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general topilogical paths are found from valleys of potential minimums. The best of these paths is selected, and three FindPath algorithms are used to refine it, until it is acceptable. The first algorithm moves along the path and reduces potential numerically. Second, a tight fit algorithm is used for small pathways. Lastly, an algorithm which will move off the given path if necessary is used, as a last resort. This method has been implemented to run on a SUN 260 for a ’Piano Movers Problem’. The total runtime is in the tens of minutes, and it does fail in certain cases.

To avoid becoming trapped when using this method, another approach was developed to mapping the potential field by P.Khosla and R.Volpe [1988]. They have developed an alternate approach which avoids the local minima found in traditional potential field methods. To do this they have used superquadratic approximation of the potential fields to drop off from obstacles swiftly. The superquadratic is used to have a gradual slope to the goal, thus to make sure that its effect is more wide spread than the obstacles. The results which they have obtained are not described, but they have written a program which will work with a two link manipulator, ignoring link collisions.

40.13 APPENDIX E - NEW AND ADVANCED TOPICS

There are some methods of path planning which cannot be easily classified into the four preceeding divisions. These are listed here, and they are devided into advanced topics, which are ahead of their time, and new topics which are still awaiting implementation.

40.13.1 ADVANCED TOPICS : DUAL MANIPULATOR COOPERATION

Dual manipulator cooperation is an interesting concept that allows maximum use of the manipulators. When a payload is encountered that is too heavy, or bulky, for a single manipulator, a second manipulator may be used in unison with the first. I.H.Suh and K.G.Shin [1989] have developed some of the theoretical requirements for two manipulators to carry a single large object. This is done through assigning one manipulator as the leader, and the second as the follower. To overcome the problem caused by the limited degrees of freedom, their method allows one manipulator to ’slide’ with respect to the other during the carrying process. If two 6 degree of freedom manipulators were to try and carry a piece together they would find limits. By allowing one manipulator to slide, it is equivalent to adding 1 degree of freedom to the system.

A paper on optimal arm configurations is given by S.Lee [1989]. A method is discussed for identifying optimal dual arm control based on manipulability ellipsoids. This is a lengthy paper outlining all of the details of the method.

40.13.2 ADVANCED TOPICS : A POSTIERI PATH PLANNER

A Sensor Based path planning strategy was devised by (E.Fruend and H.Hoyer [1988]) which allows real time trajectory planning and collision avoidance. This strategy is achieved in a hierarchical system, which is also presented in this paper. This strategy is based on non-linear