Simultaneous Distributed Formation Tracking and Self-Localization for Constrained Nonholonomic Networks

Abstract

Motivated by the deployment of autonomous vehicle networks to ensure safe navigation in unstructured environments with insufficient prior terrain data, this thesis presents a comprehensive multi-vehicle coordination system for active area surveillance and mapping. To facilitate such missions, the proposed framework addresses the network coordination task through three primary objectives: (1) establishing robust formations to maintain inter-vehicle interactions, (2) guaranteeing cohesive, safe motion along a reference mission path, and (3) leveraging these formation interactions to localize vehicles and targets when global measurements are unavailable. However, establishing robust formations without relying on global positioning, full-state sharing, or centralized computation remains a fundamental control challenge. This thesis introduces distributed frameworks for bearing-based formation tracking control and simultaneous self-localization, tailored explicitly for networked vehicles operating under strict sensing, communication, and motion constraints. The proposed methodology leverages graph rigidity properties in conjunction with constrained optimal control to address four coupled formation objectives: geometric shape maintenance, time-varying trajectory tracking, collision avoidance, and relative localization. Unlike traditional schemes based on global or relative position tracking, this research develops distributed control architectures that rely primarily on local bearing measurements. The multi-agent framework exploits the infinitesimal rigidity of the sensing graph to ensure the formation shape is unique. The control laws are then designed to minimize inter-agent bearing errors to maintain the geometric structure, while simultaneously steering the formation along time-varying reference paths by achieving velocity consensus and orientation alignment. To accommodate the practical limitations of underactuated vehicles, the control design explicitly incorporates nonholonomic kinematic constraints and input saturation. Furthermore, the framework integrates Control Barrier Functions (CBFs) to strictly enforce safety-critical requirements, including inter-agent collision avoidance and sensor Field-of-View (FOV) limits. These safety and sensing formulations are incorporated into a distributed Quadratic Programming (QP) problem, which defines control-action filters to guarantee safety and ensure that neighboring agents remain within limited sensor coverage. This architecture prevents inter-agent collisions and preserves sensing graph connectivity during dynamic maneuvers. Concurrently, a distributed estimation scheme is introduced to resolve the scale ambiguity inherent in bearing-only formations. By exploiting the relative motion profiles of the agents and relative bearing measurements, the proposed nonlinear observer recovers the inter-agent distances and the formation’s global scale without requiring external anchors, distance measurements, or global references. The estimated scale and dynamics are fed into safety filters and control loops to maintain collision-free navigation and achieve a desired formation scale and orientation in large networks. The asymptotic stability and convergence of the closed-loop system over different network topologies are established through theoretical analysis. The performance of the proposed framework is validated through extensive numerical simulations and experimental implementations on mobile robot platforms, demonstrating robustness across diverse deployment scenarios.