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Dettaglio pubblicazione

2020, Proc. 59th IEEE Conference on Decision and Control, Pages 4149-4156

On Time-Optimal Control of Elastic Joints under Input Constraints (04b Atto di convegno in volume)

Keppler Manuel, De Luca Alessandro

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 solution for the elastic and the rigid system is the same. The closed-form solutions obtained with our purely geometric approach verify the standard optimality conditions.
ISBN: 978-1-7281-7447-1
Gruppo di ricerca: Robotics
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