Taming Mismatches in Inter-agent Distances for the Formation-Motion Control of Second-Order Agents

Abstract

This paper presents the analysis on the influence of distance mismatches on the standard gradient-based rigid formation control for second-order agents. It is shown that, similar to the first-order case as recently discussed in the literature, these mismatches introduce two undesired group behaviors: a distorted final shape and a steady-state motion of the group formation. We show that such undesired behaviors can be eliminated by combining the standard formation control law with distributed estimators. Finally, we show how the mismatches can be effectively employed as design parameters in order to control a combined translational and rotational motion of the formation.

Learning Shape Control of Multi-Agent Systems with Lagrangian Neural Networks

“…A framework for G is defined as the pair (G, q). Along the remained of the paper we assume that the framework (G, q) is infinitesimally and minimally rigid to guarantee exponential convergence to desired shapes (see [12], [18] and [7] for instance). We consider the desired distance between neighboring agents over the edge E k as d k and we further define the squared distance error for the edge E k as…”

On the observability of relative positions in left-invariant multi-agent control systems and its application to formation control

“…Without loss of generality, let us analyze three practical robustness issues through an example. Example 6.1: Consider a team of three agents, whose incidence matrix B describes a complete graph, and their desired distances are all equal to d. We assume that each agent only measures distances with respect to its neighbors, and they estimate their relative positions in a Kalman filter with model dynamics (5), or alternatively (6), and observations as in (7). Note that for implementing (5) agents need to communicate their velocities with their neighbors, and we consider that all the agents have the same orientation θ.…”

Quantization effects and convergence properties of rigid formation control systems with quantized distance measurements

“…Before giving the proof of Theorem 1, we first show some properties of the function V defined in (18). For the definition of function regularity in nonsmooth analysis, see, eg, chapter 2 in the work of Clarke 36 , k ∈ {1, … , ||} } for a uniform quantizer q u , or when e = 0 for a logarithmic quantizer q l .…”

“…We remark that formation shape control with distance measurement errors or biases was discussed in other works. [18][19][20][21] Measurement errors due to quantizations are different to measurement noises, in the sense that measurement errors induced by quantizations are deterministic, and some quantizers (especially logarithmic quantizers and binary quantizers) can also distinguish whether the quantity under quantization (distance error in the context of formation control) is zero. In this respect, measurements might be coarse from quantization, but the most important information (distance error being zero or not) is known without any noise.…”