On the Optimal Resolution of Inverse Kinematics for Redundant Manipulators Using a Topological Analysis
- 10 January 2020
- journal article
- research article
- Published by ASME International in Journal of Mechanisms and Robotics
- Vol. 12 (3), 1-49
- https://doi.org/10.1115/1.4045178
Abstract
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, on the other, 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 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.Keywords
Funding Information
- Italian Ministry of University (CUP D49D17000250006)
This publication has 21 references indexed in Scilit:
- A general framework for task-constrained motion planning with moving obstaclesRobotica, 2018
- Simultaneous path placement and trajectory planning optimization for a redundant coordinated robotic workcellMechanism and Machine Theory, 2018
- On Higher Order Inverse Kinematics Methods in Time-Optimal Trajectory Planning for Kinematically Redundant ManipulatorsIEEE Transactions on Industrial Informatics, 2018
- Optimization of the robot and positioner motion in a redundant fiber placement workcellMechanism and Machine Theory, 2017
- Springer Handbook of RoboticsPublished by Springer Science and Business Media LLC ,2016
- Pareto Optimality and Multiobjective Trajectory Planning for a 7-DOF Redundant ManipulatorIEEE Transactions on Robotics, 2010
- Manipulator motion planning for high-speed robotic laser cuttingInternational Journal of Production Research, 2009
- Globally Optimal Trajectory Planning for Redundant Manipulators using State Space Augmentation MethodJournal of Intelligent & Robotic Systems, 1997
- Global versus Local Optimization in Redundancy Resolution of Robotic ManipulatorsThe International Journal of Robotics Research, 1988
- Optimal Redundancy Control of Robot ManipulatorsThe International Journal of Robotics Research, 1987