Stabilizing Angle Rigid Formations with Prescribed Orientation and Scale

Angle rigid formations have the advantage of requiring only local bearing/direction measurements in their implementation. However, the capability of controlling the orientation and scale of these formations has not been explored. This undetermined orientation and scale can degrade the robustness of the formation against measurement noise. To maintain both advantages of requiring less sensor measurements and sustaining robustness against measurement noise, this article aims to achieve a desired angle rigid formation while simultaneously controlling its orientation and scale. In this article, we first design a formation algorithm for the first three agents to achieve a desired triangular formation with prescribed orientation and scale. Using the control gain design technique, we then design formation control algorithms for the remaining agents such that the overall desired formation can be achieved under a vertex addition operation. We present the role of generic property from angle rigidity for the formation's stability analysis. We also highlight that with one additional relative position measurement or two additional communication channels, the local convergence to the corresponding desired formation can be improved to a global convergence. Experiments are conducted to validate the theoretical results and the advantages are highlighted in comparison with other two formation control laws.