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Multi-Robot Task Allocation Using Global Games with Negative Feedback: The Colony Maintenance Problem
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Proposes a global-games utility for multi-robot task allocation in which a negative feedback term in the number of foraging robots makes the colony maintenance system resilient to robot removal, validated in a Matlab simulation with 12 robots.
Problem
Multi-robot task allocation for dynamic, repeatedly played tasks (colony energy maintenance) where threshold-based global games with positive feedback are brittle to robot removal by a human and cannot adapt to changing signals.
Approach
Replaces the positive feedback of standard global games with negative feedback: each robot's marginal utility of foraging decreases in the number of foraging robots (via an exponential term), which removes the trivial all-or-none dominant strategy, yields a unique mixed Nash equilibrium, and makes the system self-correct when robots are removed.
Key results
- In a simulation with N=12 robots, the number of foraging robots tracks the mixed Nash equilibrium, with typically more robots foraging than predicted due to hysteresis.
- After removing 6 of 12 robots at t=900, only one idle robot remained in the colony at t=901, showing the system re-allocates robots to foraging.
- Qualitative comparison (Table 1) rates the proposed approach as repeated, linear complexity, and Nash-optimal, versus one-shot and heuristic prior approaches.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use negative feedback so marginal utility decreases as the number of foraging robots rises | Proposed global-game task allocation · Colony maintenance with robot recruitment | resilience to robot removal | Helped |
| Recruit a robot that is foraging | Proposed global-game task allocation · Colony maintenance | marginal utility for remaining robots | Helped |
| Remove 6 of the 12 robots at t=900 | Proposed global-game task allocation · Colony maintenance simulation | idle robots: 7 -> one | Hurt |
| Use positive feedback, making marginal utility increase with the number of foraging robots | Traditional global games task allocation · Colony maintenance with robot removal | resilience to robot removal | Hurt |
| Add action hysteresis so foraging robots continue until returning with an energy source | Proposed global-game task allocation · Colony maintenance simulation | foraging robots relative to Nash equilibrium | Hurt |
| Remove feedback with respect to the number of active robots | Proposed global-game task allocation · Colony maintenance | ability to regulate task allocation | Hurt |
Surprising findings
- Removing robots appears to enhance colony performance by reducing congestion, according to the simulation results.
- Positive feedback global games can lead to cascading failure when foraging robots are removed, with all remaining robots staying idle.
Limitations
- Evaluated only in a single simulated environment with 12 robots and no real-robot experiments.
- Simulated foraging often exceeds the Nash equilibrium count due to action hysteresis.
- Assumes centralized knowledge of the signal and number of foraging robots; no heterogeneity or multi-signal experiments.
Experimental setup
Benchmarks: Matlab simulation of colony foraging with 12 robots
Metrics: number of robots foraging vs Nash equilibrium colony energy level resilience to robot removal
Baselines: Kriger et al. Kanakia et al. MILP
Builds on: global games Kanakia et al. colony maintenance model Kriger et al. foraging approach
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