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arXiv · 2403.11816

Symmetry-based Abstraction Algorithm for Accelerating Symbolic Control Synthesis

Hussein Sibai·Sacha Huriot·Tyler Martin·Murat Arcak
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Abstract

We propose an efficient symbolic control synthesis algorithm for equivariant continuous-time dynamical systems to satisfy reach-avoid specifications. The algorithm exploits dynamical symmetries to construct lean abstractions to avoid redundant computations during synthesis. Our proposed algorithm adds another layer of abstraction over the common grid-based discrete abstraction before solving the synthesis problem. It combines each set of grid cells that are at a similar relative position from the targets and nearby obstacles, defined by the symmetries, into a single abstract state. It uses this layer of abstraction to guide the order by which actions are explored during synthesis over the grid-based abstraction. We demonstrate the potential of our algorithm by synthesizing a reach-avoid controller for a 3-dimensional ship model with translation and rotation symmetries in the special Euclidean group SE(2).

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Hussein Sibai, Sacha Huriot, Tyler Martin, Murat Arcak. 2024-03-18. Symmetry-based Abstraction Algorithm for Accelerating Symbolic Control Synthesis. https://arxiv.org/abs/2403.11816

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