Optimal placement and grasping of two robot arms holding a common object based on workspace usage

Where two robot arms hold a common object and their usable space is limited such as inside an automatic instrument it is important to determine its maximum extreme distance or reachable workspace. Obviously, the grasping orientations and placement of the two arms are crucial to maximising the distance and workspace. To date, these factors have been ignored. This problem is much more difficult than that for a single arm and many methods for a single arm are no longer applicable, due to many extra constraints, variables and joint configurations. Here, a new approach to this problem is proposed. The problem is formulated as a multivariable nonlinear constrained optimisation problem and it is solved using sequential quadratic programming (SQP). With this method, the optimal grasping with optimal placement of the two arms, the extreme joint configurations and the maximum extreme distance can be obtained The computational results show that the distance takes its maximum where a small number of joint configurations are at their singularities, which is quite different from the situations of a single arm and from intuition. This method is illustrated using an example, where a rod is held by the two-finger grippers of two SCARA-type robot arms. Objects of different shapes, such as a plate, can be treated as special cases of the rod