Special Cases in the Attitude Determination of Three-Vehicle Heterogeneous Formations

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Abstract
This paper considers the attitude determination problem of a three-vehicle heterogeneous formation, whose line of sight is constrained. By some reason, such as large distance, two of the vehicles, the deputies, cannot measure the direction of each other’s position. The deputies can only measure the relative direction relative to the chief, which is the remaining vehicle in the formation. The special cases of the problem are described in terms of the number of solutions related to each configuration. In general, there is only one solution, but infinite or even two ambiguous solutions are possible, respectively in the degenerate and ambiguous configurations. These arise due to lack of information or symmetry in the data, respectively. Furthermore, the subset of special configurations is a zero measure set of the global set of configurations, which is an important property of the problem. Simulations that test and validate the described configurations are shown as well, which also help to understand what effects the quality of the solution obtained according to a special case proximity metric.

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