Introduction

Bipedal wheeled robots combine the adaptability of legs with the efficiency of wheels, but their nonlinear, underactuated dynamics make balance control difficult. Classical PID methods fail to handle coupled dynamics in such systems. This project developed an LQR-based control framework, integrated with Virtual Model Control (VMC), to stabilize a five-bar linkage bipedal wheel robot in simulation.

 

Methods

The robot was modeled dynamically using Newton–Euler equations, with wheel, leg, and body subsystems coupled into a state-space representation. Linearization at upright equilibrium enabled full-state feedback design. An LQR controller was formulated with gain scheduling based on leg geometry, minimizing deviation and control effort while adapting to changing leg lengths.In parallel, VMC mapped virtual task-space forces (springs/dampers) to joint torques via Jacobian transformations, allowing intuitive torque distribution. The integrated control architecture combined LQR regulation of body states with VMC torque mapping for leg coordination. Simulations were performed in MATLAB with real-time feedback loops.

 

Results

Simulations demonstrated that the LQR+VMC controller maintained upright balance, stabilized body elevation, and tracked reference velocities with minimal delay. Torque responses showed smooth coordination between wheel and leg actuators, avoiding saturation. Motor speed tracking closely followed commanded trajectories, confirming real-time responsiveness. Visualization of robot trajectories verified stable, balanced locomotion under cyclic inputs.

 

Future Work

While effective in simulation, the framework must be extended to real-world conditions with sensor noise, actuator delays, and uncertain ground contact. Planned improvements include:Adaptive/learning-based LQR to dynamically tune gains beyond pre-computed schedules.Robust alignment and disturbance rejection, enabling stability on uneven terrain.Hardware validation on physical prototypes to confirm scalability and robustness.This work provides a foundational control methodology for bipedal wheeled robots, bridging the gap between simulation and practical deployment.