Trajectory Planning of a Soccer Ball Considering Impact Model of Humanoid and Aerodynamics

Usual human gait can be modeled as continual impact phenomenon that happens due to the topological change of the kinematic structure of the two feet. The human being adapts his own control algorithm to minimize the ill effect due to the collision with the environment. In order to operate a Humanoid robot like the human being, it is necessary to understand the physics of the impact and to derive an analytical model of the impact. In this paper, specially, we focus on impact analysis of the kicking motion in playing soccer. At the instant of impact, the external impulse exerted on the ball by the foot is an important property. Initially, we introduce the complete external impulse model of the lower-extremity of the human body and analyze the external impulses for several kicking postures of the lower-extremity. Secondly, a trajectory-planning algorithm of a ball, in which the initial velocity and the launch angle of the ball are calculated for a desired trajectory of the ball, will be introduced. The aerodynamic effect such as drag force and lift force is also considered. We carry out numerical simulation and experimentation to verify the effectiveness of the proposed analytical methodology