High-Efficiency Vector Field by Time-Optimal Spatial Iterative Learning

This paper presents a novel model-free spatial iterative learning (IL) framework to enhance the efficiency of vector field (VF) navigation for mobile robots. By integrating the idea of iterative learning control (ILC) with VF, this framework utilizes historical data to enhance navigation efficiency significantly, reducing traversal time and expanding the applicability of IL to rapid navigation. Importantly, it has low time complexity with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$O(n)$</tex-math></inline-formula> per iteration, where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$n$</tex-math></inline-formula> denotes the waypoints number, preventing the significant computational overhead caused by the increasing waypoints in existing methods, which often exceeds <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$O(n^{2})$</tex-math></inline-formula>, making it well-suited for real-time planning. Moreover, the approach is inherently model-free, leaning on historical data, thus enabling agile navigation with limited reliance on intricate model details. The paper presents a comprehensive theoretical analysis of the stability, time optimality, time complexity, parameter insensitivity, robustness, and usage. Extensive simulations and experiments highlight its efficiency, promising a transformative impact on mobile robot navigation through the proposed IL.