Constrained Cartesian motion control for teleoperated surgical robots

This paper addresses the problem of optimal motion control for teleoperated surgical robots, which must maneuver in constrained workspaces, often through a narrow entry portal into the patient's body. The control problem is determining how best to use the available degrees of freedom of a surgical robot to accomplish a particular task, while respecting geometric constraints on the work volume, robot mechanism, and the specific task requirements. We present a method of formulating desired motions as sets of task goals in any number of coordinate frames (task frames) relevant to the task, optionally subject to additional linear constraints in each of the task frames. Mathematically, the kinematic control problem is posed as a constrained quadratic optimization problem and is shown to be computable in real time on a PC. We will present experimental results of the application of this control methodology to both kinematically deficient and kinematically redundant robots. Specifically, we will discuss the control issues within the context of a representative set of tasks in robot-assisted laparoscopy, which includes (but is not limited to) teleoperated navigation of a laparoscopic camera attached to a surgical robot. A system based on this control formalism has been used in preclinical in vivo studies at the Johns Hopkins University Medical Center and the early experience with the system will be summarized.