Optimal robot path following for minimal time versus energy loss trade-off using sequential convex programming

This paper focusses on the time-energy optimal path following for robots. This considers the problem of moving along a predetermined geometric path with a minimal trade-off between the motion time and the two major thermal energy losses in electric actuators. Theses losses consist of resistive electrical losses and mechanical friction losses. When only taking into account the electrical losses for a simplified robotic manipulator, a convex reformulation has been derived previously [1]. In this paper we include the dynamic joint friction losses into the objective. This also implies that we have to include the dynamic joint friction into the robot equations of motion, which appear in the torque constraints. Both the resulting objective and torque constraints are non-convex. The present paper proposes an efficient sequential convex programming (SCP) approach to solve the resulting optimal control problem. A key step here is to decompose the non-convex functions involved as a difference of convex functions. Numerical simulations illustrate the fast convergence of the proposed method in only a few SCP iterations, confirming the efficiency of the proposed framework. This high efficiency allows for an efficient tool to investigate the trade off between time-optimality and energy-optimality.