To address the challenge of adaptive wheel-legged motion mode switching and motion stability control for wheel-legged hybrid robots in complex terrains.A hierarchical control method integrating wheel-leg stability index(WLSI)and trajectory optimization is proposed.An improved D-H parameter model is established to analyze workspace constraints

and the wheel-leg stability index is defined to realize a self-triggering mechanism for aperiodic gaits.The foot-end trajectories are planned using Bézier curves

and the liftoff and touchdown velocities are optimized by incorporating a tanh function-based nonlinear mapping to ach

ieve a "lift and place softly" effect.A motion control framework based on model predictive control(MPC)and differential dynamic programming(DDP)is developed to achieve real-time nonlinear optimization solution.PyBullet simulations demonstrate that the

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-axis disturbance of the robot by 42% compared with traditional methods and obstacle negotiation height reaches up to 0.75 times the wheel diameter.Physical prototype tests verify its adaptability to complex terrains such as stairs and sand ground

with a maximum obstacle negotiation success rate of 92% under a 4.5kg payload.This method provides a computationally efficient and highly adaptive solution for hybrid wheel-legged motion.