Resolution of Kinematic Redundancy using Optimization Techniques

Recent work has shown that while one can resolve kinematic redundancy by the strategy of using the additional degrees of freedom to instantaneously minimize a cost criterion, one cannot do this in a singularity-free way. This motivates the research reported below regarding path planning based on optimization of integral cost criteria. For a wide variety of such criteria, optimal paths are shown to satisfy a system of differential equations. The analysis exploits ideas from the classical calculus of variations, and it is therefore not surprising that multiplicities of extremal solutions exist. Numerical examples are given where extremal solutions fall into distinct homotopy classes, not all of which are optimal.