Task-space control of robot manipulators with null-space compliance

In this paper, the problem of controlling a robot manipulator in task space, while guaranteeing a compliant behavior for the redundant degrees of freedom, is considered. This issue may arise in the case where the robot experiences an interaction on its body, especially in the presence of humans. The proposed approach guarantees correct task execution and compliance of the robot's body during intentional or accidental interaction in the null space of the main task, simultaneously. The asymptotic stability of the task-space error is ensured by using suitable observers to estimate and compensate the generalized forces acting on the task variables, without using joint torque measurements. Two different controller-observer algorithms are designed, and they are based on the task-space error and on the generalized momentum of the robot, respectively. The performance of the proposed algorithms is verified in experiments on a 7R lightweight robot arm.