The traditional two-wheeled self-balancing robot can travel quickly in a flat road environment, and it is easy to destabilize and capsize when passing through a bumpy road. To improve the passing ability of a two-wheeled robot, a new wheel-legged two-wheeled robot is developed. A seven-link leg structure is proposed through the comprehensive design of mechanism configuration, which decouples the balanced motion and leg motion of the robot. Based on the Euler–Lagrange method, the dynamic model of the system is obtained by applying the nonholonomic dynamic Routh equation in the generalized coordinate system. The robot’s state space is divided according to the robot’s height, and the Riccati equation is solved in real-time by the linear quadratic regulator (LQR) method to complete the balance and motion control of the robot. The robot leg motion control is achieved based on the active disturbance rejection control (ADRC) way. A robot simulation model is built on Recurdyn to verify the algorithm’s feasibility, and then an experimental prototype is built to demonstrate the algorithm’s effectiveness. The experimental results show that the control method based on LQR and ADRC can make the robot pass through the bumpy road.
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