[Paper Review] Integrating active sensing into reactive synthesis with temporal logic constraints under partial observations

Jie Fu, Ufuk Topcu|arXiv (Cornell University)|Oct 1, 2014

Formal Methods in Verification8 references3 citations

TL;DR

This paper proposes an online reactive synthesis framework that integrates active sensing with temporal logic constraints under partial observations, enabling almost-sure satisfaction of LTL specifications. By alternating between a belief-based control strategy and an active sensing strategy that reduces uncertainty, the method avoids the high computational cost of full partial-observation synthesis while ensuring correctness with probability 1 under a sufficient sensor condition.

ABSTRACT

We introduce the notion of online reactive planning with sensing actions for systems with temporal logic constraints in partially observable and dynamic environments. With incomplete information on the dynamic environment, reactive controller synthesis amounts to solving a two-player game with partial observations, which has impractically computational complexity. To alleviate the high computational burden, online replanning via sensing actions avoids solving the strategy in the reactive system under partial observations. Instead, we only solve for a strategy that ensures a given temporal logic specification can be satisfied had the system have complete observations of its environment. Such a strategy is then transformed into one which makes control decisions based on the observed sequence of states (of the interacting system and its environment). When the system encounters a belief---a set including all possible hypotheses the system has for the current state---for which the observation-based strategy is undefined, a sequence of sensing actions are triggered, chosen by an active sensing strategy, to reduce the uncertainty in the system's belief. We show that by alternating between the observation-based strategy and the active sensing strategy, under a mild technical assumption of the set of sensors in the system, the given temporal logic specification can be satisfied with probability 1.

Motivation & Objective

• To address the high computational complexity of reactive synthesis under partial observations in dynamic, adversarial environments.
• To enable correct control synthesis when full environmental state information is unavailable at runtime.
• To reduce computational burden by using online replanning via sensing actions instead of solving full two-player games with partial observations.
• To ensure almost-sure satisfaction of LTL specifications through a combination of belief-based control and active sensing strategies.
• To provide a practical, scalable method for robotic motion planning and control under uncertainty.

Proposed method

• The system maintains a belief set representing all possible current states based on partial observations and history.
• A sure-winning strategy is first synthesized under complete information and transformed into a randomized, belief-based strategy for use under partial observations.
• When the belief-based strategy is undefined for the current belief, an active sensing strategy is triggered to reduce uncertainty.
• Sensing actions query propositional formulas (e.g., stench detection) to update beliefs based on sensor outcomes.
• The system alternates between the belief-based strategy and active sensing strategy at runtime.
• A sufficient condition on the sensor set ensures that the system can always resolve uncertainty and satisfy the LTL specification almost surely.

Experimental results

Research questions

• RQ1 Can active sensing reduce the computational cost of reactive synthesis under partial observations while preserving correctness?
• RQ2 How can a strategy synthesized under complete information be adapted for use in a belief-based, online control framework?
• RQ3 Under what conditions can active sensing ensure almost-sure satisfaction of LTL specifications in partially observable environments?
• RQ4 What is the role of sensor design and query selection in minimizing sensing cost while maximizing uncertainty reduction?
• RQ5 How can belief updates be efficiently computed during runtime to support real-time decision-making?

Key findings

• The method ensures almost-sure satisfaction of the given LTL specification under a sufficient condition on the sensor set.
• The maximum belief set cardinality during execution was 43, indicating manageable uncertainty propagation in the robot motion planning example.
• The average decision time per step was 8.55×10⁻⁴ seconds, demonstrating real-time feasibility on standard hardware.
• The product game computation took 40.14 seconds, and the winning strategy under complete information was computed in 14 seconds.
• In 1000 steps, the robot visited the target region set F 14 times and continued to do so infinitely often, confirming long-term specification satisfaction.
• The active sensing strategy minimized unnecessary sensing by selecting the most informative queries based on current uncertainty and specification goals.