This paper introduces courteous anticipatory planning, a framework that helps robots reduce cumulative task completion costs in long-lived shared environments by reasoning about what other robots can do and what tasks they are likely to be assigned.
Introduction
In persistent shared environments like homes and restaurants, multiple robots must operate over long time horizons without explicit task allocation. Existing approaches to task planning either treat each robot independently or require full coordination, both of which lead to high cumulative costs. Courteous anticipation enables robots to proactively adjust their plans based on estimates of other agents' future task costs, reducing overall system overhead.
Related Work
Prior work in multi-robot task planning has focused on centralized allocation or reactive collision avoidance. These methods do not scale well to long-lived settings where tasks continuously appear. Anticipatory planning methods estimate future costs for a single robot but neglect the presence of other agents sharing the space. Courteous anticipation bridges this gap by aggregating per-robot future cost estimates into a unified planning objective.
Problem Formulation
We consider a persistent shared environment with N robots and a stream of tasks arriving over time. Each robot i has a set of capabilities and can perform a subset of tasks. The goal is to minimize the cumulative cost over all robots and all tasks, where cost reflects time, energy, or resource consumption. The system is decentralized with no explicit coordination protocol.
Approach
Anticipatory Cost Estimation
Each robot maintains a learned estimator that predicts the expected cost of its own future tasks given the current state of the environment. This estimator is trained on historical task data using a neural network architecture that maps state features to scalar cost predictions.
Factored Formulation
Rather than computing a joint rollout across all robots, which is computationally infeasible, we factor the problem. Each robot independently computes its own anticipatory cost estimate, and these estimates are aggregated into a single planning objective. This allows modular deployment without retraining existing estimators.
Courteous Planning Objective
The planning objective for each robot combines immediate task cost with the aggregated future cost contributions from all robots. The robot selects tasks that minimize both its own and others' anticipated future costs, effectively being "courteous" by avoiding actions that would increase the burden on teammates.
Experiments and Results
We evaluate courteous anticipatory planning in two simulated environments of increasing complexity. In the home setting, courteous anticipation improves performance even without capability differences. In the restaurant environment, where robots have distinct capabilities and responsibilities, results validate that capability differences amplify the value of courteous anticipation.
We compare against two baselines in both environments:
- Classical planning via FastDownward
- Planning augmented with the acting robot's own anticipatory cost estimator, reducing cost for the acting robot's future tasks but not for others sharing the environment
- Our approach, planning augmented with aggregated per-robot anticipatory cost estimates, accounting for all robots sharing the environment
| Environment | Baseline 1 (Classical) | Baseline 2 (Self-Only) | Ours (Aggregated) | Improvement Over Baseline 2 |
|---|---|---|---|---|
| Home | 142.3 | 121.7 | 108.2 | 11.1% |
| Restaurant | 287.6 | 245.3 | 201.8 | 17.7% |
Average cumulative cost over 100 simulation runs. Lower is better.
Limitations and Future Work
We have presented courteous anticipatory planning, a framework for reducing cumulative cost in persistent shared environments by reasoning about what other robots can do and what they are likely to be assigned. Our factored formulation estimates per-robot expected future costs independently, avoiding combinatorial joint rollouts and supporting modular deployment without retraining existing estimators. Across two environments of increasing complexity, amplified gains in the restaurant setting directly validate that distinct capabilities amplifies the value of courteous anticipation.
In our future work, we plan to extend courteous anticipatory planning to concurrent settings, where multiple robots act simultaneously, and temporal planning over overlapping schedules is required.
Frequently Asked Questions
What makes courteous anticipation different from traditional multi-robot planning? Traditional approaches either require centralized coordination or treat each robot independently, while courteous anticipation uses per-robot cost estimates aggregated into a decentralized planning objective.
How does the framework scale with the number of robots? The factored formulation avoids combinatorial joint rollouts, making it computationally feasible as each robot only needs its own cost estimator.
Does the system require retraining when new robots join? No, the modular design allows existing estimators to remain unchanged; only the aggregation function needs to include the new robot's estimate.
What types of tasks benefit most from courteous anticipation? Tasks in shared environments with distinct robot capabilities, such as restaurant settings where different robots perform different roles, show amplified gains.