Robust Optimal Trajectory Planning for Robots by Stochastic Optimization

In the optimal control of industrial, field or service robots, the standard procedure is to determine first offline a reference trajectory and a feedforward control, based on some selected nominal values of the unknown stochastic model parameters, and to correct then the inevitable and increasing deviation of the state or performance of the robot from the prescribed state or performance of the system by online measurement and control actions. Due to the stochastic variations of the model parameters, increasing measurement and correction actions are needed during the process. By optimal stochastic trajectory planning (OSTP), based on stochastic optimization methods, the available a priori and sample information about the robot and its working environment is incorporated into the control process. Consequently, more robust reference trajectories and feedforward controls are obtained which cause much less online control actions. In order to maintain a high quality of the guiding functions, the reference trajectory and the feedforward control can be updated at some later time points such that additional information about the control process is available. After the presentation of the Adaptive Optimal Stochastic Trajectory Planning (AOSTP) procedure based on stochastic optimization methods, several numerical techniques for the computation of robust reference trajectories and feedforward controls under real-time conditions are presented. Additionally, numerical examples for a Manutec r3 industrial robot are discussed. The first one demonstrates real-time solutions of (OSTP) based on a sensitivity analysis of a before-hand calculated reference trajectory. The second shows the differences between reference trajectories based on deterministic methods and the stochastic methods introduced in this paper. Based on simulations of the robots behavior, the increased robustness of stochastic reference trajectories is demonstrated.