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.

This paper describes the control and ergonomic evaluation of a ceiling mounted (or support frame suspended) 7-axis surgical robot (HISAR) for laparoscopic camera navigation. A key feature of the robot is that it incorporates a passive wrist for natural compliance with the port of entry into the patient. The use of a previously reported constrained Cartesian controller is motivated and demonstrated, and the results of successfully applying this control methodology to the manipulator are presented. The significance of the control strategy is the ease with which control of passive axes, the fulcrum constraint, and the motion inversion effect created by the fulcrum are accommodated. We also report on the results of laboratory evaluations of the arm in terms of its work volume, ergonomic factors, ease of control, and overall design within the context of laparoscopic camera control.

A computational analysis and a comparison of line-oriented representations of general (i.e. rotational and translational) spatial displacements of rigid bodies are presented. Four mathematical formalisms for effecting a general spatial screw displacement are discussed and analyzed in terms of computational efficiency in performing common operations needed in kinematic analysis of multilinked spatial mechanisms. The corresponding algorithms are analyzed in terms of both sequential and parallel execution. It is concluded that the dual-unit quaternion representation offers the most compact and most efficient screw transformation formalism but that line-oriented methods in general are not well suited for efficient kinematic computations or real-time control applications. Owing to line-based geometry, underlying its definition, screw calculus represents a set of valuable tools in theoretical kinematics. However, the mathematical redundancy inherent in Plucker coordinate space representation makes the screw calculus computationally less attractive than the corresponding point-oriented formalisms.>

Three-dimensional modeling of rotations and translations in robot kinematics is most commonly performed using homogeneous transforms. An alternate approach, using quaternion-vector pairs as spatial operators, is compared with homogeneous transforms in terms of computational efficiency and storage economy. The conclusion drawn is that quaternion-vector pairs are as efficient as, more compact than, and more elegant than their matrix counterparts. A robust algorithm for converting rotational matrices into equivalent unit quaternions is described, and an efficient quaternion-based inverse kinematics solution for the Puma 560 robot arm is presented.>

Three-dimensional modeling of rotations and translations in robot kinematics is most commonly performed using homogeneous transforms. An alternate approach, using quaternion/vector pairs as spatial operators, is discussed and analyzed. Sequential and parallel algorithms for some of the common spatial operations are given for both homogeneous transforms and quaternion/vector pairs and compared in terms of computational efficiency. The two approaches are shown to be essentially equivalent in the absence of the need for frequent renormalization of rotational operators.>