  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.
