A virtual-variable-length method for robust inverse kinematics of multi-segment continuum robots

This paper proposes a new, robust method to solve the inverse kinematics (IK) of multi-segment continuum manipulators. Conventional Jacobian-based solvers, especially when initialized from neutral/rest configurations, often exhibit slow convergence and, in certain conditions, may fail to converge (deadlock). The Virtual-Variable-Length (VVL) method proposed here introduces fictitious variations of segments' length during the solution iteration, conferring virtual axial degrees of freedom that alleviate adverse behaviors and constraints, thus enabling or accelerating convergence. Comprehensive numerical experiments were conducted to compare the VVL method against benchmark Jacobian-based and Damped Least Square IK solvers. Across more than $1.8\times 10^6$ randomized trials covering manipulators with two to seven segments, the proposed approach achieved up to a 20$\%$ increase in convergence success rate over the benchmark and a 40-80$\%$ reduction in average iteration count under equivalent accuracy thresholds ($10^{-4}-10^{-8}$). While deadlocks are not restricted to workspace boundaries and may occur at arbitrary poses, our empirical study identifies boundary-proximal configurations as a frequent cause of failed convergence and the VVL method mitigates such occurrences over a statistical sample of test cases.

Computing forward statics from tendon-length in flexible-joint hyper-redundant manipulators

Hyper-redundant tendon-driven manipulators offer greater flexibility and compliance over traditional manipulators. A common way of controlling such manipulators relies on adjusting tendon lengths, which is an accessible control parameter. This approach works well when the kinematic configuration is representative of the real operational conditions. However, when dealing with manipulators of larger size subject to gravity, it becomes necessary to solve a static force problem, using tendon force as the input and employing a mapping from the configuration space to retrieve tendon length. Alternatively, measurements of the manipulator posture can be used to iteratively adjust tendon lengths to achieve a desired posture. Hence, either tension measurement or state estimation of the manipulator are required, both of which are not always accurately available. Here, we propose a solution by reconciling cables tension and length as the input for the solution of the system forward statics. We develop a screw-based formulation for a tendon-driven, multi-segment, hyper-redundant manipulator with elastic joints and introduce a forward statics iterative solution method that equivalently makes use of either tendon length or tension as the input. This strategy is experimentally validated using a traditional tension input first, subsequently showing the efficacy of the method when exclusively tendon lengths are used. The results confirm the possibility to perform open-loop control in static conditions using a kinematic input only, thus bypassing some of the practical problems with tension measurement and state estimation of hyper-redundant systems.