Learning Time-Varying Joint-Motor Mapping for Precise Control of Cable-Driven Humanoid Robots Under Transmission Uncertainties

Abstract

Cable-driven robots face significant challenges in achieving precise motion control due to the inherent nonlinearity, strong coupling, and time-varying transmission dynamics. Traditional model-based methods require precise parameter identification and offline calibration, while existing data-driven approaches often fail to adapt to the evolving physical couplings in real time. To bridge this gap, this paper proposes a novel Dynamic Transmission Learning (DTL) framework. Its core innovation is an Evolving Graph Structure (EGS) that explicitly models the robot's motor-joint transmission as a dynamic graph. The EGS continuously learns and adapts the time-varying coupling coefficients (represented by the mapping matrix <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {A}_{t}$</tex-math></inline-formula>) directly from sensor data, enabling a calibration-free representation of the transmission dynamics. The framework thereby captures complex deviations such as cable elasticity variations, backlash, and nonlinear damping effects. Through extensive experiments on bipedal robots, we demonstrate that our framework significantly outperforms a range of sequential and graph-based baseline models in prediction accuracy. Furthermore, integrated into a real-time Proximal Policy Optimization (PPO) control loop, the DTL framework effectively compensates for transmission errors, reduces joint tracking error by over 50%, and demonstrates robust performance across diverse locomotion scenarios.