Modular Relative Jacobian for Dual-Arms and the Wrench Transformation Matrix

Abstract—A modular relative Jacobian is recently derived and is expressed in terms of the individual Jacobians of stand-alone manipulators. It includes a wrench transformation matrix, which was not shown in earlier expressions. This paper is an experimental extension of that recent work, which showed that at higher angular end-effector velocities the contribution of the wrench transformation matrix cannot be ignored. In this work, we investigate the dual-arm force control perfor-mance, without necessarily driving the end-effectors at higher angular velocities. We compare experimental results for two cases: modular relative Jacobian with and without the wrench transformation matrix. The experimental setup is a dual-arm system consisting of two KUKA LWR robots. Two experimental tasks are used: relative end-effector motion and coordinated independent tasks, where a force controller is implemented in both tasks. Furthermore, we show in an experimental design that the use of a relative Jacobian affords less accurate task specifications for a highly complicated task requirement for both end-effectors of the dual-arm. Experimental results on the force control performance are compared and analyzed. Index Terms—Dual-arms, relative Jacobian, modular, wrench transformation matrix, force control, single manipu-lator control I