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Probabilistic Plan Legibility with Off-the-shelf Planners

Michele Persiani, Thomas Hellström

arXiv:2610.00065v1cs.ROcs.AI

TL;DR

Robot actions can be difficult to interpret when the robot’s model or beliefs differ from a human collaborator’s, creating a risk to trust. This paper extends probabilistic plan legibility to off-the-shelf PDDL planning and models the observer’s perspective. Across tested domains, more legible plans trade off against cost, with outcomes depending on the domain.

  • Problem

    Model discrepancies and information asymmetries can make robot behavior less interpretable and ultimately reduce trust in the system.

    Source: Introduction · p. 1

  • Method

    The paper formulates plan legibility probabilistically and uses second-order theory of mind to evaluate plans from an observer’s perspective across distinct task spaces.

    Source: Probabilistic Plan Legibility · p. 2, Theory of Mind · p. 4

  • Results

    Across several planning domains, the algorithm generated plans more legible than optimal plans, with legibility-cost trade-offs varying by domain and regularization playing an important role.

    Source: Discussion · pp. 6–7, Conclusions · p. 7

  • Takeaways & Limitations

    In human-robot teaming, a robot can use legibility to implicitly communicate its goal without requiring the commander to label the scene.

    Source: Conclusions · p. 7

    The tests do not establish conclusions valid for every domain, and model-reconciliation cases are outside scope under an assumption that each planner plan has a valid observer-model description.

    Source: Theory of Mind · p. 4, Conclusions · p. 8

Abstract

from arXiv · show

Legible planning is the creation of plans that best disambiguate their goals from a set of other candidates from an observer's perspective. In this paper we propose a method for legible planning for arbitrary PDDL domains, by extending previous research on legibility to classical planning without requiring to construct ad-hoc planners. We also discuss how the observer perspective may be estimated through a second order theory of mind that connects the planner's and the observer's task spaces. Our solution can for example be deployed in human-robot teaming scenarios, where an autonomous robot in a team can implicitly communicate its goal by producing legible plans. We present benchmark results on several PDDL planning domains. Our results generally show that plan legibility is a trade-off with plan efficiency, however, not all planning domains allows to increase legibility in the same way and a regularizing factor to balance legibility and efficiency was proved necessary.

Introduction

The paper frames plan interpretability as important in human-robot collaboration, where model differences or information asymmetries can make robot behavior hard to understand and weaken trust. It extends legible planning to classical PDDL planning and proposes evaluating plans from an observer’s perspective.

Introduction

  • Model discrepancies and information asymmetries can make robot behavior less interpretable and ultimately reduce trust in the system.The introduction situates this problem in human-robot interaction, where observed actions may not be understandable to a collaborator.Source: Introduction · p. 1
  • Legible planning seeks plans that help an observer distinguish the intended goal from alternatives, rather than optimizing only execution cost.The observer is modeled as inferring goals from the planner’s actions.Source: Introduction · p. 1
  • The paper extends plan-legibility formalism to classical planning methods such as PDDL without requiring ad-hoc planners.It also argues that plans should be evaluated using the observer’s possibly inaccurate model, connecting the planner’s and observer’s task spaces through second-order theory of mind.Source: Introduction · pp. 1–2
  • The authors provide an algorithm for producing legible plans with off-the-shelf PDDL planners and measure its performance across standard domains.They identify human-robot interaction and teaming as potential application settings.Source: Introduction · p. 2

Background

Prior work studies legibility through trajectories, observer beliefs, and control of observations. These approaches differ in their planning spaces and in how they balance legibility with plan cost.

Background

  • Manipulator research skewed trajectories to reduce goal-location ambiguity, while a user study found preferences for legible plans over functional or predictable trajectories.Legible trajectories also positively affected perceived interpretability, interaction fluency, and sense of collaboration.Source: Background · p. 2
  • POMDP-based transparent planning uses action sequences to communicate goals through observer beliefs; related Legible MDP work integrates observer beliefs into the actor’s beliefs.These approaches use a shared underlying MDP task space, and legibility can trade off against planning cost.Source: Background · p. 2
  • Controlled-observability planning can produce legible or obfuscating plans by combining goal-specific search heuristics, with planner and observer using different task spaces.The cited work also considers cooperative and adversarial observers simultaneously.Source: Background · p. 2

Probabilistic Plan Legibility

The section defines probabilistic legibility as distinguishing a true goal from alternatives using observer-inferred goal distributions, then models the observer’s perspective and operationalizes goal recognition with PDDL planning costs.

Probabilistic Plan Legibility

  • Legibility seeks plans whose observations make the true goal discernible among candidates by reducing the difference between the planner’s and observer’s goal distributions.Candidate plans achieve the true goal from the same starting condition; constraints may make sufficient legibility or even a valid plan impossible.Source: Probabilistic Plan Legibility · pp. 2–3
  • Prefix-based n-legibility evaluates a plan after n steps, while weighted averages over prefixes can emphasize early plan steps.Setting a step’s weight to 1 gives its individual legibility.Source: Probabilistic Plan Legibility · p. 3

Theory of Mind

  • The planner uses second-order theory of mind to estimate how the observer’s first-order model infers the planner’s goal, evaluating legibility in the observer’s model.The mapping T transforms planner task instances into observer-perspective instances and composes the planner’s and observer’s first-order models.Source: Theory of Mind · p. 3
  • The approach assumes each planner-model plan has a valid observer-model description and leaves reconciliation of sufficiently different models out of scope.When the models differ sufficiently, the observer may judge a plan non-legible, and explanations may be needed to restore compatibility.Source: Theory of Mind · p. 4

Goal Recognition using PDDL

  • Goal recognition compares an optimal plan for a candidate goal with a plan constrained to include the observed actions, using their costs to assess action rationality.The recognizer models goal probabilities from observed plans and prior goal probabilities.Source: Goal Recognition using PDDL · p. 4
  • A Boltzmann distribution maps rationality scores to plan probabilities given goals, and the PDDL formulation can represent observations with parts omitted.The temperature parameter controls the distribution; rational plans receive higher probability than irrational ones.Source: Goal Recognition using PDDL · p. 4

Production of legible plans with off-the-shelf

The method evaluates plan goals from the observer’s transformed task model, then uses diverse plans and regularization to seek legibility without ignoring cost.

