Admissible path planning for two cooperating robot arms

In this paper, a method of admissible path planning for two robot arms handling a common object is presented. Since the two arms grasp a single object rigidly, a closed-chain mechanism is formed by the arms, the object and the ground. The positions and orientations of the two cooperating arms must satisfy a set of holonomic equality constraints at each point of the path. The problem of path finding is more difficult when robots have less than six degrees of freedom. Then, the trajectories over which the object is moved from its initial to a final location are strongly restricted. The path planning problem is formulated as a functional minimization problem with equality and inequality constraints in terms of the joint variables. The essence of the method is to find joint paths, which satisfy the given constraints and minimize the proposed performance index. The infinite-dimensional optimization problem is approximated by the function minimization problem in the finite-dimensional space employing the Ritz method. A numerical example involving a system consisting of two ASEA IRb-6 robot arms handling a long beam is considered