arXiv subjects

Nelson P. K. Chan

Publications and source records attributed to Nelson P. K. Chan.

4 recordsLinked to original sources

arXiv2021

Securing Isosceles Triangular Formations under Heterogeneous Sensing and Mixed Constraints

This paper focuses on securing a triangular shape (up to translation) for a team of three mobile robots that uses heterogeneous sensing mechanism. Based on the available local information, each robot employs the popular gradient-based control law to attain the assigned individual task(s). In the current work, robots are assigned either distance and signed area task(s) or bearing task(s). We provide a sufficient condition on the gain ratio $R_{\text{Ad}}$ between the signed area and the distance control term such that the desired formation shape, an isosceles triangle, is reached from all feasible starting positions. Numerical simulations are provided to support the theoretical analyses.

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arXiv2020

Stability Analysis of Gradient-Based Distributed Formation Control with Heterogeneous Sensing Mechanism: Two and Three Robot Case

This paper focuses on the stability analysis of a formation shape displayed by a team of mobile robots that uses heterogeneous sensing mechanism. Depending on the convenience and reliability of the local information, each robot utilizes the popular gradient-based control law which, in this paper, is either the distance-based or the bearing-only formation control. For the two and three robot case, we show that the use of heterogeneous gradient-based control laws can give rise to an undesired invariant set where a distorted formation shape is moving at a constant velocity. The (in)stability of such an invariant set is dependent on the specified distance and bearing constraints. For the two robot case, we prove almost global stability of the desired equilibrium set while for the three robot case, we guarantee local asymptotic stability for the correct formation shape. We also derive conditions for the three robot case in which the undesired invariant set is locally attractive. Numerical simulations are presented for illustrating the theoretical results in the three robot case.

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arXiv2020

Angle-Constrained Formation Control for Circular Mobile Robots

In this letter, we investigate the formation control problem of mobile robots moving in the plane where, instead of assuming robots to be simple points, each robot is assumed to have the form of a disk with equal radius. Based on interior angle measurements of the neighboring robots' disk, which can be obtained from low-cost vision sensors, we propose a gradient-based distributed control law and show the exponential convergence property of the associated error system. By construction, the proposed control law has the appealing property of ensuring collision avoidance between neighboring robots. We also present simulation results for {a team} of four circular mobile robots forming a rectangular shape.

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arXiv2018

Distributed estimation from relative measurements of heterogeneous and uncertain quality

This paper studies the problem of estimation from relative measurements in a graph, in which a vector indexed over the nodes has to be reconstructed from pairwise measurements of differences between its components associated to nodes connected by an edge. In order to model heterogeneity and uncertainty of the measurements, we assume them to be affected by additive noise distributed according to a Gaussian mixture. In this original setup, we formulate the problem of computing the Maximum-Likelihood (ML) estimates and we design two novel algorithms, based on Least Squares regression and Expectation-Maximization (EM). The first algorithm (LS- EM) is centralized and performs the estimation from relative measurements, the soft classification of the measurements, and the estimation of the noise parameters. The second algorithm (Distributed LS-EM) is distributed and performs estimation and soft classification of the measurements, but requires the knowledge of the noise parameters. We provide rigorous proofs of convergence of both algorithms and we present numerical experiments to evaluate and compare their performance with classical solutions. The experiments show the robustness of the proposed methods against different kinds of noise and, for the Distributed LS-EM, against errors in the knowledge of noise parameters.

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