Hybrid Offline–Online Configuration Planning Approach for Continuum Robots Based on Real-Time Shape Estimation

Continuum robots possess highly flexible backbones, enabling remarkable adaptability and dexterity for motion in confined environments. However, this flexibility also introduces significant nonlinearities and uncertainties, making motion planning under physical constraints particularly challenging. To address this, a hybrid offline-online configuration planning framework is proposed in this work. Specifically, the configuration planning problem is formulated as a nonlinear optimization task that considers collision avoidance and structural constraints. A co-evolutionary strategy is incorporated into the differential evolution (DE) algorithm to decompose the target high-dimensional optimization problem. Then, an unscented Kalman filter (UKF)-based strategy is presented for real-time shape estimation using tip pose feedback for safe distance monitoring. Based on this shape feedback, an online configuration refiner is designed to locally adjust the preplanned configurations, thus leveraging the global perspective of the offline planning configuration to steer the continuum manipulator through constrained spaces. Validation and comparative experiments demonstrate the effectiveness of the proposed method, as well as its enhanced motion smoothness and safe motion performance in real-world environments.