Wheeled-legged humanoid robots combine the rough terrain compliance of humanoid robots with the high efficiency of wheeled robots, enabling the robot to achieve flexible and stable locomotion over multiple terrains. However, the stability control of the wheel-legged humanoid robot in dealing with rough terrains and unexpected external disturbances remains unsolved. In the current investigation, a compliant balance control framework (CBCF) is proposed, which can absorb ground shocks, withstand unexpected external disturbances, and remain stable posture during motion. The CBCF connects the control of legs movement and the wheels balance control through the movement of the robot's center of mass. The wheel balance control employs the inverted pendulum model and controls the two wheels through model prediction. The leg posture control utilizes a whole-body dynamic compensator to realize the compliant motion and remain a stable posture. Cooperating with the high-level motion planner, the CBCF can allow the BHR-WI to move quickly and perform excellent adaptation in unmodeled rough terrains, and it is able to appropriately handle unexpected external disturbances as well. It is also worth mentioning that the BHR-WI is capable of remaining balance and quickly recovering stability in the event of a disturbance, even if one of the legs leaves the ground. Finally, tests confirm that the BHR-WI could withstand sustained unexpected disturbances, could smoothly cross the grass and steps and even realize high maneuverability in jumping.

To face the challenge of adapting to complex terrains and environments, we develop a novel wheel-legged robot that can switch motion modes to adapt to different environments. The robot can perform efficient and stable upright balanced locomotion on flat roads and flexible crawling in low and narrow passages. For passing through low and narrow passages, we propose a crawling motion control strategy and methods for transitioning between locomotion modes of wheel-legged robots. In practical applications, the smooth transition between the two motion modes is challenging. By optimizing the gravity work of the body, the optimal trajectory of the center of mass (CoM) for the transition from standing to crawling is obtained. By constructing and solving an optimization problem regarding the posture and motion trajectories of the underactuated model, the robot achieves a smooth transition from crawling to standing. In experiments, the wheel-legged robot successfully transitioned between the crawling mode and the upright balanced moving mode and flexibly passed a low and narrow passage. Consequently, the effectiveness of the control strategies and algorithms proposed in this paper are verified by experiments.