Adaptive stabilization of a leaderless bearing-constrained formation with disturbances

Minh Hoang Trinh; Chuong Van Nguyen; Quoc Van Tran; Tuynh Van Pham

cs.MASep 6, 2026

Adaptive stabilization of a leaderless bearing-constrained formation with disturbances

Authors: Minh Hoang Trinh, Chuong Van Nguyen, Quoc Van Tran, Tuynh Van Pham

Organizations: East Asia University of Technology, Hanoi, Vietnam · Viterbi School of Engineering – Department of Aerospace and Mechanical Engineering, University of Southern California, CA, USA and Ghost Robotics, Philadelphia, PA, USA · Department of Mechatronics, School of Mechanical Engineering, Hanoi University of Science and Technology, Hanoi, Vietnam · Department of Automation Engineering, School of Electrical and Electronic Engineering, Hanoi University of Science and Technology, Hanoi, Vietnam

Abstract

In this paper, we consider the problem of regulating and maintaining a target formation characterized by a set of bidirectional bearing constraints under disturbances. The agents in the formation are modeled by single integrators with bounded continuous disturbances of which the upper bound is unavailable for the control design. Due to the time-varying disturbances, the target formation is time-varying. We propose adaptive sliding mode control laws to uniformly globally asymptotically stabilizes the moving target formation and reject the matched disturbances. In addition, to alleviate chattering phenomena from sliding mode control, smooth adaptive control laws are then designed to guarantee uniform global boundedness of the desired formation. Finally, simulation results are given to support the analysis.

Figures & tables

Fig. 1 : The diagram describes the system ( 38 ). If the scaling disturbance component $\mathbf{d}_{3}$ is zero, then the system is constrained on $\|\boldsymbol{\delta}+\mathbf{r}^{d}\|=\|\mathbf{r}^{d}\|=\|\mathbf{r}^{d}(0)\|$ . If the scaling disturbance $\mathbf{d}_{3}$ is nonzero, then $\|\boldsymbol{\delta}\|$ may increase or decrease.

$k$	1	2	3	4	5	6
$\mathbf{p}_{k}$	$\begin{bmatrix}{1.96}\\ {-3.24}\end{bmatrix}$	$\begin{bmatrix}{0.5}\\ {2.35}\end{bmatrix}$	$\begin{bmatrix}{-3.39}\\ {-0.2}\end{bmatrix}$	$\begin{bmatrix}{-5.6}\\ {-0.3}\end{bmatrix}$	$\begin{bmatrix}{-2.0}\\ {-5.3}\end{bmatrix}$	$\begin{bmatrix}{3.8}\\ {-1.2}\end{bmatrix}$
$\gamma_{k}$	0.13	0.51	0.18	0.79	0.85	0.5
$\gamma_{6+k}$	0.85	0.08	0.51	0.07	0.43	0.1

TABLE I : The initial positions

\mathbf{p}_{k}(0)

k=1,\ldots,6,

and adaptive gains

\gamma_{k}(0),k=1,\ldots,12

Panel of Figure 3 — Fig. 2 : A regular graph $\mathcal{G}$ of six-vertices in simulation.

Panel of Figure 4 — Fig. 3 : Simulation of six-agent system under the adaptive sliding-mode bearing-based control law ( 6 ).

Panel of Figure 5 — Fig. 4 : Simulation of 6-agent system under the adaptive bearing-based control law ( 21 ).

Panel of Figure 6 — Fig. 5 : Simulation of six-agent system under the adaptive sliding-mode bearing-only control law ( 23 ).

Panel of Figure 7 — Fig. 6 : Simulation of six-agent system under the smooth bearing-only control law ( 40 ).

Multi-Robot Formation Control

Multi-robot formation control coordinates robots to maintain, change, or navigate in groups while meeting task and safety constraints.

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Topological Online Learning for Displacement-based Formation Control

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This paper addresses the problem of robust formation control by introducing Topological Online Learning for Displacement-based (TOLD) formation control, a real-time edge-level adaptation framework. Unlike conventional node-level robust controllers that regulate individual robot inputs without modifying the interaction topology, TOLD updates the interaction topology weights online to directly minimize formation distortion. Two strategies are proposed under the TOLD formation control framework: Online Gradient Flow (OGF) with unconstrained weights and Online Exponential Gradient Flow (OExpGF) with non-negative convex weights. Theoretical analysis establishes that, for single-integrator agents over directed graphs, OExpGF guarantees asymptotic consensus, while OGF ensures bounded formation distortion. Simulations with twelve robots under intermittent disturbances show 1.2%-33.14% median cumulative Root Mean Distortion Error reduction when augmenting TOLD with node-level controllers. Hardware experiments with Crazyflie 2.0 quadrotors demonstrate over 62% (OGF) and 31.4% (OExpGF) reduction in median formation distortion compared to fixed-weight consensus.

Abstract

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