Controlling Rigid Formations of Mobile Agents Under Inconsistent Measurements

Abstract

Despite the great success of using gradient-based controllers to stabilize rigid formations of autonomous agents in the past years, surprising yet intriguing undesirable collective motions have been reported recently when inconsistent measurements are used in the agents' local controllers. To make the existing gradient control robust against such measurement inconsistency, we exploit local estimators following the well known internal model principle for robust output regulation control. The new estimator-based gradient control is still distributed in nature and can be constructed systematically even when the number of agents in a rigid formation grows. We prove rigorously that the proposed control is able to guarantee exponential convergence and then demonstrate through robotic experiments and computer simulations that the reported inconsistency-induced orbits of collective movements are effectively eliminated.

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

“…Furthermore, an incorrect shape with an undesired motion of the team of agents can be an attractive steady-state configuration as well. That creates a surprising connection with the recent findings on the robustness of undirected formations [15], [8], [12] so that the issue can be analyzed and potentially solved. Nevertheless, we will show an implementation technique for the correct estimation of the relative positions while agents run a distance-based formation algorithm.…”

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

“…In particular, deviations of up to but less than ± 90 degrees with respect to the optimal direction, ie, the one linking two (or more) neighboring agents, do not compromise the stability and convergence of the formation. On the other hand, a distance‐based formation is very sensitive to measurement errors, biases or inconsistencies of an interagent distance by its two adjacent agents as has been rigorously shown in the works of Mou et al and Garcia de Marina et al Therefore, we focus our analysis on studying the quantization in sensors that measure the distances and not the bearings, ie, in this paper, we consider the control term with quantized distance measurements in the form as . In practice, this choice of nonquantization of the bearing is also reasonable because the bearing measurement is always bounded (described by a unit vector, or by an angle in [ − π , π ) in the 2D case).…”

“…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.…”

A low cost indoor localization system for mobile robot experimental setup

“…The main contributions of this paper are as follow: i) an easy to set-open source and low cost indoor localization system, ii) a customable client-server for easy scaling up the system in terms of number of robots. This paper provides the low cost version to the solution used in (11), (14), (15), and (16).…”