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

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.