A Convex Optimization Framework for Constrained Concurrent Motion Control of a Hybrid Redundant Surgical System

We present a constrained motion control framework for a redundant surgical\nsystem designed for minimally invasive treatment of pelvic osteolysis. The\nframework comprises a kinematics model of a six Degrees-of-Freedom (DoF)\nrobotic arm integrated with a one DoF continuum manipulator as well as a novel\nconvex optimization redundancy resolution controller. To resolve the redundancy\nresolution problem, formulated as a constrained l2-regularized quadratic\nminimization, we study and evaluate the potential use of an optimally tuned\nalternating direction method of multipliers (ADMM) algorithm. To this end, we\nprove global convergence of the algorithm at linear rate and propose\nexpressions for the involved parameters resulting in a fast convergence.\nSimulations on the robotic system verified our analytical derivations and\nshowed the capability and robustness of the ADMM algorithm in constrained\nmotion control of our redundant surgical system.\n