Decentralized control of parallel rigid formations with direction constraints and bearing measurements

Abstract

Abstract-In this paper we analyze the relationship between scalability, minimality and rigidity, and its application to cooperative control. As a case study, we address the problem of multi-agent formation control by proposing a distributed control strategy that stabilizes a formation described with bearing (direction) constraints, and that only requires bearing measurements and parallel rigidity of the interaction graph. We also consider the possibility of having different graphs modeling the interaction network in order to explicitly take into account the conceptual difference between sensing, communication, control, and parameters stored in the network. We then show how the information can be 'moved' from a graph to another making use of decentralized estimation, provided the parallel rigidity property. Finally we present simulative examples in order to show the validity of the theoretical analysis in some illustrative cases.

Bearing-Based Formation Control of A Group of Agents with Leader-First Follower Structure

“…Another approach is based on bearing rigidity, in which the target formation is characterized by a set of desired bearing vectors, which are sufficient to specify the formation up to a scaling and a translation. In two-dimensional space, the concept of bearing rigidity (or parallel rigidity) has been studied in [19], [20]. Based on parallel rigidity theory, the authors in [20] defined the bearing constrained rigidity matrix.…”

“…In two-dimensional space, the concept of bearing rigidity (or parallel rigidity) has been studied in [19], [20]. Based on parallel rigidity theory, the authors in [20] defined the bearing constrained rigidity matrix. Recently, the authors of [21] developed a theory of bearing rigidity and infinitesimal bearing rigidity in R d .…”

Bearing-only formation control using an SE(2) rigidity theory

“…Recently, there has been a growing interest in formation control strategies using bearings leading to the development of the bearing rigidity theory [8], [11], [15], [16]. In this work we employ an extension of these works to frameworks embedded in the Special Euclidean Group SE(2), originally considered in our previous work [1].…”

“…Whereas rigidity theory is useful for maintaining formations specified by fixed inter-agent distances, bearing rigidity attempts to keep the bearing vector between neighboring agents constant (with no constraints on the scale of the formation). Bearing rigidity was used in [8]- [11] for deriving distributed control laws for controlling formations with bearing measurements. Bearing rigidity has also proven useful for stabilization of formations using direction-only or line-of-sight only constraints [12]- [15].…”

A Distributed Optimization Framework for Localization and Formation Control: Applications to Vision-Based Measurements

“…Approaches such as those by Bishop et al [5,7,8] and Zhao and Zelazo [77] require, during the control operations, also the distances between agents in addition to the relative directions (that is equivalent to say that they require the full relative positions, thus imposing restrictions on their application). Other approaches, such as those by Zhao and Zelazo [78], Franchi et al [27,26], and Stacey and Mahony [63] require only one or no distance measurements. This is achieved by either directly specifying a control law that does not require them (as in [78]), or by substituting the unknown distances with quantities estimated from triplets of nodes [27], distributed estimators [26], or on-line local estimators plus information on the agents' velocity [63].…”