Global Redundancy Resolution via Continuous Pseudoinversion of the Forward Kinematic Map

This paper presents a novel approach to kinematic redundancy resolution for redundant robots, which have more degrees of freedom than workspace dimensions. It introduces the concept of a global redundancy resolution, which has the convenient property that whenever the robot returns to the same workspace point, it uses the same joint-space pose. The problem is cast, as a continuous pseudoinversion of the forward kinematic map. Continuity and smoothness should be attained if possible, but otherwise the volume of the discontinuity boundary should be minimized. A sampling-based approximation technique is presented that constructs roadmaps of both the domain and image, and minimizes discontinuities of the inverse function using a maximum satisfiability problem. Applications of this map include teleoperation, dimensionality reduction in motion planning, and workspace visualization. Results are demonstrated on toy problems with up to 20 DOF and on several robot arms. Note to Practitioners—Determining whether a robot manipulator can cover a range of movement in a Cartesian workspace under joint limits and collision constraints is typically addressed by an engineer’s intuition and trial and error. This paper presents an algorithm to solve this problem systematically. The method optimizes a mapping from workspace to joint space to minimize the number of discontinuities. The resulting maps can be used to select continuous inverse kinematic solutions to follow workspace paths, and their visualizations can aid in workcell design, robot selection, and robot placement.

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