In this paper, we focus on the development of a quantitative performance analysis framework for a cooperative system of multiple wheeled mobile manipulators physically transporting a common payload. Each mobile manipulator module consists of a differentially driven wheeled mobile robot (WMR) with a mounted planar three-degree-of-freedom (DOF) revolute-jointed manipulator. A composite cooperative system is formed when a payload is placed at the end-effectors of many such modules. The system possesses the ability to change its relative configuration as well as to accommodate relative positioning errors of the wheeled agents. However, the combination of nonholonomic constraints due to the mobile bases, holonomic constraints due to the closed kinematic loops, and the different joint-actuation schema (active/passive/locked) within the system requires careful quantitative evaluation to efficiently realize the payload manipulation task. Hence, in this paper, we extend the differential kinematic model for treatment of constrained articulated mechanical systems to formulate a framework to include both the mixture effect of holonomic/nonholonomic constraints and the different possible joint-actuation schema in our system. The system-level performance is then examined quantitatively by the manipulability measure in terms of isotropy index with representative case studies.
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