Production of legible plans with off-the-shelf

  • The observer’s goal recognition uses a transformed planning instance, obtained by applying theory of mind T to the planner’s task model.The same transformation applies to the planning instance, plans, and goals.Source: planners · p. 5
  • Because plan legibility is generally non-monotonic, computing n-legibility directly requires exhaustive plan-space search up to depth n.The method instead uses diverse planning to find k plans toward the target goal and averages their i-legibility values for i = 1..n.Source: planners · p. 5
  • The algorithm generates target-goal plans, transforms the task into the observer’s model, and selects a legible plan while regularizing toward cheaper plans.Legibility is evaluated in the observer’s plan space.Source: planners · p. 5

Illustrative Example

The rescue example contrasts the robot’s obstacle-aware world with the commander’s estimated obstacle-free model, showing how a costlier route can clarify the robot’s goal.

Illustrative Example

  • The commander’s model is estimated as obstacle-free, while the robot’s real-world grid contains detected obstacles and its true goal.The estimate is computed locally by the robot through theory of mind.Source: Figure 2 · p. 5, Illustrative Example · p. 5
  • The robot estimates the commander’s candidate destinations and plans for the true goal to be best distinguished, supporting ongoing implicit communication after an initial announcement.The commander lacks access to the robot’s internal goal and to detected obstacles in the scenario.Source: Illustrative Example · p. 5
  • The legible route avoids other candidate goals and is more expensive than the optimal route because it passes over obstacles, making the true goal more discernible.In the example, both routes pursue the same true goal, g3.Source: Illustrative Example · p. 5

Evaluation

The evaluation benchmarks the method across PDDL domains using sampled observer models, diverse plans, and measures of legibility and plan-length cost.

Evaluation

  • The benchmark covers nine PDDL domains with 10 random instances each, using Forbid-Iterative for diverse planning and goal recognition.The listed domains include logistics, blocks-world, intrusion-detection, kitchen, campus, satellite, easy-ipc-grid, miconic, and ferry.Source: Evaluation · p. 6
  • For each instance, one of four candidate goals is selected as true, and k = 50, 100, or 200 plans are generated; plan legibility averages its step values.The selected diverse-planning plan sets are evaluated toward the chosen goal.Source: Evaluation · p. 6
  • Sampled observer models drop random proportions of actions and parameters, with tested drop rates of 0%, 20%, 40%, 60%, and 80%.This simulates observers who miss some actions or lack some action-parameter information.Source: Evaluation · p. 6
  • Legibility gain compares the optimal plan with the most legible generated plan, while cost gain measures the legible plan’s length cost against the optimal plan.The legibility of a plan is averaged across its steps with equal weight.Source: Evaluation · p. 6

Discussion

The discussion finds a legibility–cost trade-off, with domain-dependent effects from dropping observations and a need to regularize plan length.

Discussion

  • Legibility increased in exchange for longer plans, but the measured gains depended strongly on the domain.The authors report that increasing legibility this way was always possible in their measurements.Source: Discussion · p. 6
  • Dropping observations had opposite patterns across domains: logistics peaked with none dropped, while intrusion-detection legibility rose linearly as more were dropped.The authors hypothesize that goal-specific actions may benefit more from observation dropping than universally applicable actions.Source: Discussion · pp. 6–7
  • The authors say these results make legibility behavior difficult to predict a priori for experiments on real data.Their conclusion follows from the observed domain dependence.Source: Discussion · p. 7
  • Without regularization, action loops in blocks-world or logistics could raise legible-plan length to 3–6 times the optimal plan length.The paper reports this as a large performance drop associated with increased legibility.Source: Discussion · p. 7

Conclusions

The paper concludes that off-the-shelf PDDL planners can generate legible plans by connecting planner and observer task models through theory of mind. Benchmark results show a trade-off between legibility and plan cost that depends on the domain and theory of mind used.

Conclusions

  • The procedure uses off-the-shelf PDDL planners and connects planner and observer task models through theory of mind, modeling how the planner's actions are perceived.Source: Conclusions · p. 7
  • Table 3 summarizes average legibility and cost gains across domains for increasing values of k.Source: Table 3 · p. 7
  • Across several planning domains, the algorithm generated plans more legible than optimal plans, with legibility trading off against plan cost in a domain- and theory-of-mind-dependent way.In human-robot teaming, leveraging the robot's theory of mind does not require commander inputs such as scene labeling.Source: Conclusions · p. 7
  • Tests demonstrate the possibility of increasing legibility but do not support conclusions valid a priori across all domains; investigation must consider the specific domain and theory of mind.Source: Conclusions · p. 8
  • Evaluating legibility as perceived by humans in real scenarios remains future work, including whether the rationality-based model captures judgments in human-robot interaction domains.Source: Conclusions · p. 8
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