Sliding mode control of kicking a soccer ball in the sagittal plane

Collision modeling and control are important aspects of simulation of many human and robotic tasks. A scientific inquiry into a foot-ball collision is made in this paper from the perspective of dynamics, control, modeling, and simulation. As an extension of the Hertzian contact model, our generalized compliant collision model with nonlinear elasticity and damping is tested by a human lower limb kicking a soccer ball. The experiment-based elasticity is used to model the energy transfer of the foot-ball collision and overcome some problems caused by impulse impact modeling. The nonlinear damping in proportion to a restitution-related constant eliminates impact discontinuity. A robust sliding mode controller is developed to track the preplanned trajectory against modeling uncertainties and impact disturbances. The collision duration (about 0.014 s), the ball departure velocity (31.83 m/s), the average foot-ball collision force (about 975.5 N), and the ball peak deformation (about 0.079 m) obtained by simulation match the reported results. The observed three phases of the foot-ball collision are confirmed by our simulation, and the "follow-through" phenomenon in sports is demonstrated.