Bearing-compass formation control: A human-swarm interaction perspective

Abstract

The paper considers the distributed formation control problem given bearing-only sensing of nearby agents with respect to a global vector frame, provided by a compass. We propose a bearing-compass control law and prove its convergence to a formation that is unique up to translation and scaling. We present results that describe the formation's evolution in terms useful to a human operator, focusing on scale, translation and rotation of the formation. The results are supported with a number of illustrative examples.

Formations on directed cycles with bearing‐only measurements

“…In this section, we study planar formations under the bearing-only control law (9). We focus on a special case in this class, ie, formations with 3 agents.…”

“…A desired formation is given in A. An undesired formation is given in B, where g 1 = −g * 1 , g 2 = g * 2 , g 3 = −g * 3 , and g 4 = g * 4 FIGURE 8 Formation of n agents under control law (9) Consider a directed cycle formation in R 2 . As in the case of a triangle, let α i be the magnitude of the angle between g i and g * i , as shown in Figure 8 and note that 0 ≤ α i ≤ π.…”

“…Theorem 2. In R 2 , suppose that 0 ≤ α i (0) ≤ π 2 for i = 1, … , n. Under Assumptions 1 and 2 and the control law (9), α → 0 asymptotically, ie, the agents asymptotically converge to a formation satisfying all the desired bearing vectors. α i = α j ∀i, j = 1, … , n and one of the following conditions holds: (i) α i = α j = 0, ∀i, j = 1, … , n or (ii) there exists a straight line in 2D such that all desired bearing vectors g * i are equally inclined with it by an angle α.…”

“…Recently, as vision sensors and vision‐based techniques are becoming ubiquitous, bearing‐based formation control has generated a lot of research interest. ()…”

“…Recently, as vision sensors and vision-based techniques are becoming ubiquitous, bearing-based formation control has generated a lot of research interest. [7][8][9][10] In bearing-based formation control problems, a group of autonomous agents is required to achieve a target formation shape defined by some bearing variables. These variables are known as the subtended bearing angles or the relative bearing vectors.…”