Navigation Functions With Time-Varying Destination Manifolds in Star Worlds

This paper formally constructs navigation functions with time-varying destinations on star worlds. The construction is based on appropriate diffeomorphic transformations and extends an earlier sphere-world formulation. A new obstacle modeling method is also introduced, reducing analytical complexity and offering unified expressions of common classes of <inline-formula><tex-math notation="LaTeX">$n$</tex-math></inline-formula>-dimensional obstacles. The method allows for dynamic target tracking and is validated through simulations and experiments.

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