Dynamic compressed sensing and coverage optimization for multi-agent systems

Abstract

Sensing is a critical application in most real-life scenarios. Collecting and predicting data of large-scale dynamics quickly using very few sensors is a crucial problem in real-life applications. As we navigate this landscape of sensor-based systems, this dissertation addresses the challenges, intricacies, and details of various critical applications, starting with the pursuit of optimal coverage, robust recovery from sensor loss, and exploring an area of non-uniform coverage importance. The spotlight then shifts to dynamic compressed sensing to replace multiple static sensors with a single mobile robot, examining its applications and extending its principles to multi-robot coordination, exploring an unknown flow environment, and adaptive trajectory optimization to develop the low-rank model of the flow. Two fixed-wing unmanned aerial vehicle (UAV) area coverage algorithms are introduced in Chapters 2 and 3, leveraging their endurance advantages for long-term and large-scale deployment. The homogeneous approach deploys a UAV fleet using hexagon and square packing for continuous coverage, producing resilience against simultaneous multiple node loss. The heterogeneous approach starts with uniform coverage of an arbitrarily shaped area and enables localized and distributed recovery from multiple node failures. Chapter 4 introduces an algorithm that optimizes paths for a mobile robot exploring a target area with nonuniform importance, considering power constraints and limited movement ability at each time step to maximize coverage and net importance reward. While effective, these approaches have substantial data and communication requirements and necessitate a large sensor fleet size for the first two approaches. The core of this thesis, the dynamic compressed sensing (DCS) algorithm, is then introduced in Chapter 5. DCS is an extension of the well-established compressed sensing approach. Optimal sensing locations are identified using the fluid flow field properties to guide the planning of an optimal path for a sensor-equipped autonomous vehicle, replacing the conventional static sensors for efficient reconstruction performance using reduced sampling. The path aims for spatiotemporal efficiency, ensuring the vehicle is at crucial locations during the flow’s temporal cycle. The algorithm uses proper orthogonal decomposition (POD) techniques on known target flow fields to evaluate dataset-specific POD bases, determining when to visit subsets of locations for minimal error. Subsequently, an optimal path for fuel and time is devised for the vehicle to autonomously visit these locations at specified points in the flow cycle to capture the desired information. The multi-agent coordination dynamic compressed sensing (MAC-DCS) to explore unknown environments using a fleet of mobile robots and develop the low-rank model of the flow is discussed in Chapter 6. MAC-DCS compares various sensor deployment methods (random static, compressed sensing static, passive drifters, and random straight shooting trajectories) and reconstruction techniques (Gaussian process regression, data-based and true POD modes) for flow field estimation in a double-gyre environment to study the effect of dividing the spatiotemporal sensing load amongst the varying fleet size of static sensors or mobile robots. The simulations are extended to a real-world scale with measurement noise, and other practicalities, such as the effect of background flow, are considered to assess the efficacy of the MAC-DCS approach. This research offers a scalable solution for dynamic environmental monitoring. This applies to various scenarios, including well-studied flow fields like ocean gyres and currents and less-explored phenomena such as lava flows, floods, hurricanes, and more. MAC-DCS can significantly enhance the capabilities of data-driven sensing and modeling in fluid dynamics and atmospheric science. The preliminary results of a potential extension of this work, online dynamic compressed sensing (Online DCS), are introduced in future work (Chapter 7). Online DCS is a dynamic flow field sampling algorithm that employs static sensors and a mobile robot for collaborative measurements for low-rank model development in an unknown flow environment. The static sensors provide infinite temporal resolution measurements, and the mobile robot enhances spatial coverage through trajectories divided into fixed-interval segments, followed by an iterative predict-measure cycle. After each segment, the collected data modifies the low-rank flow model basis. The next robot waypoint is determined, and the prediction cycle uses the low-rank basis to forecast flow maps for the upcoming segment. Convergence is characterized by the narrowing progressive error, and iterations are terminated at a specified error threshold. The low-rank model identifies the flow behavior and potentially the underlying mathematical framework. The key contributions of this dissertation work include (i) resilient coverage algorithms to recover from simultaneous multiple node failures, (ii) optimal trajectory optimization for exploring an area of non-uniform coverage importance, (iii) optimized sensing locations for the DCS algorithm, prioritizing mobile robot visits over static sensors, (iv) time and energy optimal trajectory for efficient flow reconstruction, (v) MAC-DCS and Online DCS algorithms for developing the low-rank model of an unknown flow, and crucially, (v) collaborative coordination of sensor fleet for enhanced efficiency and application range.