Lyapunov Based Nonlinear Control Logic for Robotic Goalkeeper

The problem of controlling a robotic goalkeeper to intercept a soccer ball is studied within the context of the direct Lyapunov theory. The rotational dynamics of the goalkeeper body is modeled kinematically using geometric approach and dynamically via Eulerian physics. A nonlinear control law is proposed to satisfy the stability conditions in the sense of Lyapunov. Further analysis shows that the system becomes globally asymptotically stable with zero steady state error. The simulation results demonstrate the good performance, in terms of settling time and steady state error, of the proposed law in comparison with other linear control logic. Index Terms-Lyapunov Direct Method, Nonlinear controller, Lyapunov Stability Analysis, Steady State Error Analysis, Robotic Goalkeeper, Mathematical Modeling, Eulerian Physics, Rotational Motion, Rotational Dynamics