Mobile manipulators have been employed in many applications that are traditionally performed by either multiple fixed-base robots or a large robotic system. This capability is enabled by the mobility of the mobile base. However, the mobile base also brings redundancy to the system, which makes mobile manipulator motion planning more challenging. In this paper, we tackle the mobile manipulator motion planning problem under the end-effector trajectory continuity constraint in which the end-effector is required to traverse a continuous task-space trajectory (time-parametrized path), such as in mobile printing or spraying applications. Our method decouples the problem into: (1) planning an optimal base trajectory subject to geometric task constraints, end-effector trajectory continuity constraint, collision avoidance, and base velocity constraint; which ensures that (2) a manipulator trajectory is computed subsequently based on the obtained base trajectory. To validate our method, we propose a discrete optimal base trajectory planning algorithm to solve several mobile printing tasks in hardware experiment and simulations.
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