural motions, when the minimum-time solut