Using minimax approaches to plan optimal task commutation configurations for combined mobile platform-manipulator systems

Abstract

An important characteristic of mobile manipulators is their particular kinematic redundancy created by the addition of the degrees of freedom of the platform and those of the manipulator. This kinematic redundancy is very desirable since it allows mobile manipulators to operate under many modes of motion and to perform a wide variety of tasks. On the other hand, it also significantly complicates the problem of planning a series of sequential tasks, in particular for the critical times at which the system needs to "switch" from one task to the other (task commutation), with changes in mode of motion, task requirement, and task constraints. This paper focuses on the problem of planning the positions and configurations in which the system needs to be at task commutation in order to assure that it can properly initiate the next task to be performed. The concept of and need for "commutation configurations" in sequences of mobile manipulator tasks is introduced, and an optimization approach is proposed for their calculation during the task sequence planning phase. A variety of optimization criteria were previously investigated to optimize the task commutation configurations of the system when task requirements involve obstacle avoidance, reach, maneuverability, and optimization of strength. In this paper, we show that a "minimax" approach is particularly adapted for most of these requirements. We develop the corresponding criteria and discuss solution algorithms to solve the "minimax" optimization problems. An implementation of the algorithms for our HERMIES-I11 mobile manipulator is then described and sample results are presented and discussed.

Min-max redundancy resolution for a mobile manipulator

“…The redundancy allows the system to both move in Cartesian space and accomplish other objectives: avoid obstacles, avoid joint limits, avoid singularities, and minimize joint torques. In three recent papers [Pin (1990), Pin (1992), and Pin (1994)], we have reported on some numerical calculations to resolve the redundancy for mobile manipulators by minimizing the maximum value of an objective function. While most methods for redundancy resolution are based on the mean square norm, we prefer the min-max norm.…”

“…If we want to avoid obstacles, we focus on the minimum distance to an obstacle and not the average distance to an obstacle. In this paper, we define a nonlinear programming problem for the min-max problem in Pin (1994) and apply the Kuhn-Tucker conditions to derive a set of necessary conditions for the variables.…”

“…The one paper in set S9 is our paper [Pin (1994)l. Of the 26 papers in set S8, the paper by Klein) (1983) is the only one that is using the phrase min-max in the same way that we are.…”

Survey of Research for Performance Measurement of Mobile Manipulators

“…In 1994, Pin et al [45] focused on minimax planning the positions and configurations in which the system needed to be at task commutation in order to assure that it could properly initiate the next task to be performed. An implementation of the algorithms was performed using the HERMIES-III mobile manipulator.…”

Integrated Task Planning and Control for Mobile Manipulators

“…The configuration between two tasks is called commutation configuration (Pin, Culioli, and Reister 1994). In the path planning for a sequence of tasks, the motion trajectories together with commutation configuration need to be considered simultaneously.…”