Common workspace analysis for a dual-arm robot based on reachability

The analysis of the complete 6-D common workspace SE(3) (the special Euclidean group) including the position workspace R3 and the orientation workspace SO(3) (the special Orthogonal group) is important for the dual-arm robot to complete the coordinated task. In this paper, the reachability of the dual-arm robot consisting of two single redundant robot is employed to represent the capability of the common workspace. In order to analyze the reachability, the finite partition of SE(3) including partition of R3 and equivolumetric partition of SO(3) is utilized to discretize the 6-D workspace. Furthermore, an inverse kinematic method based on the joint parameterization and self-optimizing scheme for the redundant robot is proposed, which can find a closed-form solution within joint limits for an arbitrary TCP in the global workspace and a redundancy parameter don't need to be determined in advance. Finally, the reachability analysis method is not only applied to the single redundant robot, but also employed for dual-arm robot in order to obtain the better common workspace.