A mobile manipulator typically consists of a mobile platform and a robotic manipulator mounted on the platform. The base placement of the platform has a great influence on whether the manipulator can perform a given task. In view of the issue, a new approach to optimize the base placement for a specified task is proposed in this paper. Firstly, the workspace of a redundant manipulator is investigated. The manipulation capability of the redundant manipulator is maximized based on the manipulability index through the joint self-motion of the redundant manipulator. Then the maximum manipulation capability in the specified work point is determined. Next, the relative manipulability index (RMI) is defined for analyzing manipulation capability of the manipulator in its workspace, and the global manipulability map (GMM) is presented based on the above measure. Moreover, the optimal base placement related to the given task is obtained, and the motion planning is implemented by an improved rapidly-exploring random tree (RRT) algorithm with the RMI, which can enhance the manipulation capability from the initial point to the target point. Finally, the feasibility of the proposed algorithm is illustrated with numerical simulations and experiments on the mobile manipulator.

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