Bearing-based Simultaneous Localization and Affine Formation Tracking for Fixed-wing Unmanned Aerial Vehicles

TL;DR

This work addresses bearing-based simultaneous localization and affine formation tracking (SLAFT) for fixed-wing UAVs, where only some agents (leaders) know global positions while followers rely on bearing measurements. It couples a bearing-based localization algorithm with an observer-like affine formation controller, and extends the SLAFT framework to nonlinear, nonholonomic 3D UAV dynamics with time-varying inter-agent bearings. Two control schemes are proposed: a standard SLAFT and a perturbation-based variant to avoid unlocalizable configurations, with stability analyses showing convergence under appropriate conditions such as persistent excitation. Simulations in 2D and 3D validate that followers can localize globally and track time-varying affine formations while bearings converge to their targets, demonstrating practical applicability in GPS-denied and perception-restricted environments.

Abstract

This paper studies the bearing-based simultaneous localization and affine formation tracking (SLAFT) control problem for fixed-wing unmanned aerial vehicles (UAVs). In the considered problem, only a small set of UAVs, named leaders, can obtain their global positions, and the other UAVs only have access to bearing information relative to their neighbors. To address the problem, we propose novel schemes by integrating the distributed bearing-based self-localization algorithm and the observer-based affine formation tracking controller. The designed localization algorithm estimates the global position by using inter-UAV bearing measurements, and the observer-based controller tracks the desired formation with the estimated positions. A key distinction of our approach is extending the SLAFT control scheme to the bearing-based coordination of nonholonomic UAV systems, where the desired inter-UAV bearings can be time-varying, instead of constant ones assumed in most of the existing results. Two control schemes with different convergence rates are designed to meet desired task requirements under different conditions. The stability analysis of the two schemes for SLAFT control is proved, and numerous simulations are carried out to validate the theoretical analysis.

Figures (10)

• Figure 1: An illustration of bearing-based simultaneous localizationa and affine formation control scheme.
• Figure 2: Model Description of Fixed-wing UAVs in three-dimensional space.
• Figure 3: An illustration of projection-inspired control scheme for fixed-wing UAVs in three-dimensional space.
• Figure 4: The interaction topology of fixed-wing UAVs in two-dimensional space.
• Figure 5: Trajectories of six UAVs achieving target affine formations in two-dimensional space. Different colors in the trajectories represent the different stages of the affine transformation. The red wedge-shape icons indicate the leaders and the remaining three dark cyan wedge-shape icons are the followers. The dotted dashed lines among the UAVs represent the information connections.

Theorems & Definitions (19)

• Definition 1: Target Formation
• Definition 2: Affine Localizability 2018_zhao_TAC
• Lemma 1: Bearing Localizability zhao_localizability_2016
• Remark 1
• Remark 2
• Remark 3
• Remark 4
• Remark 5
• Theorem 1
• proof