Interpretable Responsibility Sharing as a Heuristic for Task and Motion Planning

This paper presents Interpretable Responsibility Sharing (IRS), a novel heuristic for Task and Motion Planning that enhances domestic robot efficiency by leveraging auxiliary objects to decompose complex tasks into manageable sub-problems, thereby aligning robotic decision-making with human intuitive patterns and significantly outperforming traditional methods.

The Gist

Imagine you are a robot tasked with cleaning up a messy kitchen. You have to move a bunch of heavy mugs from the counter to the dining table.

The Old Way (Traditional Robots):
A standard robot looks at the problem and thinks, "I will pick up Mug 1, walk to the table, put it down, walk back, pick up Mug 2..." It treats every single object as a separate, heavy burden. It's like a person trying to carry ten heavy grocery bags, one by one, making ten separate trips. It's exhausting and inefficient.

The New Way (This Paper's Solution):
This paper introduces a clever new strategy called Interpretable Responsibility Sharing (IRS). Instead of just being a robot, the robot learns to think like a human. It realizes, "Hey, there's a tray right here! If I put all the mugs on the tray first, I can carry them all in one trip."

Here is the breakdown of how this works, using simple analogies:

1. The Core Idea: "Sharing the Load"

The authors call this Responsibility Sharing.

• The Robot: The main worker.
• The Auxiliary Objects: Tools like trays, pitchers, or even a second robot.
• The Concept: Instead of the robot doing everything directly, it "shares the responsibility" with the tools. The tray takes the responsibility of holding the mugs; the robot just takes the responsibility of carrying the tray.

Think of it like moving house. You could carry one box at a time (the robot way), or you could use a dolly (the auxiliary object) to hold ten boxes. The dolly shares the burden, making the job easier for you.

2. The Problem: "When should I use the tray?"

Just because a tray exists doesn't mean you should always use it.

• If you only have one mug, using a tray is extra work (you have to walk to the tray, put the mug on it, then walk to the table).
• If you have ten mugs, the tray is a lifesaver.

The hard part is teaching the robot to know exactly when to use the tray and when to just carry the mug directly. If the robot guesses wrong, it wastes energy.

3. The Solution: "The Rulebook" (ORS)

The paper creates a system called Optimized Rule Synthesis (ORS). Think of this as a detective that studies thousands of scenarios to write a simple rulebook for the robot.

• Step 1: The Simulation (The "What If" Lab):
  The researchers run millions of computer simulations. They ask, "What if the robot uses the tray?" and "What if it doesn't?" They measure how much energy (effort) is saved. This creates a massive dataset of "Good Ideas" and "Bad Ideas."

• Step 2: Learning the Rules:
  The ORS system looks at this data and writes simple, logical rules. It doesn't use a "black box" AI that you can't understand. Instead, it writes rules like:

  "IF there are 3 or more mugs AND a tray is nearby AND the table is far away, THEN use the tray."

  This is the "Interpretable" part. A human can read the rule and say, "Ah, yes, that makes sense!"

• Step 3: The Heuristic (The Shortcut):
  When the real robot faces a task, it checks this rulebook first.

  • If the rule says "Use the tray," the robot breaks the big task into two small steps: 1) Put mugs on tray, 2) Carry tray.
  • If the rule says "Don't use the tray," it just carries the mugs directly.

4. Why is this special?

• It's Not Magic, It's Logic: Many modern robots use "Deep Learning," which is like a brain that knows how to do things but can't explain why. This paper uses Logic. It's like a robot that can say, "I used the tray because there were too many cups to carry alone."
• It Mimics Human Intuition: The researchers tested this with real humans. They found that humans naturally use trays when they have many items and skip them when they have few. The robot's rulebook learned this exact same human intuition without ever watching a human video—it just looked at the physics of the situation.
• It Saves Energy: By using the right tool at the right time, the robot moves less, saves battery, and finishes tasks faster.

Summary Analogy

Imagine you are a delivery driver.

• Old Robot: You drive to every house, drop off one package, drive back to the depot, get another package, and drive again.
• This Paper's Robot: You look at your list. You see 20 packages. You grab a hand truck (the auxiliary object). You load all 20 onto the hand truck, and you push them all to the houses in one go.

The paper teaches the robot to know when to grab the hand truck and when to just carry a package by hand, using clear, logical rules that humans can understand and trust.

Technical Summary

1. Problem Statement

Task and Motion Planning (TAMP) involves jointly solving high-level symbolic action planning and low-level geometric motion planning. While effective for household tasks (serving, cleaning, pouring), existing TAMP approaches face two main challenges:

1. Scalability: Uninformed search suffers from exponential state spaces, while heuristic-based methods often rely on low-level physical metrics (e.g., displacement) that fail to capture human strategic preferences.
2. Lack of Interpretability: Deep learning approaches can learn human biases from data but act as "black boxes," making them unsafe and untrustworthy for domestic deployment where transparency is crucial.

The paper identifies a specific gap: Human-Centric Environmental Bias. Humans design environments with auxiliary objects (trays, pitchers) to facilitate recurring tasks. Current robots often ignore these structural cues or require explicit human demonstrations to learn them. The goal is to create a planning heuristic that systematically leverages these environmental biases (e.g., using a tray to carry multiple cups) to improve efficiency while remaining interpretable to human observers.

