A port-Hamiltonian approach to formation control using bearing measurements and range observers

In this paper we consider the problem of formation control using measurements of the bearings between vehicles. We design our system using port-Hamiltonian theory and the bondgraph modelling technique. Our approach builds upon the architecture presented in [22], which relied on partial measurements of relative position rather than position measurements with respect to an inertial frame. The previous work used a generalised form of the image Jacobians employed in image-based visual servo (IBVS) control literature to compute the desired control forces. However, the implementation of these measurement Jacobians requires unknown information about the relative positions of the vehicles. A key contribution of this paper is that we show how a depth observer can be integrated into the design to overcome this problem for the case where bearing measurements are available. Assuming that a single distance measurement is also available, we can specify a rigid goal formation in terms of the available measurements of relative positions. For this system, we prove local convergence to the desired configuration. We then provide a discussion regarding the implementation, and suggest that in practice, the distance measurement may be unnecessary. This discussion is supported by simulation results.