Formation control with mismatched compasses

This article addresses the formation control problem with mismatched compasses. Depending on the sensing and communication technology, compass mismatches may arise due to biases in measurement, drift in inertial sensing despite initial alignment, and even spatial variations in the earth's magnetic field. To illustrate the key concepts underlying what happens, we first consider the two agent case and show that the agents converge to a fixed, but distorted formation exponentially fast. In contrast to the matched compass case, the formation is not asymptotically stationary. The distance error and the angular error between the actual final formation and the desired formation are explicitly given, as is the steady state velocity of the formation. The case of time-varying mismatched compasses is also studied. Based on the results, we then propose estimators to obtain the mismatched angle, which allow a compensation algorithm to be proposed such that the desired formation shape is achieved. Finally, the extensions to the n agent case are also considered and similar phenomena are encountered. Simulations are provided to validate the theoretical results.