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Plan Explicability and Predictability for Robot Task Planning

Yu Zhang, Sarath Sreedharan, Anagha Kulkarni, Tathagata Chakraborti, Hankz Hankui Zhuo, Subbarao Kambhampati

arXiv:1511.08158v2cs.AIcs.RO

TL;DR

Autonomous robots need task plans that humans can understand because incomprehensible behavior can increase cognitive load and pose safety risks. The paper defines explicability and predictability, learns human plan labeling with CRFs, and evaluates plan selection and synthesis in simulation and with physical robots. The evaluations show improved explicability and predictability, with FF-EXPD accepting about a 10% plan-cost penalty in one comparison.

  • Problem

    Autonomous plans can be difficult for humans to understand, while prior work does not provide a general solution for explicable high-level task planning.

  • Method

    The approach learns human labeling of agent actions with conditional random fields, then uses predicted labels to compute explicability and predictability for selecting or synthesizing plans.

  • Results

    The evaluations demonstrate effective plan selection and synthesis: FF-EXPD improves explicability and predictability, while penalizing plan cost by about 10% in all tested settings.

  • Takeaways & Limitations

    Plan explicability and predictability provide measures that agents can use to produce plans more comprehensible to humans.

Abstract

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Intelligent robots and machines are becoming pervasive in human populated environments. A desirable capability of these agents is to respond to goal-oriented commands by autonomously constructing task plans. However, such autonomy can add significant cognitive load and potentially introduce safety risks to humans when agents behave unexpectedly. Hence, for such agents to be helpful, one important requirement is for them to synthesize plans that can be easily understood by humans. While there exists previous work that studied socially acceptable robots that interact with humans in "natural ways", and work that investigated legible motion planning, there lacks a general solution for high level task planning. To address this issue, we introduce the notions of plan {\it explicability} and {\it predictability}. To compute these measures, first, we postulate that humans understand agent plans by associating abstract tasks with agent actions, which can be considered as a labeling process. We learn the labeling scheme of humans for agent plans from training examples using conditional random fields (CRFs). Then, we use the learned model to label a new plan to compute its explicability and predictability. These measures can be used by agents to proactively choose or directly synthesize plans that are more explicable and predictable to humans. We provide evaluations on a synthetic domain and with human subjects using physical robots to show the effectiveness of our approach

I. INTRODUCTION

Autonomous task planning can burden humans when robot behavior is incomprehensible, motivating plans that account for how humans interpret agent models. This work introduces explicability and predictability, learns human plan labeling with CRFs, and evaluates the approach in simulation and with physical robots.

  • Incomprehensible autonomous behavior can increase human cognitive load and potentially create safety risks.
  • Humans interpret agent behavior through expectations about capabilities and mental states, but their understanding of the agent model is partial and inaccurate.
  • Explicability measures how easily humans associate abstract tasks with actions, whereas predictability measures how easily they anticipate the next task.
  • The approach learns human action-labeling schemes with conditional random fields and applies the learned model to new plans.
  • Human-aware planning models human capabilities and intents, while explicable planning considers differences between the human-perspective model and the robot’s own model.
  • The approach is evaluated in a synthetic domain and with human subjects using physical robots.
  • Unlike motion-legibility work and domain-specific natural interaction research, this work targets high-level task planning.

III. EXPLICABILITY AND PREDICTABILITY

The agent plans under its own model while accounting for the human’s hidden interpretation of that model. Because this interpretation is difficult to specify directly, the approach learns plan-labeling behavior and uses it to compare candidate plans through cost and model difference.

  • The robot constructs a goal-achieving plan with its own PDDL-based model MR, while also considering the human’s interpretation M∗R.
  • The planning objective minimizes a weighted sum of agent-plan cost and differences between the robot’s plan and the human-anticipated plan.The relative weight is α, and the agent model MR is assumed to be given.
  • The human-perspective model is hidden, difficult to convey, and potentially arbitrarily different from the robot’s own model.
  • The method approximates model differences by treating human interpretation of action sequences as a labeling process over abstract tasks.
  • Training examples {Si} are used to learn a CRF model of the human labeling scheme, which then supports labeling and evaluating new plans.
  • A plan is represented as an action sequence beginning with a null action, and a provided task-label set is used to label actions.

1) Explicability Labeling:

Explicability labels each action with the abstract tasks it contributes to. A plan-level mapping then scores how explicable the resulting sequence of action labels is.

  • Explicability associates each plan action with one or more abstract task labels.
  • The action-label space is the power set of the task labels, allowing an action to contribute to multiple tasks.
  • An empty action label marks an action as inexplicable, while a nonempty label indicates task contribution.
  • Plan explicability θπ is a domain-specific mapping from the sequence of action labels to [0, 1], with 1 representing the most explicable plan.
  • The evaluation example computes explicability as the ratio of actions with nonempty labels to all actions.

