OPTIMAL TRAJECTORY PLANNING OF MANIPULATORS WITH COLLISION DETECTION AND AVOIDANCE

This article presents an optimal trajectory-planning method for robot manipulators with collision detection and avoidance. The obstacles and robot segments are represented by a set of convex polyhedra. The collision detection is performed at each discretized robot configuration by an efficient procedure developed with the computational geometry method, which computes a distance function of the robot segments and the obstacles. By introducing this function for specifying the collision-free constraint, the path-planning problem is formulated as an optimal control problem using rhe augmented Lagrangian, which may be considered as a combination of the duality, penalty and constraint relaxation methods. The problem is solved by a robust UZAWA-like algorithm, where a subgradient method is applied for the primal optimization, as the distance function is not everywhere differentiable. An example is given for the trajectory planning of a robot arm with three revolute joints.