Real-Time Whole-Body Safe Motion Generation for Multi-Segment Tendon-Driven Continuum Robots

Fangju Yang, Siyi Ma, Tonghao Guan, Tingcong Liu, Hang Yang, Zhengqiang Zhang, Jian S. Dai, Ke Wu · N/A · 2026

Summary

Abstract Summary

Real-time motion generation for tendon-driven continuum robots requires accurate modeling of nonuniform bending and whole-body collision avoidance. This paper presents a unified actuation-space framework for planar multi-segment tendon-driven continuum robots. An energy-based variable-curvature model captures spatially varying tendon spacing and bending stiffness and provides analytical Jacobians for differential inverse kinematics and safety monitoring. A multipoint CBF-QP enforces backbone clearance under obstacle motion and actuation-velocity bounds, while its decision dimension depends only on the number of independently actuated segments. The model closely agrees with GVS references, with a maximum curvature error of $5.223 \times 10^{-2}\,\mathrm{m}^{-1}$. Over 100 MuJoCo trials, the proposed method achieves collision-free success rates of 96% and 100% in static and dynamic scenarios, respectively, compared with approximately 60% and 80% without CBF constraints. Hole-traversal tests further demonstrate safe motion in constrained environments. With 600 backbone monitoring points, the mean control-step time is 6.66 ms, demonstrating real-time whole-body safe motion generation.

Key Points

Real-time motion generation for tendon-driven continuum robots requires accurate modeling of nonuniform bending and whole-body collision avoidance.
This paper presents a unified actuation-space framework for planar multi-segment tendon-driven continuum robots.
An energy-based variable-curvature model captures spatially varying tendon spacing and bending stiffness and provides analytical Jacobians for differential inverse kinematics and safety monitoring.
A multipoint CBF-QP enforces backbone clearance under obstacle motion and actuation-velocity bounds, while its decision dimension depends only on the number of independently actuated segments.
The model closely agrees with GVS references, with a maximum curvature error of $5.223 \times 10^{-2}\,\mathrm{m}^{-1}$.

Variable-Curvature Kinematic Modeling in Actuation Space

This paper considers the $n$-segment planar tendon-driven continuum robot (TDCR) shown in Fig. 1 and develops a general variable-curvature kinematic model in actuation space. The robot comprises $n$ serially connected flexible segments, where the $i$-th segment is denoted by $\mathcal{S}_{i}$ and has length $L_{i}$, yielding the total robot length $L=\sum_{i=1}^{n}L_{i}$.

The arc-length coordinate $s\in[0,L]$ specifies a material point along the backbone.

Variable-Curvature Kinematic Modeling in Actuation Space — Real-Time Whole-Body Safe Motion Generation for Multi-Segment Tendon-Driven Continuum Robots — Fig. 1: Real-time whole-body safe motion generation for continuum robots. (A) Robot and kinematics. (B) Whole-body collision avoidance. (C) Real-time CBF-QP control framework.

Real-Time Whole-Body Collision-Avoidance Framework

Building on the multi-segmen continuum-robot kinematics, this section develops a real-time whole-body safety-control framework. Unlike methods that impose collision-avoidance constraints only at the robot tip, the proposed framework selects multiple safety-monitoring positions along the flexible backbone and constructs control barrier function constraints using their actuation-space point Jacobians.

Tip trajectory tracking and whole-body collision avoidance are thereby unified in an actuation-space quadratic program.

Real-Time Whole-Body Collision-Avoidance Framework — Real-Time Whole-Body Safe Motion Generation for Multi-Segment Tendon-Driven Continuum Robots — (a) Robot shape comparison

Numerical Validation

Numerical simulations evaluate the kinematic accuracy, whole-body collision avoidance, and computational efficiency of the proposed framework. Kinematic predictions are compared with GVS results [ 22 ] . Whole-body collision avoidance is then evaluated with static obstacles and during trajectory tracking with moving obstacles. Table I summarizes the parameters used for the kinematic validation in Fig. 2 .

The proposed model and GVS use identical geometric and material properties and tendon-length inputs.

Numerical Validation — Real-Time Whole-Body Safe Motion Generation for Multi-Segment Tendon-Driven Continuum Robots — (b) $S_{1}$ curvature error

Sources and Demonstrations

Figures are reproduced from Yang et al. See the full paper for experimental details and the project page, when the paper links one, for demonstrations and videos.