(Preprint) AAS RELATIVE ATTITUDE DETERMINATION FROM PLANAR VECTOR OBSERVATIONS Richard Linares ∗ , Yang Cheng † , and John L. Crassidis ‡ A method for relative attitude determination from planar line-of-sight observations is presented. Three vehicles are assumed to be equipped with sensors to provide measurements of the three inter-vehicle line-of-sight vectors. The line-of-sight vectors are further assumed to be always in the same plane. This information is combined with all the available measurements to find an optimal relative attitude estimation solution. Covariance analysis is provided to help gain insight on the statistical properties of the attitude errors of the solution. INTRODUCTION Formation flying employs multiple vehicles to maintain specific relative attitude/position config- urations. Here relative is defined as being between any two vehicles of interest. Applications of formation flying are numerous, involving all types of vehicles, including land (robotics 1 ), sea (au- tonomous underwater vehicles 2 ), space (spacecraft formations 3 ) and air (uninhabited air vehicles 4 ) systems. Relative attitude information is needed to maintain formation attitude through control. The problem under consideration is to determine the relative attitude of three vehicles from inter- vehicle line-of-sight (LOS) vector measurements. 5 Each vehicle is equipped with optical-type sen- sors, such as a beacon or laser communication system. Through the sensors a vehicle measures the LOS vector to the two other vehicles, and this applies to each vehicle, making three pairs of LOS vector measurements. Reference 5 shows that one LOS vector between each two vehicles provides sufficient information to determine all three relative attitudes in a three-vehicle formation. Because of the symmetric role of the three relative attitudes, they can be determined individually using a de- terministic method from Reference 6, which determines an attitude from a vector and the cosine of angle. Here a deterministic attitude estimation method is defined as (1) using the minimum number of measurements (three for three-axis attitude estimation) and (2) finding the attitude without need to minimize a cost function. When all the LOS vectors are in the same plane, however, covariance analysis shows that the deterministic attitude estimation method of Reference 5 has an observability problem (to first order). Although the problem can be relieved by not placing the LOS sensors of one vehicle in the same plane as that formed by the sensors of the other two vehicles, the remedy is effective only when the vehicles are large and sufficiently close to each other. A more subtle issue with the deterministic * Graduate Student, Department of Mechanical & Aerospace Engineering, University at Buffalo, State University of New York, Amherst, NY. Email: linares2@buffalo.edu. † Assistant Professor, Department of Aerospace Engineering. Email: cheng@ae.msstate.edu. Senior Member AIAA. ‡ Professor, Department of Mechanical & Aerospace Engineering, University at Buffalo, State University of New York, Amherst, NY. Email: johnc@buffalo.edu. Associate Fellow AIAA. 1