Higher Order Real-Time Approximations in Optimal Control of Multibody-Systems for Industrial Robots

Abstract

The multibody system of an industrial robot leads to a mathematical model described by ordinary differential equations. Control functions have to be determined to calculate robot trajectories which are optimal due to a given performance index subject to additional constraints. In order to solve such optimal control problems, computationally expensive methods exist. These methods have no real-time capability, since perturbations during the motion of the robot require a recalculation of the optimal trajectory within a time frame much smaller than the operating-time of the robot. Hence, a robust numerical method based on the parametric sensitivity analysis of nonlinear optimization problems is suggested. Optimal control approximations of perturbed optimal solutions can be obtained in real-time by evaluating a first order Taylor expansion of the perturbed solution. Successive improvements to the constraints in the direction of the optimal perturbed solution lead to an admissible solution with a higher order approximation of the objective. The proposed numerical method is illustrated by the optimal control of an industrial robot with three degrees of freedom subject to deviations in the payload and initial values.