Signal Temporal Logic Synthesis as Probabilistic Inference
This work addresses the challenge of handling uncertainty in temporal logic synthesis for robotics, offering a novel probabilistic approach that is incremental in extending existing methods.
The authors tackled the problem of signal temporal logic (STL) synthesis by reformulating it as a probabilistic inference task, introducing random STL (RSTL) to enable differentiable, gradient-based synthesis and demonstrating scalability with GPU acceleration in robotics applications like target tracking and occupancy grids.
We reformulate the signal temporal logic (STL) synthesis problem as a maximum a-posteriori (MAP) inference problem. To this end, we introduce the notion of random STL~(RSTL), which extends deterministic STL with random predicates. This new probabilistic extension naturally leads to a synthesis-as-inference approach. The proposed method allows for differentiable, gradient-based synthesis while extending the class of possible uncertain semantics. We demonstrate that the proposed framework scales well with GPU-acceleration, and present realistic applications of uncertain semantics in robotics that involve target tracking and the use of occupancy grids.