Formation stabilization and resizing based on the control of inter-agent distances

Abstract

We propose a control strategy that could steer the group of mobile agents in the plane to achieve a specified formation. The control law could be implemented in a fully decentralized manner so that each agent moves on their own local reference frame. Under the acyclic minimally persistent graph topology, each agent measures the relative displacements of neighboring agents and then adjusts the distances between them to achieve the desired formation. As well as achieving a fixed formation, we could resize the formation only by changing the leader edge, which connects the leader with the first-follower in acyclic minimally persistent graph, without changing the structures of the control law.A directed graph, which is denoted by G D .V; E/, is a pair of two sets, where V D ¹1; 2; : : : ; N º is a set of vertices, and E Â V V is a set of edges. Thus, we have jVj D N . We assume that there is no self edge, that is, .i; i/ … E for all i 2 V, and there are no multiple edges between By stacking the relative displacements, we have § The derivative of g is the sum of products consisting of e 12 ; e 13 ; e 23 ; O e 13 ; O e 23 ; z 12 ; z 13 , and z 23 terms that are bounded. ProofFrom (17), if .z 0 / D 0, then .z.t // D 0 for all t > 0 along the solution trajectory of (9). Corollary 3.2 means that if the agents are initially collinear, then they are collinear ever after. This result is the same as the cases that could be found in the literature dealing with distance-based formation control problems [6-8, 13, 15].

Exponential and practical exponential stability of second-order formation control systems

“…On a more intuitive level, one can say that the sinusoidal perturbations in (15) allow the agents to explore changes of their local potential functions in a small neighborhood of their current position. In this way they can gather gradient information, which in turn allows an approximation of the gradient-based control (5). The oscillations are required to compensate the reduced amount of information of distanceonly measurements.…”

“…In this section, we provide simulation results to demonstrate the behavior of (2) under the distance-only control law (15) and to allow a comparison with the behavior of (2) under the gradient-based control law (5). We consider a system of N = 4 double-integrator agents in the Euclidean space of dimension n = 2.…”

Adaptive estimator‐based formation maneuvering control of nonholonomic mobile robots

“…Different from position‐ and displacement‐based formation control, distance‐based formation control focuses on the distances between agents such that the formation achieves a particular shape described by the desired distances between pairs of agents. Utilizing relative position obtained in the local frames instead of global position information in controller design, gradient‐based control laws have been widely used to address formation shape control problem . Although the nonlinearity of the proposed control laws complicates the stability analysis of the multiagent system, much effort has been made in this research area.…”

“…Utilizing relative position obtained in the local frames instead of global position information in controller design, gradient-based control laws have been widely used to address formation shape control problem. [2][3][4][5][6][7] Although the nonlinearity of the proposed control laws complicates the stability analysis of the multiagent system, much effort has been made in this research area.…”

Translational and Scaling Formation Maneuver Control via a Bearing-Based Approach

“…By adjusting the scale of a formation, a team of agents can dynamically respond to their surrounding environment to, for example, avoid obstacles. The problem of formation scale control has been studied by the relativeposition and distance-based approaches in [17], [18]. However, since neither the relative positions nor distances are invariant to the formation scale, these two approaches result in complicated estimation and control schemes in which follower agents must estimate the desired formation scale known only by leader agents.…”