2) Predictability Labeling:

Predictability captures how task labels connect across a plan by labeling both the current task and the next anticipated task. Its evaluation mapping measures how often the next task is correctly predicted.

  • 2) Predictability Labeling:: Predictability concerns connections between tasks across the plan rather than action-task association alone.
  • 2) Predictability Labeling:: Each predictability label contains a current label and a next label specifying tasks anticipated after the current task.
  • 2) Predictability Labeling:: Multiple next-task labels represent multiple candidate tasks, while an empty next label indicates unpredictability or task completion.
  • 2) Predictability Labeling:: Plan predictability βπ is computed by applying a mapping Fβ to the sequence of predictability labels.
  • 2) Predictability Labeling:: The evaluation example computes predictability as the ratio of actions for which the next task is correctly predicted to all actions.

B. A Concrete Example

The rover example illustrates how humans interpret task plans by assigning abstract task labels to observed actions. These sequential labels provide training data for a CRF that models human plan interpretation.

  • Rover domain: The rover domain includes navigate, observe, load, and unload actions for collecting resources, storing one, and observing locations.The goal is to make the storage area non-empty and observe two locations.
  • Abstract task labels: Humans interpret the rover plan using abstract tasks COLLECT, STORE, and OBSERVE without specifying task arguments.The example allows the human interpretation model to differ arbitrarily from the agent model.
  • Human labeling: As actions are observed incrementally, each action receives labels based only on the plan prefix, the environment, and the known goal.For example, the initial navigation action can be labeled as starting the COLLECT task.
  • Learning labels: The labeling challenge is addressed by learning human labels from training examples and applying the learned model to new plans.The labels are needed to compute plan explicability and predictability.
  • CRF formulation: A CRF models the sequential action-labeling process using plan-execution observations and cognitive cues as observations.CRFs are selected because they model sequential data without requiring the stronger distributional assumptions associated with HMMs.

A. Features for Learning

The learning representation combines plan and state information with motion, environmental, and human-interaction signals. Some dynamic human features are unavailable during testing and must therefore be estimated.

  • Feature sources: A plan’s immediate features include its actions and associated state trajectory, with motion features derivable when agent dynamics are known.These features can also support analysis of the low-level commands implementing the plan.
  • Feature sources: Sensor data such as video and depth can provide environmental features, including workspace crowding.Sensors can also provide dynamic information such as the human’s location.
  • Testing constraint: Human-location features are unavailable during testing and must be estimated from other information, such as a projected human plan.Plan-recognition techniques are suggested for producing these estimates.
  • Training representation: The learning examples pair each action’s feature set with its action label for predictability and explicability.The paper uses a linear-chain CRF, while noting that the formulation can extend to more general CRFs.

1) Plan Features:

The framework extracts features from action descriptions, resulting states, motion, and human interaction. A trained CRF then labels candidate plans so explicability and predictability can guide plan choice.

  • Plan features: Agent-model features for an action include its description and state variables after executing the preceding action sequence.In the rover example, features include navigation and the rover’s locations relative to resources and storage.
  • Action features: Motion features capture action dynamics and execution smoothness, which can influence how humans interpret an action.The same river-crossing action may be interpreted differently depending on whether the robot swims, pedals, or propels itself.
  • Interaction features: Interaction features represent the agent’s influence on the human, including their distance and the human’s concurrent activity.These features can come from sensors or estimates based on the human’s projected plan.
  • Using features: The trained CRF labels actions in each candidate plan, after which explicability and predictability are computed from the resulting label mappings.Candidate plans may be cost-bounded or generated to be diverse under plan-distance measures.

2) Plan Synthesis:

The synthesis procedure can either select among candidate plans or incorporate explicability and predictability into heuristic search. The relative importance of these measures depends on the interaction domain.

  • Heuristic synthesis: An alternative integrates the measures as heuristics into FastForward planning with enforced hill climbing.The relaxed planning graph supplies remaining planning steps for heuristic evaluation.
  • Domain weighting: In close human-robot settings, plans with greater explicability and predictability receive more preference because unexpected behavior carries higher risk.The relative weights can vary; predictability may matter less when robots do not closely interact with humans.
  • Heuristic synthesis: Algorithm 1 combines the relaxed planning heuristic with estimated explicability and predictability to rank successor states.The search computes labels for a concatenated current-plus-relaxed plan and uses a combination function for the heuristic.

