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With advancements in mobile robot technology, wheel-legged robots have emerged as promising next-generation mobile solutions, reducing design costs and enhancing adaptability in unstructured environments. As underactuated systems, their balance control has become a prominent research focus. Despite there being numerous control approaches, challenges remain. Balance control methods for wheel-legged robots are influenced by hardware characteristics, such as motor friction, which can induce oscillations and hinder dynamic convergence. This paper presents a friction feedforward Linear Quadratic Regulator (LQR) balance control method. Specifically, a basic LQR controller is developed based on the dynamics model of the wheel-legged robot, and a Stribeck friction model is established to characterize motor friction. A constant-speed excitation trajectory is designed to gather data for friction identification, and the Particle Swarm Optimization (PSO) algorithm is applied to determine the optimal friction parameters. The identified friction model is subsequently incorporated as feedforward compensation for the LQR controller’s torque output, resulting in the proposed friction feedforward LQR balance control algorithm. The minimum standard deviation for friction identification is approximately 0.30, and the computed friction model values closely match the actual values, indicating effective and accurate identification results. Balance experiments demonstrate that under diverse conditions—such as flat ground, single-sided bridges, and disturbance scenarios—the convergence performance of the friction feedforward LQR algorithm markedly surpasses that of the baseline LQR, effectively reducing oscillations, accelerating convergence, and improving the robot’s stability and robustness.

The wheel-legged biped robot is a typical ground-based mobile robot that can combine the high velocity and high efficiency pertaining to wheeled motion and the strong, obstacle-crossing performance associated with legged motion. These robots have gradually exhibited satisfactory application potential in various harsh scenarios such as rubble rescue, military operations, and wilderness exploration. Wheel-legged biped robots are divided into four categories according to the open–close chain structure forms and operation task modes, and the latest technology research status is summarized in this paper. The hardware control system, control method, and application are analyzed, and the dynamic balance control for the two-wheel, biomimetic jumping control for the legs and whole-body control for integrating the wheels and legs are analyzed. In summary, it is observed that the current research exhibits problems, such as the insufficient application of novel materials and a rigid–flexible coupling design; the limited application of the advanced, intelligent control methods; the inadequate understanding of the bionic jumping mechanisms in robot legs; and the insufficient coordination ability of the multi-modal motion, which do not exhibit practical application for the wheel-legged biped robots. Finally, this study discusses the key research directions and development trends for the wheel-legged biped robots.