Risk-Aware Control of Tendon-Driven Continuum Robots Via CVaR-MPPI with Residual Learning for Hysteresis Compensation : A Pilot Study

Abstract

Tendon-driven Continuum Robots (TDCRs) are widely used in confined operating systems due to their thin shape, flexibility, and compliance making them easily deployable in narrow or contact-rich environments. However, real-time safe control near obstacles remains challenging. Computationally expensive dynamic models, such as the Cosserat rod model, are impractical for real-time control. Conventional model predictive control (MPC) methods require linearization of the dynamics, limiting their applicability to the complex nonlinear behavior of TDCRs, including hysteresis. In this paper, we adopt the Piecewise Constant Curvature (PCC) model, which assumes constant curvature for each link. While computationally cheap, this approximation contains modeling errors that, combined with mechanical friction, backlash, and misalignment at the rolling joints, result in unpredictable hysteresis. Also, we propose CVaR-MPPI(Conditional Value-at-Risk Model Predictive Path Integral), a controller that combines sampling based planning with probability safety under uncertainty environment, improving both worst-case risk managing and sampling efficiency. In simulation with 100 iterations, CVaR-MPPI improves the success rate from 80% to 85% and the mean safety clearance by 129%, while maintaining end-effector tracking error compared to standard MPPI, as detailed in the simulation results. The controller runs at 50Hz with 8192 samples, demonstrating real-time feasibility.