The vast majority of work to date concerned with obstacle avoidance for manipulators has dealt with task descriptions in the form ofpick-and-place movements. The added flexibility in motion control for manipulators possessing redundant degrees offreedom permits the consideration of obstacle avoidance in the context of a specified end-effector trajectory as the task description. Such a task definition is a more accurate model for such tasks as spray painting or arc welding. The approach presented here is to determine the required joint angle rates for the manipulator under the constraints of multiple goals, the primary goal described by the specified end-effector trajectory and secondary goals describing the obstacle avoidance criteria. The decomposition of the solution into a particular and a homogeneous component effectively illustrates the priority of the multiple goals that is exact end-effector control with redundant degrees of freedom maximizing the distance to obstacles. An efficient numerical implementation of the technique permits sufficiently fast cycle times to deal with dynamic environments.

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In this paper, we have proposed a number of measures for the quantification of dexterity of manipulators. The use of such measures is especially important for kinematically redundant manipulators since they can satisfy secondary cri teria in addition to satisfying a specification of end-effector motion. We will compare several measures for the problems offinding an optimal configuration for a given end-effector position, finding an optimal workpoint, and designing the op timal link lengths of an arm.

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