Collision-free path planning for a robot with two arms cooperating in the 3-D work space

Investigates the collision-free path planning problem for a robot with two arms cooperating in 3-D work space. We have shown that motion constraints placed on the given robot can be equivalently represented as motion constraints placed on the end effector of the robot if two robot arms simultaneously hold the same object. By using this representation the given robot is shrunk to a point with its position being represented by its end effector and the obstacles are represented as forbidden regions in the work space. Thus, the problem of planning the motion for a robot is reduced to that of planning the motion for its end effector. The mapping function which maps the obstacles into their corresponding forbidden regions has been derived. We have proved that the forbidden region of an obstacle can be computed by mapping the boundary of the obstacle with the use of the derived mapping function. A potential field which is governed by a harmonic function in the 3-D work space has been computed and its gradient has been utilized in searching for the collision-free path. Simulation results are reported to verify the proposed method