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

TL;DR

This paper introduces a convex optimization-based control framework for a redundant surgical robotic system, utilizing an ADMM algorithm with proven convergence for efficient and robust constrained motion control.

Contribution

It develops a novel convex optimization controller for redundant surgical robots and proves the global linear convergence of an ADMM-based redundancy resolution algorithm.

Findings

ADMM algorithm converges globally at a linear rate.

Simulation results confirm robustness and efficiency.

The framework effectively manages constraints in surgical robotic control.

Abstract

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