An adaptive geometric iterative algorithm for constrained inverse kinematics and motion planning of continuum robots

Continuum robots with floating bases demonstrate exceptional operational capabilities in confined spaces, such as those encountered in medical surgeries and equipment maintenance. However, developing computationally efficient and development-light 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. Comparative simulations with representative baseline methods demonstrate that the proposed framework provides improved empirical convergence reliability and competitive computational efficiency in the tested inverse-kinematics tasks. Physical experiments, including continuous trajectory tracking with physical obstacles and follow-the-leader motion in a simulated pipeline environment, further verify the feasibility and practical applicability of the proposed framework for representative constrained tasks.