Symmetry-based Abstraction Algorithm for Accelerating Symbolic Control Synthesis
CoRR(2024)
摘要
We propose an efficient symbolic control synthesis algorithm for equiv-
ariant 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 an-
other 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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