Trajectory Planning for Coordinated Motion of a Robot and a Positioning Table: Part 2—Optimal Trajectory Specification

Document Type

Letter to the Editor

Date of Original Version



A robot and a positioning table system is a kinematically redundant system with respect to planar motion. Two strategies were developed in Part I of this paper to resolve this redundancy and to specify path shapes that make the best utilization of the workspace and speed characteristics of the two devices. In this paper, a one-variable dynamic programming approach is developed to obtain the near minimum time and/or energy trajectory of the two devices. The developed strategies were studied using this path-planning algorithm on a model of 3 degree-of-freedom robot and a two-axes linear positioning table for a variety of path shapes and constraints. In addition, experiments were performed in a typical workcell to show the feasibility of the developed strategies. In moving the two devices in opposite directions, the least travel time is obtained when the original path is resolved more in favor of the faster device, whereas the quality of resultant motion is dependent on the controller performance of each device. In addition, this strategy makes better utilization of robotic devices with variable torque-speed characteristics. For the sharp-cornered path strategy, both devices’ capabilities affect the tracking time and the proposed strategy give a least-travel-time scenario similar to that of using the faster device. However, the strategy is effective in tracking a sharp corner while keeping the speed of one manipulator (the robot) constant. © 1990 IEEE

Publication Title

IEEE Transactions on Robotics and Automation