Continuum robots with floating bases demonstrate exceptional operational capabilities in confined spaces, such as those encountered in medical surgeries and equipment maintenance. However, developing low-cost solutions for their motion and planning problems remains a significant challenge in this field. This paper investigates the application of geometric iterative strategy methods to continuum robots, and proposes the algorithm based on an improved two-layer geometric iterative strategy for motion planning. First, we thoroughly study the kinematics and effective workspace of a multi-segment tendon-driven continuum robot with a floating base. Then, generalized iterative algorithms for solving arbitrary-segment continuum robots are proposed based on a series of problems such as initial arm shape dependence exhibited by similar methods when applied to continuum robots. Further, the task scenario is extended to a follow-the-leader task considering environmental factors, and further extended algorithm are proposed. Simulation comparison results with similar methods demonstrate the effectiveness of the proposed method in eliminating the initial arm shape dependence and improving the solution efficiency and accuracy. The experimental results further demonstrate that the method based on improved two-layer geometric iteration can be used for motion planning task of a continuum robot with a floating base, under an average deviation of about 4 mm in the end position, an average orientation deviation of no more than 1 degree, and the reduction of average number of iterations and time cost is 127.4 iterations and 72.6 ms compared with similar methods, respectively.

翻译：浮动基座连续体机器人在医疗手术、设备维护等受限空间作业中展现出卓越的操作能力。然而，为其运动与规划问题开发低成本解决方案仍是该领域的重要挑战。本文研究几何迭代策略方法在连续体机器人中的应用，提出一种基于改进双层几何迭代策略的运动规划算法。首先，我们深入研究了多段腱驱动浮动基座连续体机器人的运动学与有效工作空间。随后，针对此类方法应用于连续体机器人时表现出的初始臂形依赖等一系列问题，提出了适用于任意分段连续体机器人的广义迭代算法。进一步，将任务场景扩展至考虑环境因素的跟随引导任务，并提出了相应的扩展算法。与同类方法的仿真对比结果表明，所提方法能有效消除初始臂形依赖，并提高求解效率与精度。实验结果进一步证明，基于改进双层几何迭代的方法可用于浮动基座连续体机器人的运动规划任务，在末端位置平均偏差约4 mm、平均姿态偏差不超过1度的条件下，相较于同类方法，平均迭代次数与耗时分别减少127.4次和72.6毫秒。