Hybrid Supervised Learning and Constrained Optimization for Task-Space Trajectory Generation in Tendon-Driven Continuum Robots

Abstract Tendon-driven continuum robots (TDCRs) offer exceptional dexterity and compliance, making them suitable for manipulation in constrained and complex environments. However, solving the inverse-kinematics (IK) problem with sufficient accuracy and physical feasibility remains challenging due to nonlinear curvature coupling and actuation uncertainties. This paper presents a hybrid inverse-kinematics framework that integrates supervised deep learning with constrained optimization to achieve precise and physically consistent task-space trajectory tracking. Neural networks provide fast initial pose-to-configuration estimates, which are subsequently refined through constraint-aware optimization, ensuring geometric and actuation feasibility. The training data were generated from optimal IK solutions obtained via constrained optimization across sixteen trajectory–constraint combinations, covering four representative trajectories circular, elliptical, helical, and butterfly, and four end-effector orientation modes. Extensive simulations on a two-segment tendon-driven continuum robot demonstrated statistically significant improvements (p ≤ 0.01) in both position and orientation accuracy compared with standalone neural or optimization-based approaches. The hybrid method achieves micrometer-level positional accuracy and micro-degree-level orientation precision while maintaining computational efficiency suitable for real-time applications. The present work focuses on a quasi-static modeling and trajectory-generation framework. Future work will extend constraint handling to include dynamic obstacle avoidance and smoothness optimization, explore global solvers such as genetic algorithms and particle swarm optimization, and address sim-to-real transfer through adaptive learning for multi-segment robots in realistic environments.