During a Robot-Assisted Minimally Invasive Surgery (RA-MIS), a robot inserts a surgical tool into the patient's body through a surgical device placed at the incision position, known as the trocar. A kinematic constraint, known as Remote Center of Motion (RCM) constraint, is then generated since the tool axis must always pass through the trocar position while the tool-tip executes the surgical task. When a serial manipulator is used, the RCM constraint must be guaranteed by the control system. In this paper, we provide a generalized framework for the dynamic control of redundant manipulators used for RA-MIS. Moreover, we consider the event of desired or unexpected collisions between the robot's body and its environment, e.g. medical staff or operating room equipments.

In order to guarantee the accomplishment of the surgical task in the event of collisions, we propose a joint compliance strategy, by exploiting the Jacobian null-space. The proposed control framework deals simultaneously with the surgical tool-tip trajectory, the RCM constraint and collisions in the robot's body.

Simulations were conducted to validate the effectiveness of the proposed formulation, using the dynamic model of a Kuka LBR 7 iiwa R800 robot arm. Results showed that the distance between the tool axis and the trocar position never increases more than 0.5 mm, even in case of collisions.

The results showed the capacity of the proposed framework to simultaneously comply the three tasks: the tool-tip trajectory, the RCM constraint and joint compliance in case of collisions in the robot's body, always respecting the priority order between the tasks.