Model Predictive Impedance Control and Gait Optimization for High-Speed Quadrupedal Running

Controlling legged robots to run at high speeds or to traverse complex terrains remains challenging due to the difficulty of handling the interaction between the robot and the ground. Impedance control and model predictive control are widely used to account for ground reaction forces (GRFs) during dynamic locomotion. This paper introduces a model predictive impedance control (MPIC) method that combines the advantages of both strategies and applies it to a quadruped robot. The proposed approach reformulates MPIC within the single rigid body model (SRBM) framework and derives linear inequality constraints for the equivalent wrench, allowing explicit consideration of GRF limits while retaining compliant behavior against ground impacts and external disturbances. Furthermore, a novel optimized gait pattern based on a simplified dynamic model is introduced to minimize the effect of GRFs on the robot. The resulting gait improves stability compared to conventional gait patterns while maintaining a similar level of energy efficiency. The proposed method is validated through various simulations under diverse conditions. The results demonstrate that it enables the quadruped robot to run at a speed of 12 m/s while maintaining stability against repeated lateral disturbances.