No‐overshoot control of robotic manipulators in the presence of obstacles

Abstract

Abstract The long standing problem of guiding robotic manipulators in cluttered workspaces is treated here by a unified approach, taking into account both motion planning and control aspects. Planning the collision‐free operation is based on the notion of roadmaps. To reduce the complexity of the roadmaps, the real problem is approximated by a simplified but still realistic graph structure. Motion planning relies on the robot closely following the defined collison‐free path, so the errors in robot control must be contained within bounded regions. Satisfying this assumption ideally requires no‐overshoot control. Overshooting demands special attention in tasks that require high speed operations of robots in the presence of obstacles. To stabilize at the specified collision‐free trajectory, before going actually beyond it, joint control schemes demand slow movements through a number of intermediate subgoals. This significantly delays the completion of the task. By using ideas from variable structure control (VSC), a control policy is suggested here that switches between PD + and CEA + (constant error acceleration) schemes, where the CEA + scheme applies a “constant error acceleration” of the largest possible magnitude in the appropriate direction. The performance of the path planning and the control algorithms is presented through simulations of a four‐link SCARA robot in various cluttered workspaces. © 1994 John Wiley & Sons, Inc.