  In robot-assisted minimally invasive surgery (RMIS), inverse kinematics (IK)
must satisfy a remote center of motion (RCM) constraint to prevent tissue
damage at the incision point. However, most of existing IK methods do not
account for the trade-offs between the RCM constraint and other objectives such
as joint limits, task performance and manipulability optimization. This paper
presents a novel method for manipulability maximization in constrained IK of
surgical robots, which optimizes the robot's dexterity while respecting the RCM
constraint and joint limits. Our method uses a hierarchical quadratic
programming (HQP) framework that solves a series of quadratic programs with
different priority levels. We evaluate our method in simulation on a 6D path
tracking task for constrained and unconstrained IK scenarios for redundant
kinematic chains. Our results show that our method enhances the manipulability
index for all cases, with an important increase of more than 100% when a large
number of degrees of freedom are available. The average computation time for
solving the IK problems was under 1ms, making it suitable for real-time robot
control. Our method offers a novel and effective solution to the constrained IK
problem in RMIS applications.
