Bilateral Teleoperation of Flexible Surgical Robots Mohsen Mahvash and Pierre Dupont Abstract—We introduce a position-exchange controller for bilateral teleoperation of flexible surgical robots. The controller requires the position of the master arm and the deformed shape of the slave arm, but no force information is required. The position-tracking controller of the master arm causes the master arm to follow the position of the tip of the slave arm. The position tracking controller of the slave arm causes the slave to follow the position of the master and also deforms the shape of the slave arm until the force generated at its tip matches the force applied to the master. The position exchange controller is illustrated using two systems. The first is a simple one degree of freedom flexible robot. The second system is a surgical robot constructed from a set of precurved superelastic concentric tubes. The control structure enables fast computation of the deformed shape kinematics of the slave arm using Cosserat rod theory. Simulation results show that the controller provides transparency at the low frequencies necessary for palpation of soft tissue. I. I NTRODUCTION Robots for minimally invasive surgery have a small cross section and thus often flex during interaction with the surgical environment. This is true of snake-like surgical robots built from superelastic beams [1], [2], [3] as well as the slave manipulator of the da Vinci surgical system (Intuitive Surgical Inc.) [4], [5]. Link flexibility of the slave manipulator modifies its kinematic map and consequently reduces the transparency of the system in transmitting the environment stiffness to the user. A position-tracking controller is often used for teleop- eration of a surgical robot [6]. The position controller commands the surgical robot to follow the position of a master manipulator. Bilateral or force-feedback teleoperation is established by adding a position tracking controller to the master manipulator. The master position tracking controller applies force to the master when the slave is displaced from its goal position. The position-exchange controller does not require a force sensor to generate force feedback. However, it provides transparency at low frequencies for interaction with soft environments if the master and slave manipulators are rigid and the resistance dynamic of the robots are cancelled [6], [7]. For a flexible slave robot, a position-exchange controller transmits the series combination of the stiffness of the envi- ronment and the stiffness of the links of the robot. When the robot stiffness is less than the stiffness of the environment, the stiffness of the environment is not transmitted to the This work was supported by the National Institutes of Health under Grant R01 HL087797. M. Mahvash and P. Dupont are with the Department of Aerospace and Mechanical Engineering, Boston University, Boston, 02215, USA,email pierre/mahvash@bu.edu user. This makes force feedback based on position exchange ineffective for palpation tasks [8] since the flexibility of slave does not allow the user to detect a hard spot on the surface of a soft object (for example, due to a tumor below the surface of a tissue). We introduce a new position-exchange control strategy for bilateral teleoperation of a flexible surgical robot. The posi- tion controller of the master manipulator uses the difference between the tip positions of the master manipulator and the flexible slave robot to calculate the force that is applied to the master manipulator. The position controller of the slave manipulator deforms the slave manipulator to a desired shape that generates the master manipulator force at the tip of the slave manipulator. In steady state, when the manipulators do not move, the forces generated by master master manipulator and the slave manipulator match. The position error between the tip of the slave manipulator and the master manipulator is small and depends on the gain of the position tracking controllers. Thus, the controller provides transparency at low frequency. Implementation of the slave position controller depends on the efficient solution of the inverse kinematics problem for the deformed manipulator. The solution presented here achieves efficiency by decomposing this problem into two steps. In the first step, a deformation model is used to compute the unloaded slave configuration that produces the desired tip force when in contact with the environment. De- pending on the initial shape and the amount of deformation, the Cosserat rod model or the Euler-Bernoulli beam model can be used for this step. In the second step, the desired joint angles of the slave robot are computed from a kinematic model that assumes no forces are applied to the slave. The first step of the slave position controller requires the shape of the slave manipulator. There are several different approaches available for measuring its shape. These include fiber optic shape sensors mounted inside or on the exterior of the arm [9], extracting the shape from real-time images of the slave robot and the use of electromagnetic trackers mounted at intervals along the manipulator to estimate its shape. The remainder of the paper is organized as follows. To introduce the concepts, Section II explains the control law for bilateral teleoperation of a one degree of freedom flexible robot. Section III presents simulation results for this flexible robot illustrating the enhanced transparency and consequent improvement in transmitting environment stiffness for palpa- tion. Section IV presents the controller for a concentric tube robot using a Cosserat rod model of deformation. Section V concludes the paper. 58 Proceedings of the New Vistas and Challenges in Telerobotics Workshop, IEEE 2008 International Conference on Robotics & Automation, Pasadena, CA, 19-23 May, 2008.