Smith et al. Encode TWTL Robustness as MILP for Faster Robot Control
New method guarantees boolean satisfaction while optimizing robustness for time-constrained tasks.
Time Window Temporal Logic (TWTL) allows cyber-physical systems to express sequential tasks with explicit timing constraints—critical for robots and autonomous vehicles. In this paper, Smith, Ahmad, and Leahy propose encoding the quantitative semantics (robustness) of TWTL formulas directly into a Mixed-Integer Linear Program (MILP). The solver maximizes a robustness degree, and the authors prove that any feasible solution with a positive objective value ensures Boolean satisfaction of the specification. This bridges the gap between formal verification and practical optimization.
They introduce two synthesis settings: an open-loop formulation that computes the full control sequence from the initial state, and a closed-loop receding-horizon Model Predictive Controller (MPC). The MPC's key innovation is a task-adaptive horizon—using the TWTL Deterministic Finite Automaton (DFA) to identify the active sub-task at each step, it limits the prediction horizon to the remaining window of the current task. This makes each re-solve significantly cheaper than the full open-loop solve, enabling real-time deployment on resource-constrained robots. The work was submitted to arXiv (2606.30820) and targets robotics and formal methods communities.
- Robustness degree for TWTL is encoded via MILP constraints, maximizing a quantitative measure while guaranteeing Boolean satisfaction for any positive feasible solution.
- Closed-loop MPC with task-adaptive horizon uses a DFA to limit prediction to the active sub-task window, cutting computation per step compared to full-horizon approaches.
- Two formulations offered: open-loop (full sequence from initial state) and closed-loop (re-solves at each step with current state feedback).
Why It Matters
Enables faster, more reliable control for robots and autonomous systems handling complex time-constrained tasks.