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.

翻译：在机器人辅助微创手术（RMIS）中，逆运动学（IK）必须满足远程运动中心（RCM）约束，以防止在切口点造成组织损伤。然而，现有的大多数IK方法并未考虑RCM约束与关节限位、任务性能及可操作性优化等其他目标之间的权衡。本文提出了一种用于手术机器人约束逆运动学中可操作性最大化的新方法，该方法在遵守RCM约束和关节限位的同时，优化了机器人的灵巧性。我们的方法采用分层二次规划（HQP）框架，该框架求解一系列具有不同优先级层次的二次规划问题。我们在仿真中评估了我们的方法，针对冗余运动链，在约束与非约束IK场景下执行了6D路径跟踪任务。结果表明，我们的方法在所有情况下都提高了可操作性指标，当可用自由度数量较大时，其提升幅度显著超过100%。求解IK问题的平均计算时间低于1毫秒，使其适用于实时机器人控制。我们的方法为RMIS应用中的约束IK问题提供了一种新颖且有效的解决方案。