Trajectory Preshaping for High-Speed Articulated Systems

This paper presents a method for reducing the tracking errors of articulated systems, moving along specified paths at high speeds. It consists ofpreshaping the reference trajectory to account for the dynamics of the feedback controller. The trajectory is assumed to be feasible, satisfying the known manipulator dynamics and the actuator constraints. The correction term, added to the nominal trajectory, is computed by filtering the nominal control inputs through the inverse of the feedback controller. A learning procedure is also presented to account for unknown parameters of the feedback controller andfor unmodeled dynamics. It consists of an iterative parameter optimization that minimizes the tracking error along the path at each joint. The initial guesses for this optimization are selected to ensure that the tracking error is not worse than the error with no preshaping. The method is demonstrated experimentally for the UCLA Direct Drive Arm and for the AdeptOne industrial robot, achieving mean tracking errors as low as 0.11 mm at top speeds of 1.8 m/s. however, is that they are task specific and, thus, require repeti- tion of the learning process for every new task. In this paper, we combine trajectory preshaping with some aspect of learning control. The reference trajectory is preshaped to account for the dynamics of the feedback controller. This is done by adding a correction term, which is computed by filtering the nominal control input through the inverse of the feedback controller, to the reference trajectory. The reference trajectory is assumed to be feasible, i.e., satisfying manipulator dynamics and actuator constraints. The controller is assumed to b e im- proper to avoid differentiating (when inverted) the potentially discontinuous controls. To account for the unknown parameters of the feedback con- troller, we propose a learning procedure, based on a parameter optimization, that minimizes the actual tracking errors at each joint. Essential to this procedure is the selection of the initial guess for the unknown parameters. A simple analysis of the error transfer function allows for the selection of an initial guess that yields smaller errors tha n no preshaping. It is shown that for a PD controller, it is safer to overestimate the unknown gains, whereas underestimating these gains may result in an unstable error transfer function, and hence excessive tracking errors. The differences between this and other learning control- lers are that, here, the open loop system is assumed to be known, and the parameters learned along one trajectory can be used to reduce the tracking errors along other trajectories. The method is demonstrated experimentally for the UCLA Direct Drive Arm (DDA) and the AdeptOne industrial robot. For the UCLA DDA, the mean geometric error (error normal to the path) was reduced to 0.07 mm at top speeds of 1. 8 m/s, which is eight percent of the error achieved with high gains and no preshaping. The mean tracking error was reduced to 0.11 mm, 5 percent of the error with no preshaping. This is comparable to (if not better than) the accuracy reported in (Youcef-Toumi and Kuo, 1993), except that here no effort was made to decouple the manipulator dynamics. The experimental results for the AdeptOne robot demonstrate impressive improve- ments of 95 percent in the tracking errors, with no knowledge of the feedback controller and only partial knowledge of the