V. EVALUATION

The evaluation tests whether the labeling approach captures human-style interpretations and whether plan selection or synthesis improves explicability and predictability. It uses a synthetic rover domain with hidden goals and evaluations involving both simulated data and physical-robot subjects.

  • The approach is evaluated first on a synthetic rover dataset and then with human subjects using physical robots in a blocks-world domain.
  • The evaluation measures both the labeling model’s ability to capture arbitrary labeling schemes and the effectiveness of plan selection and synthesis.
  • The synthetic rover domain adds randomly selected hidden-goal locations, producing behaviors that may appear unexpected under the public goal alone.The rover’s full goal G′ includes the public goal G and hidden goals requiring visits to additional locations.
  • Rover plans are labeled incrementally by associating each action with current and next task labels selected from COLLECT, STORE, OBSERVE, and ∅.
  • An action receives the inexplicable label ∅ when applying it does not reduce the remaining-plan length; otherwise, its label depends on target distances, rover state, and movement toward targets.
  • The evaluation generates 1–3 resources, storage areas, and observation locations in a 4 × 4 environment, whose state space is on the order of 10^20.The public goal fills storage areas and achieves observations, while the rover’s goal additionally includes hidden goals.

2) Results:

The evaluations test CRF-based prediction, plan selection, and plan synthesis using explicability and predictability measures. Results show generally effective prediction and improved human-oriented plan quality, with about a 10% plan-cost penalty for FF-EXPD.

  • Using CRFs for Plan Explicability and Predictability: CRF-based prediction performance generally ranges from 50%–150%, and oscillation level has little apparent influence.Testing varies the maximum number of hidden goals from 1 to 6; the approach remains effective when the two models are similar or largely different.
  • Selecting Explicable and Predictable Plans: EXPD-SELECT increasingly outperforms RAND-SELECT as the number of hidden goals increases, although its performance also tends to decrease.The model was trained with samples containing at most 3 hidden goals.
  • Using CRFs for Plan Explicability and Predictability: The linear-chain CRF does not directly model correlations among observations across states, so more general CRFs may improve performance.Such correlations are common in the rover domain, including navigating back and forth.
  • Synthesizing Explicable and Predictable Plans: Incorporating θ into FF produces significant explicability differences across all trials, while predictability differences are less significant.The evaluation suggests that the heuristic search can produce plans with high explicability.
  • Synthesizing Explicable and Predictable Plans: Incorporating β produces significant differences in both explicability and predictability across all trials.Improving predictability also improves explicability, consistent with the definitions of the two measures.
  • Plan Cost: FF-EXPD produces longer plans than FF but penalizes plan cost by about 10% to improve explicability and predictability.FF considers only plan cost, whereas FF-EXPD incorporates predicted human-oriented measures into its heuristic.

B. Evaluation with Physical Robots

The physical-robot evaluation studies tower-building plans in a smart-manufacturing setting, comparing explicable plans with cost-optimal plans when heavy and light blocks have different action costs.

  • The evaluation uses a physical robot working beside humans, even though the robot’s goal is independent of the human’s.The setting treats explicability as relevant because it can help humans concentrate on their own tasks.
  • The robot must build towers of specified heights using externally indistinguishable light and heavy blocks that the robot identifies through markers.Picking up heavy blocks is more costly, so cost and explicability can favor different plans.
  • Training uses 23 manually generated height-3 tower-building problems, including four where the optimal plan is not the most explicable.

2) Experimental Setup:

The experiment tests generalization on eight tower-building problems by comparing OPT with FF-EXPD, using human-labeled explicability and plan scores. FF-EXPD produces substantially more explicable plans, while the conclusion situates the approach within broader human-aware robot planning and notes observer-only human involvement.

  • Experimental Setup: Eight testing problems cover tower heights from 3 to 5, with OPT and FF-EXPD generating two plans for each problem.Testing focuses on cases where plans are more likely to be inexplicable.
  • Experimental Setup: The evaluation uses about 15,000 training samples created by permuting manually generated plans, then tests whether the approach generalizes to varied tower heights.
  • Results: 97.3% of FF-EXPD actions were explicable versus 77.8% for OPT, while average explicability measures were 0.98 and 0.78, respectively.Average human-subject scores were 9.65 for FF-EXPD and 6.92 for OPT; both comparisons were significant at p < 0.001.
  • Results: A representative scenario contrasts OPT’s lower-cost light-block actions with FF-EXPD’s more costly movement of the heavy block.
  • Scope: The approach is evaluated in a synthetic domain and with human subjects using physical robots, while current human participants serve as observers rather than close teammates.
  • Applications: The measures can also support applications that require inexplicable or unpredictable plans by minimizing, rather than maximizing, θ and β.
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