A hypertext software package to help document system designs

VII. CONCLUSION In this paper, optimal path planning for robot manipulator is presented that utilizes a variational technique. A simplified robot arm is considered to facilitate geometric collision checking scheme. This is incorporated in the variational technique to develop a collision avoidance strategy. The collision checking scheme is rather stringent. However, it reduces the computational requirements. Different path planning problems are considered in an unified treatment. The method adopted is very flexible and can handle various criterion functions. It can also take into account different kinds of obstacles. The efficacy of the method is demonstrated through numerical examples and digital simulation of a PUMA 560 type of robot arm. The obstacles considered in the numerical examples are simplistic in nature. This however, is not a restriction as the method can be extended to consider multiple static or dynamic obstacles at an increased cost of computation. Finally, a couple of words about the scope of this paper. Firstly, the path planning procedures proposed here are very effective in repetitive pick-and-place operations rather than in assembly operations. In a much cluttered workspace, the objective is to choose a path that avoids all the obstacles and to travel cautiously through it. Optimum paths are fairly meaningless in such situations. Secondly, the global convergence property of the MLV have not been proved. It is possible that such variational technique may lead to a local optimum. However, this should not cause any difficulty to the MTPP problem. In the MEPP problem the final trajectory may depend on the nominal trajectory chosen. One way of choosing the nominal trajectory is using the joint interpolation technique. One can also use the trial and error method. In either case, the trajectory chosen will not be very far away from the optimal path and the MLV can be effectively applied. In cases where there are many posisible choices of the nominal trajectory, it is advisable to compute the optimal path for each and compare them. Near minimum time control of open loop articulated kinematic chains, " Trans. ASME Minimum time along the path for a mechanical arm, " in Proc. Optimum path planning for mechanical manipulators, " Trans. ASME Time optimal control of robotic manipulators along specified paths, " Int. Optimal robot path planning using the minimum-time criterion, " IEEE Minimum time control of robotic manipulator with geometric path constraints, " IEEE Trans.