Biped wheel-legged robot is an important configuration of ground mobile robot. In the existing research, in order to deploy the model on an embedded system with limited computing power, the balance control of the robot is usually decoupled from the body posture and steering, which reduces the control coordination of the robot. In order to solve the above problems, firstly, the novel Full-State Dynamics Model(FSDM) is introduced, and the model is linearized by Taylor expansion and solving the limit of multivariate function. Secondly, a novel Forward Kinematics(FK) solution method based on trajectory equation is proposed for Virtual Model Control(VMC). Compared with the general FK solution method, it can further significantly improve the calculation speed of VMC on the embedded platform. Furthermore, the Linear Quadratic Regulator(LQR) controller is optimized, and the weight matrix value can be automatically adjusted according to the error of the state variable. At the same time, simulation results show that the motion performance of the robot can be improved by actively adjusting the posture. Therefore, an adaptive LQR controller, a steering compensator and a gravity compensator are designed. Simulation and physical experimental results verify the effectiveness of the proposed model, controller and control strategy.