On the Optimal Resolution of Inverse Kinematics for Redundant Manipulators Using a Topological Analysis
| Autor: | Enrico Ferrentino, Pasquale Chiacchio |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
0209 industrial biotechnology
020901 industrial engineering & automation Inverse kinematics Computer science Mechanical Engineering Resolution (electron density) 0202 electrical engineering electronic engineering information engineering 020201 artificial intelligence & image processing 02 engineering and technology Topology Theoretical kinematics |
| Zdroj: | Journal of Mechanisms and Robotics. 12 |
| ISSN: | 1942-4310 1942-4302 |
| DOI: | 10.1115/1.4045178 |
| Popis: | The redundancy resolution schemes based on the optimization of an integral performance index are investigated from the topological point of view. The topological notions of self-motion manifold, C-path-homotopy and extended aspect are clarified in relation to the limitations of the necessary conditions of optimality provided by calculus of variations. On one hand, they do not guarantee the achievement of the optimal solution, and on the other hand, they translate into a two-point boundary value problem (TPBVP), whose resolution, under certain circumstances, may not lead to a feasible solution at all. In response to the limitations of calculus of variations, a dynamic-programming-inspired formalism is developed, which is based on the discretization of the state space and on its representation in the form of multiple grids. Building upon the topological analysis, effective algorithms are designed that are able to find the optimal solution in any condition, across all C-path homotopy classes and self-motion manifolds, with no limitation due to the passage through singularities. Moreover, if the grids are representative of the manipulator’s extended aspects, the topological notion of the transitional point can be used to reduce the computational complexity of the optimal redundancy resolution algorithm. The results are demonstrated on a canonical 4R planar robot in two different scenarios. |
| Databáze: | OpenAIRE |
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