2. Methodology

The authors propose Interpretable Responsibility Sharing (IRS), a meta-heuristic framework that decomposes complex TAMP problems into manageable sub-problems by delegating tasks to auxiliary objects. The framework operates in three stages:

A. Data Generation: Counterfactual Plan Generation (CPG)

To train the system without human labeling, the authors use CPG to generate a labeled dataset.

• Process: For a given task configuration, the system generates two plans:
  1. Real Plan ($P$): A standard uninformed search (baseline, $W=0$).
  2. Counterfactual Plan ($P'$): A constrained search that forces the use of an auxiliary object (e.g., placing objects on a tray first) ($W=1$).
• Labeling: The system calculates the Individual Treatment Effect (ITE): $ITE = Cost(P') - Cost(P)$.
  • If $ITE < 0$ (using the object reduces effort), the label is Positive (Responsibility Sharing is beneficial).
  • If $ITE > 0$, the label is Negative.
• This creates a dataset $D$ mapping state-goal pairs to binary labels indicating whether "sharing responsibility" with an auxiliary object is optimal.

B. Rule Synthesis: Optimized Rule Synthesis (ORS)

The core innovation is ORS, which learns interpretable logical rules from the CPG dataset to predict when to use auxiliary objects. ORS acts as an ensemble selector combining two generators:

1. Rule-Based Representation Learner (RRL): Extracts structural logic from discretized continuous features using Gradient Grafting.
2. Correlation and Order-Aware Rule Learning (CARL): Extracts relational dependencies from a knowledge graph, modeling the semantic order of relations (e.g., spatial topology).

Optimization Strategy:
Instead of using these models directly, ORS aggregates their candidate rules and performs a bounded greedy search to select a subset $S$ that maximizes a Balance Score:
$$\text{Score}(S) = \alpha \cdot \text{Accuracy}(S) + (1-\alpha) \cdot \text{Interpretability}(S)$$

• Interpretability Definition: Unlike standard ML where sparsity is preferred, the authors define interpretability as informational sufficiency. Rules must be descriptive enough to explain why an action is valid (e.g., "Use tray IF object count > 2 AND tray exists").
• The process filters out unstable rules, ensuring the final policy is both highly accurate and logically grounded.

C. Heuristic Planning: IRS Execution

During inference, the IRS module acts as a meta-heuristic for the TAMP solver (specifically Logic-Geometric Programming with Multi-Bound Tree Search):

1. Rule Check: The system evaluates the current state against the synthesized rules ($S_c$).
2. Decision:
   • If Rules Trigger (Positive): The planner decomposes the task into sub-problems (e.g., "Move objects to tray" $\to$ "Move tray to target"). It solves these sequentially using Mini-LGP (a relaxed formulation) to find a mode-switch sequence, then validates the full motion.
   • If Rules Do Not Trigger (Negative): The planner defaults to standard TAMP search without auxiliary objects.

3. Key Contributions

1. Interpretable Responsibility Sharing (IRS): A novel heuristic that treats auxiliary objects as "responsibility sharers," dynamically decomposing tasks based on environmental structure rather than fixed rules.
2. Optimized Rule Synthesis (ORS): A framework integrating RRL and CARL with a Balance Score objective. It successfully bridges the gap between high predictive power and the need for descriptive, causal rules in robotics.
3. Counterfactual Plan Generation (CPG): A method to automatically generate ground-truth labels for "when to use tools" by comparing counterfactual scenarios, eliminating the need for expensive human demonstrations.
4. Human-Centric Validation: Demonstrated that the learned rules align with human intuition, validating the concept of "Human-Centric Environmental Bias."

4. Experimental Results

The framework was evaluated on three household tasks: Serving (transporting objects), Pouring (distributing liquid), and Handover (multi-robot transfer).

• Performance (Effort): IRS achieved the lowest physical effort (joint displacement) compared to baselines.
  • IRS: $11.05 \pm 4.79$
  • LGP (Baseline): $13.47 \pm 6.21$
  • Control (Always use tray): $13.37 \pm 5.83$
  • Insight: Always using tools is suboptimal; IRS dynamically selects the best strategy, reducing effort by ~18% compared to standard LGP.
• Decision-Making Accuracy: ORS significantly outperformed other interpretable and black-box baselines.
  • ORS Accuracy: 96.3% (vs. 95.0% for CARL, 80.5% for ANN).
  • Stability: ORS reduced the standard deviation of accuracy by an order of magnitude compared to CARL, proving the effectiveness of the greedy selection and balance score.
• Human Alignment: In physical experiments with 6 human subjects, ORS's decisions matched human intuition in 13 out of 15 scenarios (86.7% agreement), confirming that the system captures genuine human strategic biases.
• Interpretability: The generated rules were highly descriptive (e.g., combining object counts, locations, and helper existence), providing clear causal explanations for robotic actions.

5. Significance

This work represents a significant step toward safe and trustworthy domestic robotics.

• Bridging the Gap: It solves the trade-off between the adaptability of deep learning and the transparency of rule-based systems.
• Efficiency: By leveraging the "inductive bias" of human-designed environments, robots can plan more efficiently without needing massive datasets or explicit human teaching.
• Scalability: The approach is modular; the "responsibility sharing" concept can be applied to various auxiliary objects (trays, carts, other robots) and different domains.
• Human-Robot Trust: By providing interpretable rules that align with human intuition, the system enhances user trust, a critical factor for robots operating in shared human spaces.

The code and dataset are available at the provided GitHub repository, facilitating further research in interpretable TAMP.