Jacobian Exploratory Dual-Phase Reinforcement Learning for Dynamic Endoluminal Navigation of Deformable Continuum Robots

While Jacobian-based approaches offer theoretical foundations for rigid manipulators, their direct application to DCRs remains limited by time-varying kinematics and underactu-ated deformation dynamics. This paper proposes Jacobian Exploratory Dual-Phase RL (JEDP-RL), a framework that decomposes planning into phased Jacobian estimation and policy execution. During each training step, we first perform small-scale local exploratory actions to estimate the deformation Jacobian matrix, then augment the state representation with Ja-cobian features to restore approximate Markovianity. Extensive SOF A surgical dynamic simulations demonstrate JEDP-RL's three key advantages over proximal policy optimization (PPO) baselines: 1) Convergence speed: 3.2 faster policy convergence, 2) Navigation efficiency: requires 25% fewer steps to reach the target, and 3) Generalization ability: achieve 92% success rate under material property variations and achieve 83% (33% higher than PPO) success rate in the unseen tissue environment.