A real-time capable method for planning minimum energy trajectories for one degree-of-freedom mechatronic systems

The synthesis of optimal motion profiles has shown to be a successful and virtually inexpensive solution for enhancing energy efficiency of mechatronic systems. A typical application is the design of point-to-point motion profiles for one-degree-of-freedom mechatronic systems. This paper proposes a new method for designing minimum energy trajectories for servo-actuated systems. The problem is solved by exploiting the knowledge of the structure of the optimal solution. That allows to solve the motion design problem by solving a set of nonlinear equations and, if needed, some basic optimization procedures, formulated after some suitable continuity conditions. The herein proposed method applies to systems with and without energy regeneration capability, for maximum adaptability to most industrial applications. The method also handles jerk, acceleration, and velocity constraints, which are typical requirements in many practical applications. The number of equations and thereby the computational time depends on the number of active constraints and on whether negative power is dissipated or regenerated. Overall, the method results to be suitable for Real-Time applications, also in the most challenging case in which all the constraints are active and the system cannot regenerate negative electric power. The accuracy and the effectiveness of the planning method is tested numerically, by comparing the solution to the one obtained by a general purpose optimal control solver and then also experimentally using a lab prototype.