Multi-Resolution for Efficient, Scalable and Accurate Volumetric Mapping and Planning in Robotics

Abstract

As robots evolve beyond industrial settings to address broader challenges, such as autonomous inspection, home assistance, and search and rescue, there is a growing demand for them to autonomously navigate and perform meaningful tasks in increasingly large, unstructured, and unknown environments. Despite improvements in hardware, sensing, and computational technologies enabling greater robot agility and perception, a significant bottleneck remains in their software, particularly in autonomous mapping and navigation capabilities. Volumetric maps offer a general, safe, and task-agnostic representation of the environment but are hindered by their excessive computational and memory demands, limiting their practical use on small and affordable robots. This doctoral thesis investigates the use of adaptive representations as a solution to these challenges, focusing on enhancing the scalability, efficiency, and accuracy of volumetric maps. Recognizing that the value of volumetric maps is determined by the benefits they bring to downstream tasks, we study local and global planning as two representative applications. Leveraging hierarchical, multi-resolution approaches, this work aims to dynamically balance the trade-off between detail and computational cost, tailored to the mission's needs. The main contribution of this thesis is the development of a mathematically rigorous multi-resolution mapping framework, named wavemap, that adjusts the map's resolution based on the environment's geometry without reliance on heuristics. The MRA theory guarantees that using wavelet decomposition, new observations can safely and efficiently be integrated into the map in a coarse-to-fine manner. The resulting gains in computational efficiency, together with early stopping criteria for the integrator, allow us to use a more complex measurement model that improves the capture of thin objects, thereby enhancing the safety and reliability of robotic operations. The framework is extensively evaluated on synthetic and real data, and shown to efficiently reconstruct large-scale environments while accurately capturing fine details. Beyond significant improvements in terms of scalability and map quality, the framework's flexibility facilitates its use across a wide range of sensors and applications. Our second and third contributions are efficient methods for reactive obstacle avoidance and deterministic global path planning, utilizing hierarchical representations and algorithms alongside the wavemap framework to enable rapid, reliable navigation through complex environments. Experimental evaluations on maps of diverse, real environments and deployments on a micro aerial vehicle demonstrate the superiority of these approaches over existing methods in terms of efficiency, accuracy, and flexibility, underscoring their potential to significantly advance the field of robotic mapping and navigation. In sum, this doctoral thesis presents a comprehensive solution to the challenges of volumetric mapping and planning in robotics, paving the way for more autonomous, efficient, and versatile robotic systems capable of operating in diverse and changing environments.