Trajectory generation for two robots cooperating to perform a task

This paper formulates an algorithm for trajectory generation for two robots cooperating to perform an assembly task. Treating the two robots as a single redundant system, this paper derives two Jacobian matrices which relate the joint rates of the entire system to the relative motion of the grippers with respect to one another. The main advantage of this method over previous methods is that operations may be described in the coordinates of the assembly rather than in world coordinates. To join parts using this algorithm, the desired relative position is specified and the algorithm automatically determines where the robots perform the assembly. In the process of generating the trajectory, the dexterity of the highly redundant dual-robot system is taken advantage of to satisfy a variety of secondary constraints. Secondary constraints may include obstacle and joint limit avoidance and constraints to satisfy certain absolute position and orientation goals. The algorithm typically involves two phases. First the parts to be assembled are brought from an arbitrary initial configuration to an approach configuration. This phase uses a newly derived relative distance Jacobian formulation which inherently avoids collisions. Then, a more traditional Jacobian formulation is used to join the parts