An End-to-End Framework for Optimizing Foot Trajectory and Force in Dry Adhesion Legged Wall-Climbing Robots

Foot trajectory planning for dry adhesion legged climbing robots presents challenges, as the phases of foot detachment, swing, and adhesion significantly influence the adhesion and detachment forces essential for stable climbing. To tackle this, an end-to-end foot trajectory and force optimization framework (FTFOF) is proposed, which optimizes foot adhesion and detachment forces through trajectory adjustments. This framework accepts general foot trajectory constraints and user-defined parameters as input, ultimately producing an optimal single foot trajectory. It integrates three-segment $C^2$ continuous Bezier curves, tailored to various foot structures, enabling the generation of effective climbing trajectories. A dilate-based GRU predictive model establishes the relationship between foot trajectories and the corresponding foot forces. Multi-objective optimization algorithms, combined with a redundancy hierarchical strategy, identify the most suitable foot trajectory for specific tasks, thereby ensuring optimal performance across detachment force, adhesion force and vibration amplitude. Experimental validation on the quadruped climbing robot MST-M3F showed that, compared to commonly used trajectories in existing legged climbing robots, the proposed framework achieved reductions in maximum detachment force by 28 \%, vibration amplitude by 82 \%, which ensures the stable climbing of dry adhesion legged climbing robots.