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

Deformable continuum robots (DCRs) present unique planning challenges due to nonlinear deformation mechanics and partial state observability, violating the Markov assumptions of conventional reinforcement learning (RL) methods. While Jacobian-based approaches offer theoretical foundations for rigid manipulators, their direct application to DCRs remains limited by time-varying kinematics and underactuated 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 Jacobian features to restore approximate Markovianity. Extensive SOFA surgical dynamic simulations demonstrate JEDP-RL's three key advantages over proximal policy optimization (PPO) baselines: 1) Convergence speed: 3.2x 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.