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
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 d3 is zero, then the system is constrained on ∥δ+rd∥=∥rd∥=∥rd(0)∥ . If the scaling disturbance d3 is nonzero, then ∥δ∥ may increase or decrease.
k
1
2
3
4
5
6
pk
[1.96−3.24]
[0.52.35]
[−3.39−0.2]
[−5.6−0.3]
[−2.0−5.3]
[3.8−1.2]
γk
0.13
0.51
0.18
0.79
0.85
0.5
γ6+k
0.85
0.08
0.51
0.07
0.43
0.1
TABLE I : The initial positions pk(0) , k=1,…,6, and adaptive gains γk(0),k=1,…,12 .
Fig. 2 : A regular graph G of six-vertices in simulation.
Fig. 3 : Simulation of six-agent system under the adaptive sliding-mode bearing-based control law ( 6 ).
Fig. 4 : Simulation of 6-agent system under the adaptive bearing-based control law ( 21 ).
Fig. 5 : Simulation of six-agent system under the adaptive sliding-mode bearing-only control law ( 23 ).
Fig. 6 : Simulation of six-agent system under the smooth bearing-only control law ( 40 ).
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.
Saksham Sharma, Shubhankar Gupta, Sumant A Gunagi +1
ArtGarage, Indian Institute of Science, India · Department of Aerospace Engineering, Indian Institute of Science, India
This paper investigates a planar tracking problem between a leader and follower agent. We propose a novel feedback speed control law, paired with a constant bearing steering strategy, to maintain an abreast formation between the two agents. We prove that the proposed control yields asymptotic stability of the closed-loop system when the steering of the leader is known. For the case when the leader's steering is unavailable to the follower, we show that the system is still input-to-state stable with respect to the leader's steering viewed as an input. Furthermore, we demonstrate that if the leader's steering is periodic, the follower will asymptotically converge to a periodic orbit with the same period. We validate these results through numerical simulations and experimental implementations on mobile robots. Finally, we demonstrate the scalability of the proposed approach by extending the two-agent control law to an N-agent chain network, illustrating its implications for directional information propagation in biological and engineered flocks.
Xincheng Li, Tengyue Liu, Udit Halder
Department of Mechanical and Aerospace Engineering, University of South Florida
This paper considers the perception safety problem in distributed vision-based leader-follower formations, where each robot uses onboard perception to estimate relative states, track desired setpoints, and keep the leader within its camera field of view (FOV). Safety is challenging due to heteroscedastic perception errors and the coupling between formation maneuvers and visibility constraints. We propose a distributed, formation-aware adaptive conformal prediction method based on Risk-Aware Mondrian CP to produce formation-conditioned uncertainty quantiles. The resulting bounds tighten in high-risk configurations (near FOV limits) and relax in safer regions. We integrate these bounds into a Formation-Aware Conformal CBF-QP with a smooth margin to enforce visibility while maintaining feasibility and tracking performance. Gazebo simulations show improved formation success rates and tracking accuracy over non-adaptive (global) CP baselines that ignore formation-dependent visibility risk, while preserving finite-sample probabilistic safety guarantees. The experimental videos are available on the project website\footnote{Project Website: https://nail-uh.github.io/iros2026.github.io/}.
Richie R. Suganda, Bin Hu
Department of Electrical and Computer Engineering, University of Houston, Houston, TX 77004, USA. · Department of Engineering Technology, University of Houston, Houston, TX 77004, USA.