Park Wooram, Wang Yunfeng, Chirikjian Gregory S
Int J Rob Res. 2010 Jun 1;29(7):813-830. doi: 10.1177/0278364909357228.
In this paper we develop a new framework for path planning of flexible needles with bevel tips. Based on a stochastic model of needle steering, the probability density function for the needle tip pose is approximated as a Gaussian. The means and covariances are estimated using an error propagation algorithm which has second order accuracy. Then we adapt the path-of-probability (POP) algorithm to path planning of flexible needles with bevel tips. We demonstrate how our planning algorithm can be used for feedback control of flexible needles. We also derive a closed-form solution for the port placement problem for finding good insertion locations for flexible needles in the case when there are no obstacles. Furthermore, we propose a new method using reference splines with the POP algorithm to solve the path planning problem for flexible needles in more general cases that include obstacles.
在本文中，我们开发了一种用于带斜角尖端的柔性针路径规划的新框架。基于针转向的随机模型，针尖姿态的概率密度函数近似为高斯分布。使用具有二阶精度的误差传播算法估计均值和协方差。然后，我们将概率路径（POP）算法应用于带斜角尖端的柔性针的路径规划。我们展示了我们的规划算法如何用于柔性针的反馈控制。我们还推导了一个封闭形式的解，用于在没有障碍物的情况下为柔性针找到良好插入位置的端口放置问题。此外，我们提出了一种将参考样条与POP算法相结合的新方法，以解决更一般情况下（包括有障碍物的情况）柔性针的路径规划问题。
