Attraction-Based Receding Horizon Path Planning with Temporal Logic Constraints

Our goal in this paper is to plan the motion of a robot in a partitioned environment with dynamically changing, locally sensed rewards. We assume that arbitrary assumptions on the reward dynamics can be given. The robot aims to accomplish a high-level temporal logic surveillance mission and to locally optimize the collection of the rewards in the visited regions. These two objectives often conflict and only a compromise between them can be reached. We address this issue by taking into consideration a user-defined preference function that captures the trade-off between the importance of collecting high rewards and the importance of making progress towards a surveyed region. Our solution leverages ideas from the automata-based approach to model checking. We demonstrate the utilization and benefits of the suggested framework in an illustrative example.

💡 Research Summary

The paper tackles the problem of planning a robot’s motion in a partitioned environment where rewards appear, disappear, and change over time, while the robot must also satisfy a high‑level mission expressed in Linear Temporal Logic (LTL). Traditional approaches either focus on guaranteeing mission satisfaction (often using model‑predictive control or receding‑horizon planning) or on locally maximizing collected rewards, but they treat the two objectives as mutually exclusive. This work introduces a unified framework that allows a user‑defined trade‑off between the two goals and can accommodate arbitrary assumptions about reward dynamics.

The authors model the environment as a weighted deterministic transition system (TS) whose states correspond to regions and whose weighted edges encode travel time. An LTL specification φ is translated into a Büchi automaton Bφ. By taking the synchronous product of the TS and Bφ, they obtain a weighted product automaton P. Runs of P that reach accepting states correspond to robot trajectories that satisfy φ. The product automaton thus provides a formal guarantee that any control strategy operating on it will respect the mission.

Two novel constructs are introduced: (1) a preference function that, based on the robot’s history, indicates whether moving toward a surveillance region (i.e., making progress on the LTL mission) or collecting immediate rewards should be prioritized; and (2) a state‑potential function pot(q, prefix, h) that captures the user’s assumptions about reward dynamics (e.g., bounded change per time unit, probabilistic appearance, disappearance after collection) and evaluates the expected or worst‑case reward that can be gathered from state q within a planning horizon h. The horizon h limits the total travel time of a locally planned finite path, while the visibility radius v determines which states’ rewards are observable at the current location.

At each control step k the algorithm proceeds as follows:

1. Sense rewards in the visibility set V(qk).
2. For every candidate successor state q′ reachable from qk, compute its potential pot(q′, prefixk, h) using the chosen reward‑dynamics model.
3. Read the current value of the preference function; this determines weighting coefficients α (for reward potential) and β (for mission progress).
4. For each transition (qk, q′) in the product automaton, compute an attraction value A = α·pot(q′) + β·pref(q′), where pref(q′) reflects the distance (in weighted steps) to an accepting state of the product automaton.
5. Select the transition with maximal attraction, execute it, and update the prefix.

The attraction‑based selection guarantees that, when β dominates (high preference for mission), the robot is driven toward accepting states, ensuring eventual satisfaction of the LTL formula. When α dominates (low preference), the robot behaves like a reward‑maximizing explorer within the visible region. The framework therefore interpolates continuously between pure mission‑driven and pure reward‑driven behaviors.

The authors provide theoretical results proving correctness (any infinite run generated by the strategy satisfies the LTL mission) and completeness (if a satisfying run exists, the algorithm can find one). They also discuss optimality: the local horizon optimization maximizes the potential reward among all locally feasible paths that still make progress according to the current preference level, yielding a provably near‑optimal trade‑off.

A series of simulations illustrate the approach. Example scenarios include:

• Static rewards with a linearly increasing preference function, showing the robot first harvest high‑reward regions and later switch to periodic visits of surveillance zones.
• Rewards that change linearly over time, where the potential function accounts for bounded growth/decay, leading to paths that anticipate future reward peaks while still respecting mission constraints.
• Probabilistic reward appearance, where the potential is defined as the expected sum of rewards; the robot preferentially moves toward regions with higher expected gain, yet still visits required surveillance locations within the specified frequency.

These experiments demonstrate that the method can handle diverse reward dynamics, adapt to user‑specified trade‑offs, and maintain formal guarantees of mission satisfaction.

In summary, the paper contributes a generalized receding‑horizon planning framework that (i) integrates formal LTL verification via product automata, (ii) introduces a flexible preference mechanism to balance mission progress against reward collection, and (iii) supports arbitrary reward‑dynamics models through a state‑potential abstraction. The approach advances the state of the art by allowing dynamic, user‑controlled prioritization and by extending beyond the restrictive assumption of static, fully known rewards found in earlier work. Future directions suggested include multi‑robot extensions, handling nondeterministic transition systems, and real‑world robot deployments.