MATHEMATICAL ANALYSIS OF KINEMATIC REDUNDANCY AND CONSTRAINTS ON ROBOTIC MOBILE MANIPULATORS

Abstract

A mobile manipulator composed of a robotic manipulator mounted on a mobile platform as shown in figure 1. Such a combined system is able to perform manipulation tasks in a much larger workspace than a fixed based manipulator. However, to fully utilize the advantages offered by a mobile manipulator, it is necessary to understand how to properly and effectively coordinate the motions of a mobile platform and the manipulator. The new issues introduced by combined system that are not present in the individual component. 1 The mobile base subsystem is subject to nonholonomic constraints due to rolling contact between the platform wheels and the ground, whereas the constraints are holonomic for the manipulator. 2 The combining a mobile platform and a multi-link manipulator creates redundancy. Figure 1. Schematic diagram of a mobile manipulator. In this paper, kinematic model of a non holonomic mobile robot is formulated. Kinematic model of the overall system is derived by combining the motion of the mobile base by a planar two links arm. The motion constraints and kinematic redundancy are considered and analyzed in both conditions. These concepts are expanded to general cases by using special subjects on linear algebra and functional analysis. Finally, for a predefined variables a useful and unique kinematical model of redundancy resolution is introduced