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On the structure of minimum effort solutions with application to kinematic redundancy resolution (2000)
| Content Provider | CiteSeerX |
|---|---|
| Author | Gravagne, Ian A. Walker, Ian D. |
| Abstract | Abstract—There exist in robotics, as in many other disciplines, problems described by an underdetermined set of constraints, possessing an infinite number of solutions. The problem of robot manipulator redundancy reso-lution is just such a situation, requiring that a particular solution be chosen according to some type of optimization criterion. One possibility employs a type of optimization which minimizes the maximum magnitude of the so-lution vector. This is the minimum infinity norm solution, also known as the “minimum effort solution. ” This paper explores the details of least in-finity norm optimization, using kinematic redundancy resolution as a test case to explore the details of infinity-norm optimization. We introduce for the first time a closed-form expression for minimum effort solutions, illus-trating the heretofore unknown properties of nonuniqueness and disconti-nuity in time-varying situations, and postulating a possible remedy for the discontinuity problem. Additionally, to reinforce the mathematics, simula-tions of four-link robots are included, as well as an extended discussion of minimum-effort solutions from a geometric point of view. Index Terms—Infinity-norm, kinematics, manipulators, minimum effort, redundancy, underdetermined. |
| File Format | |
| Journal | IEEE Trans. Robot. Automat |
| Language | English |
| Publisher Date | 2000-01-01 |
| Access Restriction | Open |
| Subject Keyword | Minimum Effort Solution Redundancy Resolution Minimum Effort Time-varying Situation Infinity-norm Optimization Minimum Infinity Norm Solution Heretofore Unknown Property Optimization Criterion Infinite Number Underdetermined Set Particular Solution Four-link Robot Index Term Infinity-norm Geometric Point Closed-form Expression Maximum Magnitude Test Case Possible Remedy Many Discipline So-lution Vector Discontinuity Problem Minimum-effort Solution First Time In-finity Norm Optimization Robot Manipulator Redundancy Reso-lution Kinematic Redundancy Resolution Extended Discussion |
| Content Type | Text |
| Resource Type | Article |
