Constrained control for surgical assistant robots

Abstract

This paper presents an approach to implement virtual fixtures for surgical robot assistants. Our approach uses a weighted, multi-objective (both linear and nonlinear) constrained optimization framework to formalize a library of virtual fixtures for task primitives. By our formulation, we provide a library of virtual fixtures on task primitives and a way to assemble multiple virtual fixture objects. We implement the constrained optimization problem with both linear and nonlinear constraints, and discuss the trade-offs between them. Moreover, we introduce the notion of soft virtual fixture mechanism for robotic surgical assistance. The soft virtual fixtures enable a surgical tool to have some resistance inside safety regions and no resistance in preferred regions. I. INTRODUCTION This paper presents an approach to implement virtual fix- tures for surgical robot assistants. Most robotic assisted sur- gical procedures are characterized by restricted access to the workspace as well as constrained manipulation of a surgical tool. In such cases, the surgeons' ability can be augmented by techniques such as virtual fixtures (VF). Virtual fixtures (1), which have been discussed previously in the literature for both telerobotic and cooperative robots, are algorithms which provide anisotropic behavior to surgeons' motion commands in addition to filtering out tremor to provide safety and precision. An important case of virtual fixtures is forbidden regions, where the surgical tool is restricted to certain regions in the workspace. Davies et al. (2) set active constraints to constrain the robot to cut the femur and tibia within a permitted region for prosthetic knee surgery. Park et al. (3) developed sensor- mediated virtual fixtures that constrain the robot's motion or create haptic feedback directing the surgeon to move the surgical instruments in a desired direction. The recent work by Bettini et al. on virtual fixtures (4) used admittance control laws to implement guidance virtual fixtures. These works are based either on a specific robot type or on a specific task. Path planning and motion control is a well discussed area with a wide variety of proposed optimality criteria (5), (6), (7), (8). Funda et al. (9) presented an optimal motion control method to control both redundant and deficient robotic systems in constrained working volumes. We extend Funda's work by applying the method to generate complicated virtual fixtures based on user input for surgical assistant robots. Typically, surgical tasks have a certain degree of uncertainty that arises from factors such as registration errors, variations in anatomy and changes during procedures. Consider an example task of placing a surgical tool at a point in space. Depending on the nature of the procedure, one can define a region and tool placement within this region that would lead to the expected outcome. This region could be on the order of a few microns for retinal vein cannulation or hundreds of microns for a biopsy procedure. Furthermore, we can define another region where the surgeon might deliberately want to place the instrument to account for some uncertainties inherent in surgical procedures. In other words, we would like to have some compliance in the virtual fixture, while maintaining a preferred motion. Therefore, we define 3 different regions: A) Preferred region: this region defines expected outcome. B) Safety region: the tool could temporarily be in this region for fulfilling some expected task. C) Forbidden region: The tool never could be here for safety purposes. The relationship of these three regions depends on the surgical task. Figure 1 shows two typical examples.