Using min-max of torque to resolve redundancy for a mobile manipulator
We have considered the problem of determining the time trajectories of the joint variables of a mobile manipulator with many redundant degrees of freedom that will minimize the maximum value of the torque during a large scale motion by the manipulator. To create a well defined problem, we will divide the problem into two components: path planner and surveyor. The path planner will choose a path (between two points in Cartesian space) that will minimize the maximum value of the torque along the path. The input to the path planner is a network of path segments with the maximum value of the torque on each segment. The surveyor will find the points in joint space that are local minimums for the maximum value of the torque at each Cartesian position and define the network of path segments. In this paper, our focus will be on the surveyor and not on the path planner. Our min-max problem has an extra constraint on the joint variables. We seek a min-max at each Cartesian position rather than a global min-max. We have used the Kuhn-Tucker conditions to derive necessary conditions for the solution of our min-max problem. We find that the necessary conditions require that at one or more of the joints the magnitude of the normalized torques will be equal to the min-max value. We have explored the torque surfaces for two mobile manipulators: a planar manipulator and the CESARm. The CESARm is a manipulator with three joint angles controlling the height of the arm. The paths with three equal torques have low values for the torque but they only cover part of the workspace and do not join together. Paths with two equal torques cover the workspace and bridge between the disjoint path segments. We have evaluated the necessary conditions for both the paths with three equal torques and the paths with two equal torques. In most cases, the paths satisfy the necessary conditions.
- Research Organization:
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
- Sponsoring Organization:
- USDOE, Washington, DC (United States)
- DOE Contract Number:
- AC05-84OR21400
- OSTI ID:
- 10110752
- Report Number(s):
- ORNL/TM-12489; ON: DE94004669
- Resource Relation:
- Other Information: PBD: Nov 1993
- Country of Publication:
- United States
- Language:
- English
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