Like Playing a Video Game: Spatial-Temporal Optimization of Foot Trajectories for Controlled Football Kicking in Bipedal Robots

Humanoid robot soccer presents several challenges, particularly in maintaining system stability during aggressive kicking motions while achieving precise ball trajectory control. Current solutions, whether traditional position-based control methods or reinforcement learning (RL) approaches, exhibit significant limitations. Model predictive control (MPC) is a prevalent approach for ordinary quadruped and biped robots. While MPC has demonstrated advantages in legged robots, existing studies often oversimplify the leg swing progress, relying merely on simple trajectory interpolation methods. This severely constrains the foot's environmental interaction capability, hindering tasks such as ball kicking. This study innovatively adapts the spatial-temporal trajectory planning method, which has been successful in drone applications, to bipedal robotic systems. The proposed approach autonomously generates foot trajectories that satisfy constraints on target kicking position, velocity, and acceleration while simultaneously optimizing swing phase duration. Experimental results demonstrate that the optimized trajectories closely mimic human kicking behavior, featuring a backswing motion. Simulation and hardware experiments confirm the algorithm's efficiency, with trajectory planning times under 1 ms, and its reliability, achieving nearly 100 % task completion accuracy when the soccer goal is within the range of -90{\deg} to 90{\deg}.