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Most rigid formation controllers reported in the literature aim to onlystabilize a rigid formation shape, while the formation orientation is notcontrolled. This paper studies the problem of controlling rigid formations withprescribed orientations in both 2-D and 3-D spaces. The proposed controllersinvolve the commonly-used gradient descent control for shape stabilization, andan additional term to control the directions of certain relative positionvectors associated with certain chosen agents. In this control framework, weshow the minimal number of agents which should have knowledge of a globalcoordinate system (2 agents for a 2-D rigid formation and 3 agents for a 3-Drigid formation), while all other agents do not require any global coordinateknowledge or any coordinate frame alignment to implement the proposed control.The exponential convergence to the desired rigid shape and formationorientation is also proved. Typical simulation examples are shown to supportthe analysis and performance of the proposed formation controllers.

Distributed stabilization control of rigid formations with prescribed orientation