Energy-optimal motion laws for servo-actuated systems considering asymmetric transmission efficiency

The synthesis of optimal motion trajectories is a well-established and cost-effective approach to improving the energy performance of mechatronic systems. This work introduces a method for the generation of energy-optimal trajectories in servo-actuated systems incorporating transmissions with non-unitary efficiency and with asymmetric (direct/reverse) power transmission behavior.The importance of incorporating the efficiency effect relies on the fact that the actual dynamics shows a not-smooth behavior, making the ideal system prediction erratic and the solution of the minimum-energy problem challenging. The proposed approach takes advantage of the known structure of the optimal solution, allowing the motion planning problem to be reformulated as an iterating quadratic programming problem. Optionally, a set of nonlinear equations has to be solved if acceleration/jerk limits are considered. These are constructed on the basis of continuity conditions that ensure physical and dynamical consistency. The formulation allows for real-time implementation, thus extending the applicability of minimum-energy trajectories in industrial scenarios, as general-purpose solvers do not cope with real-time requirements. Finally, the energy-saving capabilities are shown through comparison with a standard double-S law.