Navigation function tuning using randomized algorithms
Date
2025
Authors
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Publisher
University of Delaware
Abstract
This thesis proposes an approach to quantitatively optimize navigation function parameters for robot motion planning in sphere worlds, utilizing randomized algorithms with statistical learning theory. ☐ Our methodology employs a Monte Carlo simulation-based sampling protocol to tackle the intricacies of navigation parameter optimization. Importantly, we use randomized algorithms in conjunction with desired probability levels to determine the appropriate sample sizes. We also introduce two key navigation performance metrics: average maximum curvature difference along paths and average bounded area deviation along a path for assessing the impact of parameter k on navigation smoothness and convergence efficiency. Finally, we identify an optimal k value that balances navigation efficiency and trajectory smoothness under certain probability levels. ☐ Our work validates the efficacy of applying randomized algorithms and statistical learning to navigation function optimization under probabilistic constraints. Despite computational time limitations and inherent simulation uncertainties, this study advances the field by proposing a quantitatively rigorous, probability-based method for automatic navigation function tuning. ☐ This research represents the first data-driven attempt to quantitatively optimize navigation function parameters and achieves state-of-the-art performance. The findings of this thesis contribute to robot motion planning, paving the way for enhanced navigation in complex environments and marking a crucial step towards more adaptable, efficient, and provably correct motion planning methodologies.
Description
Keywords
Statistical learning, Robot motion planning, Statistical learning theory, Probability levels