In this paper, we provide a generalized framework for the dynamic control of redundant manipulators applied to robot-assisted minimally invasive surgeries (RA-MIS), dealing simultaneously with kinematic constraints, surgical tool trajectory and collisions in the robot’s body. During a RA-MIS, a robot inserts a surgical tool into the patient’s body through an incision point, known as the trocar point. A kinematic constraint is then generated since the tool axis must always pass through the trocar point, i.e. Remote Center of Motion (RCM) constraint, while the tool tip executes the surgical task. When a serial manipulator is used, the RCM constraint must be guaranteed by the control system. Moreover, during the event of desired or unexpected collisions between the robot’s body and its environment, e.g. medical staff or operating room equipment, during the surgical procedure, we propose a joint compliance strategy to preserve the surgical task,by exploiting the robot Jacobian null-space.Simulations were conducted to validate the effectiveness of the proposed formulation, using a Kuka LBR 7 iiwa R800 robot arm.