⚡ electrical engineering

Model-Free Adaptive Parameter Tuning for Efficient Multi-Robot Warehouse Operations

This paper presents a model-free adaptive parameter tuning framework based on Extremum Seeking Control that continuously optimizes multi-robot warehouse digout strategies in real-time, achieving significant throughput improvements over fixed policies by dynamically adjusting to varying facility configurations and operational conditions.

Original authors: Pratap Tokekar, Mouhacine Benosman, Rahul Chandan, Alexandre Ormiga Galvao Barbosa, Michael Caldara, Joseph W. Durham

Published 2026-08-25

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CC BY 4.0

Original authors: Pratap Tokekar, Mouhacine Benosman, Rahul Chandan, Alexandre Ormiga Galvao Barbosa, Michael Caldara, Joseph W. Durham

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Inside the vast, humming warehouses that power modern e-commerce, thousands of small robots move with the precision of a well-rehearsed orchestra. Their job is to retrieve shelves, known as pods, that hold the items customers have ordered. These pods are stacked in dense, grid-like blocks to save space. When a robot needs to grab a specific shelf buried deep inside a block, it cannot simply reach in; it must first move the shelves blocking the way. This process, called digging out, requires a central computer to decide the best sequence of moves. The computer uses a set of rules, or parameters, to weigh different options: should it send the obstructing shelves to a completely different part of the warehouse, or should it shuffle them around within the same block? Sending them away uses more robots in the main aisles and can cause traffic jams, while shuffling them locally avoids the aisles but takes longer to clear the path. Finding the perfect balance for these rules is incredibly difficult because the warehouse is a living, changing environment. The best setting for a quiet morning might be terrible during a busy afternoon, and a configuration that works for one warehouse layout often fails in another. Traditionally, engineers have had to manually test thousands of combinations in simulations to find a good setting, a slow and expensive process that still cannot keep up with real-time changes.

A team of researchers at Amazon Robotics has developed a new way to solve this problem, allowing the warehouse software to tune itself in real time. Instead of relying on a human to guess the right settings or running endless simulations, they applied a control technique called extremum seeking. This method treats the warehouse like a system that can learn from its own mistakes. The computer makes tiny, rhythmic adjustments to its decision-making rules, nudging them slightly up and down like a hand testing the temperature of a shower. It then watches how these small nudges affect the overall speed of the warehouse, measured by how many items are retrieved per hour. By correlating these tiny changes with the results, the system can figure out which direction leads to better performance without needing to understand the complex physics of every robot movement. It is a model-free approach, meaning it does not require a perfect mathematical description of the entire warehouse to work; it simply observes cause and effect.

The researchers tested this self-tuning system in a highly detailed computer simulation that mimicked real warehouse operations, including the movement of hundreds of robots and the flow of thousands of orders. They wanted to see if the system could actually detect a signal in the noise. In a real warehouse, the effect of changing a rule might take several minutes to show up in the total number of items retrieved, as the robots finish their current tasks and the new plan ripples through the floor. The study confirmed that the rhythmic nudges did indeed create measurable changes in the throughput, proving the system could "hear" the signal. They also measured the delay, finding that it took about four minutes for a change in the digging rules to fully impact the overall speed. With this knowledge, the system was programmed to wait for the dust to settle before making its next adjustment, ensuring it was reacting to the right cause.

When the adaptive system was put to the test against fixed, pre-set rules, it consistently outperformed them. In simulations where the warehouse layout or the number of robots changed, the fixed rules often struggled, leading to a drop in efficiency. The self-tuning system, however, automatically adjusted its parameters to match the new conditions, recovering an average of five percent in throughput. This might sound like a small number, but in a facility processing millions of items, that difference translates to thousands of extra orders fulfilled every day. The advantage grew even larger when the researchers simulated sudden disruptions, such as half of the human workstations logging off for a shift change. In these dynamic scenarios, the adaptive system improved throughput by more than eight percent overall, and by over fourteen percent in the period immediately following the disruption. It did this by automatically increasing the allowed queue size at the stations, allowing the remaining robots to work more efficiently without getting stuck waiting for human help.

The study also demonstrated that the system could find the optimal settings on its own, regardless of where it started. Whether the initial rules were set to be very conservative or very aggressive, the system consistently drifted toward a narrow, optimal range of values. This suggests that the method does not just improve a bad starting point; it actively searches for the true best setting for the current environment. The researchers found that this approach works well even when the warehouse is very large, with over a thousand robots, and that the system remains stable as it converges on the best solution. By eliminating the need for manual tuning and allowing the warehouse to adapt instantly to changing demands, this work offers a new paradigm for managing complex robotic fleets. It turns a static, rigid planning process into a fluid, responsive one, ensuring that the warehouse operates at its peak efficiency no matter how the conditions change.

Technical Summary: Model-Free Adaptive Parameter Tuning for Efficient Multi-Robot Warehouse Operations

Problem Statement

Robotic Fulfillment Centers (FCs) utilize fleets of mobile robots to retrieve inventory pods from dense storage blocks. A critical operational challenge is the "digout" problem: when a target pod is buried deep within a block, obstructing pods must be moved to access it. Multi-robot planners resolve this using parameterized cost functions that dictate the trade-off between two primary strategies:

External Digout: Sending obstructing pods to other blocks, which utilizes travel lanes and increases traffic congestion.
Internal Shuffling: Moving obstructing pods within the block using free cells, which avoids lane congestion but increases extraction time.

