Inverse kinematics (IK) of concentric tube continuum robots (CTRs) is associated with two main problems. First, the robot model (e.g., the relationship between the configuration space parameters and the robot end-effector) is not linear. Second, multiple solutions for the IK are available. This paper presents a general approach to solve the IK of CTRs in the presence of constrained environments. It is assumed that the distal tube of the CTR is inserted into a cavity while its proximal end is placed inside a tube resembling the vessel enabling the entry to the organ cavity. The robot-tissue interaction at the beginning of the organ-cavity imposed displacement and force constraints to the IK problem to secure a safe interaction between the robot and tissue. The IK in CTRs has been carried out by treating the problem as an optimization problem. To find the optimized IK of the CTR, the cost function is defined to be the minimization of input force into the body cavity and the occupied area by the robot shaft body. The optimization results show that CTRs can keep the safe force range in interaction with tissue for the specified trajectories of the distal tube. Various simulation scenarios are conducted to validate the approach. Using the IK obtained from the presented approach, the tracking accuracy is achieved as 0.01 mm which is acceptable for the application.

中文翻译：

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存在环境约束的同心管机器人的逆运动学

同心管连续体机器人 (CTR) 的反向运动学 (IK) 与两个主要问题有关。首先，机器人模型（例如，配置空间参数和机器人末端执行器之间的关系）不是线性的。其次，有多种 IK 解决方案可用。本文提出了一种在存在约束环境的情况下解决 CTR 的 IK 的通用方法。假设 CTR 的远端管插入腔内，而其近端放置在类似于血管的管内，从而能够进入器官腔。器官腔开始时的机器人与组织相互作用对 IK 问题施加了位移和力约束，以确保机器人与组织之间的安全相互作用。CTR 中的 IK 是通过将问题视为优化问题来进行的。为了找到 CTR 的优化 IK，成本函数被定义为进入体腔的输入力和机器人轴体占据的区域的最小化。优化结果表明，对于远侧管的指定轨迹，CTR 可以保持与组织相互作用的安全力范围。进行了各种模拟场景以验证该方法。使用从所提出的方法获得的 IK，跟踪精度达到 0.01 毫米，这是应用程序可以接受的。进行了各种模拟场景以验证该方法。使用从所提出的方法获得的 IK，跟踪精度达到 0.01 毫米，这是应用程序可以接受的。进行了各种模拟场景以验证该方法。使用从所提出的方法获得的 IK，跟踪精度达到 0.01 毫米，这是应用程序可以接受的。