A new bio-inspired gait control method was proposed to address the challenges of insufficient locomotion stability and environmental adaptability of quadruped robots in complex terrains. A bio-inspired gait encoder module based on dynamic time warping (DTW) and convolutional processing was constructed to extract spatiotemporally correlated gait features through inverse kinematics solution and joint velocity differentiation calculation. A geometric constraint mechanism driven by differential kinematics was incorporated, and the coupled mapping between task-space trajectories and joint torques was embedded into the proximal policy optimization (PPO) network to enhance the joint motion coordination and the sampling efficiency. A hierarchical reward function combining energy efficiency factors and the Lyapunov stability was designed, the and multi-objective collaborative control of bio-inspired gaits was achieved via exponential energy efficiency rewards and stability rewards. The experimental results demonstrated that the proposed method outperformed the comparative algorithms in terms of indicators such as average collision value and adaptive loss function in the simulation environment, and effectively mitigated the joint ground contact phenomenon. This method significantly enhanced the motion stability and the environmental adaptability of the quadruped robot in the deployment test of the real robot in complex terrains.