Error-State Model Predictive Path Integral Control of Tendon-Driven Continuum Robots using Cosserat Rod Dynamics with Strain Parametrization.

This paper presents an error-state Model Predictive Path Integral (MPPI) framework for tendon-driven continuum robots (TDCRs). Tracking-error dynamics are formulated on a Lie group to preserve full pose geometry, yielding precise position-orientation error metrics. A nonlinear Cosserat-rod model with strain parameterization provides a closed-form TDCR dynamics representation and updates in 0.3 ± 0.3ms. The model is calibrated via weight-release and actuation experiments on robotic ablation catheters, and its generalized coordinates are estimated through nested optimization. The MPPI controller parallelizes trajectory sampling and evaluation, uses tendon-displacement actuation computed via optimization to eliminate force sensors, and is uncertainty-aware through a simple and efficient exponentially weighted moving-average (EWMA) estimator embedded in the running cost. Control trajectories are sampled around the current best sequence and evaluated with an adaptive cost and exponential weighting to bias low-cost solutions. Experiments comparing conventional model predictive control (MPC), Lie-group MPC, offline Implicit Q-Learning (IQL), and MPPI formulated with Cartesian errors show that our MPPI method achieves the highest accuracy, significantly better computational efficiency than MPC, and better overall accuracy than all baselines. The model further extends naturally to multi-segment TDCRs and can incorporate tendon-actuation friction.