Farber M. Topology and AI...Aspects of Algorithms for Autonomous Motion 2024

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Farber M. Topology and AI...Aspects of Algorithms for Autonomous Motion 2024

Textbook in PDF format The task of programming a machine to move autonomously and to make autonomous decisions is one of the major challenges of AI. The algorithms generating autonomous robot motions and autonomous decisions are sections of certain fibre bundles and their complexity and structure can be understood using tools of algebraic topology. The book gives an overview of the current achievements in the field of topological robotics concerned with motion algorithms, and in particular how their complexity depends on the topology of the configuration space of the system and the external conditions. The book is a collection of survey articles written by leading researchers in the fields of mathematics, engineering and computer science, with each chapter surveying a different theme or technique. Frontmatter Preface Autonomous robots, motion algorithms and topology Equivalent environments and covering spaces for robots Some geometric and topological data-driven methods in robot motion path planning Towards control, learning and intelligence in reconfigurable systems Geometric and topological properties of manifolds in robot motion planning Equivariant topological complexities Computing with the TC-canonical class Motion planning in real projective spaces Generalized topological complexity and its monoidal version Robotics and the fundamental group Geodesic complexity Farber’s conjecture and beyond Topological complexity of a map Distributional topological complexity and LS-category List of contributors