Trajectory generation for cooperating robots

A formulation for online trajectory generation for two robots cooperating to perform an assembly task is derived. The two robots are treated as a single redundant system. A Jacobian is formulated that relates the joint rates of the entire system to the relative motion of one of the hands with respect to the other. The minimum norm solution of this relative Jacobian equation results in a set of joint rates which perform the cooperative task. In addition to the cooperative task, secondary goals, which include obstacle and joint limit avoidance, are specified using velocities in the null space of the relative Jacobian. This formulation also allows the robots to be controlled in parallel on independent tasks