RL-accelerated OSQP for real-time asymmetric corotational beam contact simulation in continuum robots

Abstract

The real-time simulation of highly deformable slender structures interacting with complex, irregular boundaries remains a computationally demanding challenge in computational mechanics. A prominent motivating application for this fundamental problem is the navigation of continuum surgical robots within narrow anatomical cavities, which involves extensive beam-surface multi-point contacts and significant bending deformations. While integrating the 3D co-rotational finite element method (FEM) with variational inequality (VI) formulations effectively models these dynamics, the special choice of rotation parameterization yields an asymmetric tangent stiffness matrix. This asymmetry severely precludes the direct application of standard quadratic programming (QP) solvers. To bridge this methodological gap, this paper proposes a robust numerical framework featuring a novel adaptation of an Operator Splitting Quadratic Program (OSQP) approach pecifically extended to resolve asymmetric contact systems. To overcome the slow convergence typically associated with asymmetric formulations, a reinforcement learning (RL) strategy is uniquely integrated to dynamically tune the solver’s hyperparameters, significantly accelerating algorithmic convergence. Furthermore, trajectory prediction via the HHT- α method is employed to restrict contact analysis to local convex regions, mitigating spurious contacts. Complemented by GPU parallelization, the proposed methodology is comprehensively validated using the demanding scenario of a transbronchial continuum robot. Experimental results demonstrate that the RL-accelerated asymmetric solver delivers high-fidelity, real-time performance — reaching 285 FPS in a 200-node simulation — while exhibiting strong scalability (5.7 FPS in a massive 5000-node system).