This work presents a new formulation of a modular relative Jacobian used to control combined manipulators as a single manipulator with a single effector. The trajectory generation method was extended to represent the constraints related to tasks involving contact between objects using the concept of virtual mechanism. The simplicity of screw theory was exploited additionally for parametrized generation of generalized second order trajectories for tasks requiring simplified motion, like translation, rotation and screw motion around an arbitrary 6D screw-axis given in a known reference frame. Additionally, it also led to lower oscillations in the joint torque command when implemented for the control of one of the arms of Baxter dual-arm robot.Finally, a complete framework for the coordination of bi-arm robotic systems was proposed with the addition of a cooperative task planner. The coupled resolved rate acceleration controller was found to be capable of tighter trajectory control, specially for error terms related to orientation, compared to the conventional decoupled controller that treated the position and orientation setpoints separately and ignored the inherent effect of rotation on translational motion. The trajectory controller hence designed was capable of tracking pose, velocity and acceleration setpoints for the end-effector using inverse dynamic model of the robot. The coupled Jacobian of the robotic finger was used for inverse kinematic control, while allowing easy integration with a robotic arm.The idea of coupled treatment of position and orientation variables was capitalized further with the design of a second-order trajectory tracker using dual quaternions. Additionally, the coupling of joints in the underactuated fingers of the robotic hand was represented with a coupled finger Jacobian. The coupled controller demonstrated better tracking of pose and orientation in terms of accuracy and stability compared to the decoupled controller for tasks requiring faster operation in the relative task space of dual-arm manipulators.The cooperative task space modelling and control approach using screw-based kinematics and dual quaternions were extended for the cooperation modelling of the fingers of an anthropomorphic robotic hand. simultaneous control of both position and orientation setpoints of relative and absolute task space was compared against the performance of a proportional decoupled controller treating position and orientation error separately. The proposed coupled control of cooperative task space, i.e. The classical approach for dual-arm cooperative task space control was revisited and the symmetric formulation of dual arm coordination using virtual sticks was implemented using screw-based kinematics with dual quaternion representation. Experimental results on the force control performance are compared and analyzed. 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. Two experimental tasks are used: relative end-effector motion and coordinated independent tasks, where a force controller is implemented in both tasks. The experimental setup is a dual-arm system consisting of two KUKA LWR robots. We compare experimental results for two cases: modular relative Jacobian with and without the wrench transformation matrix. In this work, we investigate the dual-arm force control performance, without necessarily driving the end-effectors at higher angular velocities. 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. It includes a wrench transformation matrix, which was not shown in earlier expressions. A modular relative Jacobian is recently derived and is expressed in terms of the individual Jacobians of stand-alone manipulators.
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