An Optimization-Driven Foot Placement Controller for Quadruped Landing

In this paper, we propose a new optimization-based foot placement controller for the landing of legged robots on flat ground. The stance phase is modeled using a template-based approach, and a stance controller is designed accordingly. The foot placement controller utilizes analytical solutions from the template model to predict stance motion and determine the optimal foot placement, minimizing the difference between template-generated moments and body moments induced by ground reaction forces at touchdown while accounting for the ground's friction coefficient. The proposed approach ensures that the robot's landing dynamics closely follow the template model, resulting in a more controlled and predictable touchdown. This problem is formulated as a nonlinear model predictive control (NMPC) problem. The effectiveness of the proposed approach is demonstrated through both simulation and real-robot experiments. Simulation results show that the controller enables successful landings at horizontal velocities up to 5 m/s and outperforms existing methods in landing stability and performance.