STL-GCS: A Planner-Controller Framework for Signal Temporal Logic via Graphs of Time-varying Convex Sets

What the math gives to ML

The paper offers a constructive mechanism for converting Signal Temporal Logic (STL) requirements into time-varying convex sets whose forward invariance guarantees satisfaction with a prescribed robustness margin. It combines this representation with convex-set graph planning and B-spline convex-hull constraints, so continuous-time safety and temporal constraints can be enforced using finite-dimensional convex conditions. A transferable neural-network version is a constrained neural state-space or neural ODE whose hidden/output trajectory is corrected by a small differentiable safety controller that keeps it inside time-indexed convex STL tubes. The key falsifiable signature is that violations should disappear once the learned correction gain exceeds the boundary rate induced by the moving convex sets, while slack should decay exponentially when the invariance inequalities are feasible.