A new kinematic formulation of the RCM constraint for redundant torque-controlled robots

In this paper, we provide a new generalized kinematic formulation of the Remote Center of Motion (RCM) constraint for serial robotic arms to be useful for implementation in torque-controlled robots. A minimally invasive surgery assisted by a serial robot could be used for inserting a surgical tool through a desired insertion position, i.e. trocar position. The restricted movement caused by the trocar, i.e. the RCM constraint, must be guaranteed by the robotic system in order to avoid injury to the patient. The generalized formulation, presented in this paper, associates the task-space with the RCM constraint coordinates, which are described by the minimum distance between the surgical tool and the trocar position. In order to simultaneously achieve the surgical tool-tip trajectory and the RCM constraint, two control methods are proposed and compared, one using a projection in the null-space, the other by combining both tasks using a task-space augmentation method. Moreover, when additional lower priority tasks have to be implemented in the null-space of the two higher priority tasks, the kinematic formulation simplifies the calculation of the null-space projectors. Furthermore, unlike the previous studies, the formulation represented can be applied not only in a kinematic control but also in a dynamic control approach. Simulations were conducted to validate effectiveness of the proposed formulation, using a planar 4-DOF system as well as the dynamic model of a Kuka LBR 7 iiwa R800 robot arm.