Triangular formation maneuver using designed mismatched angles

This paper investigates the problem of triangular formation maneuver control for mobile 3-agent systems with bearing measurements. Different from controlling rigid formations' maneuvering by introducing a pair of mismatches per distance constraint, we introduce a pair of designed-mismatches per angle constraint which leads to the desired triangular formation shape. Considering that for the control of triangular formations with angle constraints, each agent aims at maintaining its own interior angle, to realize the formation maneuver control we design the mismatches into each agent's own desired interior angle. Two types of designed-mismatch are investigated: time-varying case and constant case. For the time-varying case, under the assumption that each agent can additionally measure the relative position from itself to the formation centroid, the triangular formation maneuver control algorithm is designed such that the desired maneuvering in terms of translation, rotation, and scaling can be realized. For the constant case, under the constraint that the desired triangular shape is known only once for the mismatch design, the triangular formation maneuver control algorithm is also proposed, and the angle dynamics are derived by using the dot product of two bearing vectors. Finally, simulation examples demonstrate the effectiveness of the theoretical results.