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Rigid formation control with prescribed orientation

Most rigid formation controllers reported in the literature aim to only stabilize a rigid formation shape, while the formation orientation is not controlled. This paper studies the problem of controlling rigid formations with prescribed orientations in both 2-D and 3-D spaces. We propose two control approaches, one with centroid invariance and the other without preserving invariant formation centroid. The proposed controllers involve the commonly-used gradient descent control for shape stabilization, and an additional term to control the directions of certain relative position vectors associated with some chosen agents. The asymptotic convergence of the desired equilibrium is proven using the convergence property of gradient systems. Typical simulation examples are shown to support the analysis and performance of the proposed formation controllers.