Solving Poisson's equation on an occupancy map with a tunable negative forcing function yields a smooth safety function that can be used as a control barrier function for collision-free robot control.
Around the normal derivative lemma
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abstract
This survey provides a description of the history and the state of the art of one of the most important fields in the qualitative theory of elliptic partial differential equations including the strong maximum principle, the boundary point principle (the normal derivative lemma) and related topics.
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Dynamic Safety in Complex Environments: Synthesizing Safety Filters with Poisson's Equation
Solving Poisson's equation on an occupancy map with a tunable negative forcing function yields a smooth safety function that can be used as a control barrier function for collision-free robot control.