Terrain‐Adaptive Quadrupedal Locomotion Using Model Predictive Control With Impedance Control and SINDy Model Enhancement

ABSTRACT Quadrupedal robots operating in unstructured environments require adaptive control systems that can handle diverse terrain conditions without prior surface characterization. This paper presents an integrated control architecture that combines Model Predictive Control (MPC) with adaptive impedance control and SINDy‐based model corrections for robust terrain‐adaptive locomotion. The system automatically detects surface properties through a four‐state contact detection mechanism and adapts control parameters in real‐time based on measured ground reaction forces. The impedance controller reduces foot slippage by 40% on challenging slopes, while an admittance control component improves force tracking accuracy by 40%–60% on compliant surfaces. SINDy corrections to angular velocity dynamics enhance yaw tracking performance by 80% compared to nominal rigid body models. Comprehensive validation in PyBullet demonstrates the system's effectiveness across diverse scenarios including slope navigation, soft surface adaptation, and complex trajectory tracking. The integrated approach establishes a robust framework for autonomous quadrupedal locomotion in unstructured environments without requiring prior terrain knowledge.