Cooperative circular pattern target tracking by multiple UAVs using navigation function

Abstract

If the UAVs measure only the range from the target in a two-dimensional space and the range sensor has the minimum error covariance at some distance from the target (the so-called sweet spot), then an optimal configuration is the one in which the UAVs are uniformly placed in a circular fashion around the target. The determinant of the Fisher Information Matrix (FIM) is very sensitive to changes in range but exhibits far less sensitivity to changes in angular separation. If the gradient descent method using the FIM is employed, which is considered an appropriate algorithm for real-time applications, it first reduces the range as much as possible. It results in the UAV configuration at the same distance from the target, but not in evenly spaced positions according to the initial condition.

From the point of view of information, the optimal position of UAVs for minimizing the uncertainties of the target information is evenly spaced positions around the target. Our study proved that the proposed guidance law made multiple UAVs to be deployed at the optimal positions. To prove the validity of the proposed guidance law, the results were compared with the previous approach, which considered specific conditions because such an observation helped us to anticipate how the guidance law works properly. From a simulation with ten UAVs which started from random positions, it was verified that the proposed guidance law steered the UAVs to the sweet spot in evenly spaced locations. It was also showed that ten UAVs never collided with each other and automatically maximized the Fisher Information Matrix.