Analytical computation of the energy-efficient optimal planning in rest-to-rest motion of constant inertia systems

Among the techniques to improve energy efficiency of mechatronic systems, the synthesis of optimized motion profiles has been proved to be an effective and almost costless method. In order to boost the use of this approach, this paper proposes an analytical method for improving energy efficiency in rest-to-rest motion through optimal planning, by selecting both the optimal motion law and the optimal motion time (duration). The proposed technique is suitable for constant inertia systems. As a matter of fact, this kind of mechatronic systems covers a wide range of applications in production, packaging or logistic plants.The method practical application is straightforward, since it just relies on the knowledge of the task specifications and of some system parameters to compute the optimal motion time for each selected trajectory and to compare analytically different motion profiles. The limitations due the servo-actuator (torque, speed, bandwidth), to machine throughput requirements, as well as the smoothness specifications (acceleration and jerk limitations, degree of continuity) are explicitly accounted for through bounds, to ensure the feasibility of the motion profiles developed.Since the proposed method proposes an analytical algebraic equation, it does not require either time-consuming simulations and trial-and-error evaluations, or numerical optimizations. Hence, it is well suited for industrial mechatronic applications.