Adaptive Fuzzy-LQR for Stability Control of Bipedal Wheel-Legged Robots on Variable Terrain

Wheel-legged robots offer high mobility on flat terrain and adaptability in complex environments, yet achieving stable motion under uncertain ground conditions and during height variations poses significant control challenges. This study presents a control framework for a bipedal wheel-legged robot (BWLR) to enable stable locomotion and posture transitions on uneven and inclined terrains. An adaptive Fuzzy-linear quadratic regulator (Fuzzy-LQR) controller is presented, where a fuzzy supervisory layer dynamically tunes the LQR gains and estimates the center of mass (CoM) using intermediate postures. Additionally, a proportional-derivative (PD)-based hip stabilization controller is integrated to regulate the roll angle via coordinated hip joint actuation, enhancing balance on uneven surfaces. The framework is implemented in a Robot Operating System (ROS)2-based architecture with torque-level joint control. Its effectiveness is validated through high-fidelity simulations in ROS2–Gazebo and real-world experiments on a physical BWLR prototype, including detailed aspects of multiplugin integration and torque-feedback hip control. Results demonstrate robust height adaptation during locomotion and stable balance on inclined terrain, highlighting the adaptability of the combined Fuzzy-LQR and PD approach for wheel-legged robotic systems.