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Figure 7.1b A Comparative Chart of Path Planning Methods

40.8 CONCLUSIONS

This is the most interesting section, but unfortunately, very vague. In the next few years Powerful computer hardware advances will allow low cost, but extremely powerful operations. This will make many memory intensive path planning methods feasible, the very complex operations will now be reasonable for calculation. If computers become powerful enough, then an expert path planning system would be a definite asset, making the robots flexible over a number of different frontiers, without any programming. The advance of customized computer hardware which now does graphics indicates that it is very feasible to convert complex robotic path planning from a software to a hardware domain. The potential of parallel processing also opens doors to solving very complex and involved problems.

A good direction for robotics research is to allow a path planning system which will combine the various problems and solutions. This will allow the robot to switch modes with an expert system and thus chose the solution to fit the problem, and not try to make the problem fit the solution, as is commonly done now. This would involve the use of rules and heuristics (based on the elements discussed in this paper) to build up a very complex and complete path planner from very simple methods (which are currently being researched). The multi-level path planning strategies are seen to also hold promise for robotic development (the author prefers the Dynamics Path Planning approach). These approaches allow the best of all planning methods.

40.9 APPENDIX A - OPTIMIZATION TECHNIQUES

Optimization involves modelling a system as a function of some variables, then deriving some cost, or measurement of performance from it. The variables are then adjusted to get the best measure of performance out. These methods give the best results, but they can be tricky to set up,

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and they can be very slow.

40.9.1 OPTIMIZATION : VELOCITY

By optimizing the manipulator velocity the path time can be reduced, and the robot used to its full ability. One approach was made by S.Dubowsky, M.A. Norris and Z.Shiller [1986]. The thrust of their research was production of a Path Planning CAD System called OPTARM II. Their program will produce a path which is made up of smooth splines. The optimization is done to keep either the maximum or minimum torque on the robot actuators. Their success was in producing path within 5% of optimal value based on collision avoidance and motion limits on the joints. For a six degree of freedom manipulator the program produces smooth motion on the microVAX in a few minutes of CPU time, which will give optimal paths up to twice as fast as the constant velocity method for path motion.

A different approach to the velocity optimization problem was taken by B.Faverjon and P.Tournassoud [1987]. A fast method was found for finding distances of separation between objects in space. The world was modelled as geometrical primitives, and the primitives could be used to represent the world to various depths of complexity.

Figure A.1 Various Levels of Geometrical Representation

Using the distance of separation in a function for a velocity damper, the collisions were incorporated as a constraint. When the cost function was optimized for velocity the tendency was to avoid obstacles where velocity was damped. This method was also made to work with moving objects.

This method was intended for use with a 10 link nuclear manipulator, and it has been implemented on a SUN 3 computer. The actual run time was not given, but the routine ran at a tenth of the speed possible with the manipulator. The manipulator was said to have approached objects to within 1 cm.

40.9.2 OPTIMIZATION : GEOMETRICAL

A different approach based on the calculus of variations has been developed by R.O.Buchal and D.B.Cherchas [1989]. The techniques use convex polygons to represent objects, and an iterative technique to find the best path which avoids these polygons. The path is subdivided into