Version 1.0, August 31, 2001, Copyright, Hugh Jack 1993-2001
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.