Robotic surgery for minimally invasive surgery can reduce the surgeon's workload by autonomously guiding robotic forceps. Movement of the robot is restricted around a fixed insertion port. The robot often encounters angle limitations during operation. Also, the surface of the abdominal cavity is non-concave, making it computationally expensive to find the desired path.In this work, to solve these problems, we propose a method for path planning in joint space by transforming the position into a Riemannian manifold. An edge cost function is defined to search for a desired path in the joint space and reduce the range of motion of the joints. We found that the organ is mostly non-concave, making it easy to find the optimal path using gradient descent method. Experimental results demonstrated that the proposed method reduces the range of joint angle movement compared to calculations in position space.

翻译：微创手术中的机器人手术可通过自主引导机器人钳来减轻外科医生的工作负担。机器人的运动围绕固定插入端口受限。机器人在操作过程中常遇到角度限制。此外，腹腔表面为非凹面，导致计算期望路径的计算成本高昂。本研究针对这些问题，提出了一种通过将位置转换为黎曼流形来实现关节空间路径规划的方法。通过定义边代价函数，在关节空间中搜索期望路径并减小关节运动范围。我们发现器官表面大多为非凹面，这使得使用梯度下降法易于找到最优路径。实验结果表明，与位置空间中的计算相比，所提方法显著减小了关节角度运动的范围。