The optimal balance between these strategies (controlled by cost parameters) is not static. It depends on specific facility configurations (map layout, robot count, storage density) and dynamic operational conditions (station demand, congestion patterns). Traditional approaches rely on offline grid searches over expensive simulations to find optimal parameters. However, these fixed parameters often fail to transfer to new configurations or adapt to real-time changes, leading to suboptimal throughput. Furthermore, there is no closed-form model relating planning parameters to system-level throughput, and the effects of parameter changes are delayed by minutes, complicating credit assignment.

Methodology

The authors propose a Model-Free Adaptive Parameter Tuning framework based on Extremum Seeking Control (ESC). This approach eliminates the need for analytical models or offline grid searches by continuously adjusting planner parameters in response to real-time throughput measurements.

Core Mechanism

The ESC controller operates by perturbing the planning cost parameters (specifically the dig cost $\gamma$ and queue size parameter $\rho$ ) with sinusoidal dither signals. The system correlates these perturbations with changes in the measured throughput to estimate the gradient of the performance function.

Continuous-Time Formulation: The control law adds a sinusoidal signal $\xi(t) = a \sin(\omega t)$ to the parameter estimate. The resulting throughput signal is high-pass filtered to remove DC components, demodulated (multiplied by the dither signal), and low-pass filtered to estimate the gradient. The parameter is then updated via gradient ascent.
Discrete-Time Implementation: Since updates occur periodically, the algorithm is discretized using backward Euler for high-pass filtering and exponential smoothing for low-pass filtering.
Phase Delay Compensation: Recognizing that throughput changes lag behind parameter changes (due to the time required for planning decisions to propagate through the system), the demodulation signal is phase-shifted to align with the system's response delay.
Multi-Parameter Extension: For tuning multiple parameters simultaneously, the framework employs orthogonal dither frequencies to prevent cross-coupling between updates.

Convergence Guarantees

The paper provides theoretical analysis (Lemma 1) demonstrating local practical convergence under assumptions of bounded, smooth performance functions and sufficiently small dither amplitudes and high frequencies. The method is robust to noise, unmodeled dynamics, and the delayed effects inherent in large-scale FC operations.

Key Contributions

Adaptive Framework: Introduction of an ESC-based framework that automatically tunes digout planner parameters in real-time, eliminating the need for manual parameter sweeps or offline optimization.
Model-Free Optimization: Demonstration that gradient-based optimization is feasible for complex, discrete-event robotic systems without requiring a closed-form model of the relationship between planning costs and throughput.
System Characterization: Empirical validation of the system's responsiveness to parameter perturbations and the quantification of the phase delay (approx. 4 minutes) between cost changes and throughput response.
Dynamic Adaptation: A mechanism that allows the system to self-tune in response to dynamic operational shifts, such as changes in station availability or workload patterns.

Experimental Results

The framework was evaluated using a high-fidelity discrete-event simulator modeling two different warehouse maps (MAP1 and MAP2) with varying robot fleet sizes (up to 1,600 robots).

Gradient Estimation (RQ1): Power Spectral Density analysis confirmed that dither signals in the dig cost parameter produce observable oscillations in throughput, validating the feasibility of gradient estimation.
Phase Delay (RQ2): Cross-correlation analysis identified a ~4-minute delay between parameter changes and throughput response, informing the selection of update periods and filter time constants.
Nominal Performance (RQ3):
- The adaptive ESC policy consistently outperformed fixed policies across various robot counts and initial parameter settings.
- ESC automatically converged to an optimal queue size range ( $\rho \approx 1.6 - 2.0$ ) regardless of initialization.
- Improvements were most significant (24–42%) when starting from suboptimal initial conditions, with modest gains (1–2%) when starting near the optimum.
Transfer Regret (RQ3): When fixed policies tuned on one configuration were applied to different maps or robot counts, they incurred an average throughput loss of 5.0%. The ESC policy, by adapting online, eliminated this transfer regret.
Dynamic Conditions (RQ4): In a scenario where 50% of pick stations logged off mid-operation, the ESC policy adapted the queue size parameter to match the reduced capacity. This resulted in an 8.4% overall throughput improvement and a 14.3% improvement in the post-disturbance period compared to fixed policies.

Significance and Claims

The paper claims to bridge the gap between search-based planning and adaptive control, providing a self-tuning paradigm for dense FC operations. The significance of this work lies in:

Eliminating Manual Tuning: Removing the impractical need for configuration-specific parameter sweeps.
Real-Time Adaptability: Enabling systems to maintain optimal performance as operational conditions (e.g., demand, congestion, station availability) shift dynamically.
Robustness: Offering a solution that is robust to the delayed, cascading effects of planning decisions in large-scale multi-robot systems where traditional model-based control is infeasible.

The authors note that while the work focuses on digout cost and queue size parameters, the ESC framework is generalizable to other planning parameters and systems where the relationship between control inputs and performance metrics is complex and time-varying.