Asymmetrical Artificial Potential Field as Framework of Nonlinear PID Loop to Control Position Tracking by Nonholonomic UAVs

Precise position tracking plays a key role in formation flights of UAVs (unmanned aerial vehicles) or other applications based on the idea of the leader–following scheme. It decides on the integrity of a formation or increasing the position error when a UAV follows the desired flight path. This is especially difficult in the case of nonholonomic vehicles having limited possibilities of making turns, causing a lack of stability. An asymmetrical artificial potential field (AAPF) is the way to achieve the stability of position tracking by nonholonomic UAVs, but it is only a nonlinear proportional relation to feedback given by a tracking error. Therefore, there can still be a steady-state error or error overshoots. Combining an AAPF with integral and derivative terms can improve the response of control by damping overshoots and minimizing the steady-state error. Such a combination results in a regulator whose properties allow defining it as nonlinear PID. Numerical simulation confirms that integral and derivative terms together with an AAPF create a control loop that can minimize overshoots of the tracking error and the steady-state error and satisfy conditions of asymptotical stability.