40.13 APPENDIX E - NEW AND ADVANCED TOPICS

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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 control theory, and it considers four cases,

1. Moving Arms, Stationary Robots, Stationary Obstacles, and Constant Obstacle Size.

2. Stationary Arms, Mobile Robots, Moving Obstacles, and Constant Obstacle Size.

3. Moving Arms, Mobile Robots, Moving Obstacles, and Variable Obstacle Size.

4. Moving Arms, Mobile Robots, Moving Obstacles, and Constant Obstacle Size.

the calculations of the trajectories in this technique are done on the order of milliseconds, and this shows great potential as the low end of a Dynamic Planner, which is completly autonomous. This method considers the Dynamics of manipulators as well, and attempts to generate a minimum time trajectory, which is collision free.

40.13.3 NEW TOPICS - SLACK VARIABLES

The use of slack variables has been suggested vaguely in a paper by S.C.Zaharakis and A.Guez [1988]. This uses a 2D environment filled with boxes, in which an A* algorithm is used to find paths. This method finds paths considering bang-bang (full on or full off) control theory, and the manipulator dynamics, to find minimum time paths. The implementation was done on a MAC II, and found results in under a minute.