Optimum path planning for robot manipulators amid static and dynamic obstacles

Optimum path planning algorithms for robot manipulators are presented. It is assumed that a manipulator is working in an environment that contains a static obstacle or another manipulator. A collision avoidance strategy is developed based on a simplified representation of the robot arm. The two different path planning problems addressed are the minimum-time path planning and the minimum-energy path planning. These problems are solved using a variational approach called the method of local variations (MLV). This method finds a solution to the optimal control problem iteratively under constraints on state and control variables. To solve these problems, a collision-free path is first chosen. Then the MLV is applied based on a discrete-time state-space model of the manipulator. The collision checking strategy is incorporated in the variational structure to obtain the optimal paths. The proposed algorithms are tested through digital computer simulations