A Revisit to Gradient-Descent Bearing-Only Formation Control

Abstract

This paper addresses the problem of bearing-only formation control of multi-agent systems, where each agent can merely obtain the relative bearing measurements of their neighbor neighbors whereas relative distance or position measurements are unavailable. In particular, we revisit a bearingonly formation control law proposed in [1]. Unlike many other existing ones, this control law is gradient-descent, which is favorable from the stability analysis point of view. It has the potential to be extended to handle more complex agent models and moving target formations. Up to now, this control law has not attracted sufficient attention probably because its stability analysis is based on optimization techniques and challenging to generalize. The contribution of this paper is to present a new stability analysis of this formation control law based on Lyapunov approaches. The new stability analysis reveals some new properties of the control law such as exponential convergence rate and lays a foundation for deriving new bearing-only control laws in the future.

A scalable algorithm for the decomposition of minimally rigid graph

“…There have been three approaches describing multi-agent formation, that is, displacementbased formation control, [2][3][4][5][6] distance-based formation control, [7][8][9] and bearing-only formation control. [10][11][12][13] Among the three approaches, distance-based formation control is regarded as a more ideal distributed approach, since the collision between the neighboring agents can be avoided. In the distance-based formation control, graph rigidity was crucial for the formation control, since it could maintain the specified geometry, as discussed in the work by Eren et al 14 It is showed that if the communicated topology graph is rigid, the formation shape could be maintained.…”

“…, and the edges in E c are assigned to n À 2 distinct vertices belong to V s in a scalable way via communication. We choose the initialized edge as (1,15; the initialized edge is not unique), and the output of the algorithm is as follows (3,9), (1, 10), (2, 11), (8,12), (4, 13), (7,14), (1,16), (11,17), (9,18), (3,19), (8,20)g 3, 4, 5, 6, 7, 15, 8, 9, 10, 11, 12, f 13, 14, 16, 17, 18, 19, 20g E c = f(3, 2), (4, 3), (5,4), (6,4), (7, 6), (7,15), (8,5), (9,8), (10,3), (11,3), (12,11), (13,11), (14,13), (16,13), (17,12), (18,11), (19,12), (20,…”

Securing and Maneuvering Heterogeneous Mobile Robot Formations: Distributed Control Design and Stability Analysis

“…Each type of robots is required to maintain on the individual level some constraints relative to members of the other type, i.e., a distance (or bearing) robot is tasked to maintain distance (or bearing) constraints relative to some bearing (or distance) robots within the team. In performing these individual tasks, existing gradient-based control laws in literature [48,53] are implemented. Curious to what collective formation the team may display, we analyze the team consisting of two and three members.…”

“…When the formation shape is specified by inter-robot relative positions [41], then the consensus-based formation control approaches, which are linear, can be used directly. For realizing a formation shape using only distance [23,28], bearing [53], or angle constraints [16], the notion of rigidity [6,16,55] for the underlying interconnection topology is required. The condition of rigidity describes the motions for the whole formation which preserve the formation shape.…”

“…The condition of rigidity describes the motions for the whole formation which preserve the formation shape. Gradient-based control laws are a popular approach for realizing the formation shape specified by distance [48] or bearing constraints [53]. A formation shape can also be realized by a set of mixed constraints; see, among others, [9,29,31].…”