title: Lower bounds on the optimal control of soft tissue grasping.
abstract: The interaction between surgical tools and soft tissue has nonlinear mechanical properties. In robot-assisted surgery, a pre-specified trajectory of tool positions (or applied forces) is desired for achieving a surgical treatment. Due to the computational complexity involved in solving the nonlinear optimal trajectory following problem, a tractable path is to find lower bounds on the optimal cost. The lower bound serves as a reference to evaluate the goodness of any specific controller. A mathematical derivation of a lower bound on the optimal cost of the dynamic optimization problem, using a linear matrix inequality (LMI) approach, is developed. Semi-definite programming is used to solve the LMIs. This approach is demonstrated for a previously studied soft tissue grasping control problem.
authors.affiliation: Department of Electrical Engineering, University of Washington, Seattle, WA 98195-2500, USA.
authors.forename: Xiaolong
authors.initials: X
authors.lastname: Yu
authors.forename: Howard Jay
authors.initials: HJ
authors.lastname: Chizeck
mesh_terms: D000465:Algorithms; D001696:Biomechanical Phenomena; D001698:Biomedical Engineering; D006801:Humans; D016014:Linear Models; D017711:Nonlinear Dynamics; D012371:Robotics / Q000706:statistics & numerical data*; D025321:Surgery, Computer-Assisted / Q000706:statistics & numerical data*