An Approach to Optimal Motion Planning for Robotic Applications

This paper focuses on time and energy optimal control methods in the modern field of robotics and their verification by experiment. Considering a typical scenario where a robot manipulator's trajectory is known in advance, a feed forward control - weighting time and energy to obtain optimal controls - is presented in this document. By introducing trajectory parameters which effectively describe the progress of the trajectory as a function of time, optimal control variables can be found. The controls however are subject to different limits arising from physical restrictions like limited joint angles, velocities, jerks and available motor torques. Taking these aspects into account the necessary and highly nonlinear dynamical model of the robot is computed with the projection equation in subsystem representation. An optimization problem will be formulated and then numerically solved including the robots' complete dynamics. To verify the calculations the offline-computed and optimized trajectory will be followed with a Stäubli industrial robot and the calculated and measured motor torques are compared. To counter model inaccuracies, like friction or temperature dependencies, an additional feedback control loop assures stability. The measurements and simulations will be accordingly compared and discussed.