Collision-free trajectory planning for a 3-DoF robot with a passive joint

This paper studies motion planning from one zero-velocity state to another for a three-joint robot in a horizontal plane with a passive revolute third joint Such a robot is small-time locally controllable on an open subset of its zero-velocity section, allowing it to follow any path in this subset a rbitrarily closely. However; some paths are "preferred" by the dynamics of the manipulator in that they can be followed at higher speeds. In this pape r, the authors describe a computationally efficient trajectory planner that finds fast, collision-free trajectories among obstacles. The planner decou ples the problem of planning feasible trajectories in the robot's six-dimen sional state space into the computationally simpler problems of planning pa ths in the three-dimensional configuration space and time scaling the paths according to the manipulator dynamics. This decoupling is made possible by the existence of velocity directions, fixed in the passive link frame, whi ch can be executed at arbitrary speeds. Results of the planner have been im plemented on an experimental underactuated manipulator To the authors' know ledge, it is the first implementation of a collision-free motion-planning a lgorithm for a manipulator subject to a second-order nonholonomic constrain t.