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Dynamic manipulations require attaining high velocities at specified configurations, all the while obeying geometric and dynamic constraints. This paper presents a motion planner that constructs a trajectory that passes at an intermediate state through a dynamic objective region, which is comprised of a certain lower dimensional submanifold in the configuration/velocity state space, and then returns to rest. Planning speed and reliability is greatly improved using optimizations based on the fact that ramp-up and ramp-down subproblems are coupled by the choice of intermediate state, and that very few (often less than 1%) intermediate states yield feasible solution trajectories. Simulation experiments demonstrate that our method quickly generates trajectories for a 6-DOF industrial manipulator throwing a small object.
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