💻 computer science

Data-Driven Autoregressive Power Prediction for GTernal Robots in the Robotarium

This paper presents a lightweight, data-driven autoregressive predictor for GTernal robots in the Robotarium that achieves high-accuracy, real-time power consumption forecasting by leveraging strong temporal autocorrelation, thereby enabling energy-aware multi-robot algorithms with zero-shot transfer across unseen robots and behaviors.

Original authors: Yassin Abdelmeguid, Ammar Hasan

Published 2026-03-17

📖 4 min read☕ Coffee break read

CC BY 4.0

Original authors: Yassin Abdelmeguid, Ammar Hasan

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

Imagine you have a fleet of tiny, remote-controlled robots buzzing around a giant, high-tech playground called the "Robotarium." These robots are like energetic puppies; they run, turn, stop, and dance. But just like a puppy, they get tired. Their "tiredness" is battery life.

The big problem for the scientists running these robots is: How do we know exactly when a robot is going to run out of juice?

The Old Way: Guessing Based on Speed

Previously, engineers tried to predict battery drain using a simple rule: "If the robot runs fast, it uses more energy. If it stops, it uses less."

Think of this like trying to guess how much gas a car uses just by looking at the speedometer. It's a decent guess, but it misses the messy reality. It doesn't account for the engine getting hot, the radio playing loudly, or the car struggling to start on a cold morning. In the robot world, these "messy realities" are things like motor heat, Wi-Fi glitches, and electronic hiccups. Because of this, the old guessing game was often wrong, leading to robots suddenly dying in the middle of a mission.

The New Discovery: The "Echo" Effect

The authors of this paper decided to stop guessing based on speed and start listening to the robot's "heartbeat."

They collected data from 48,000 moments of robot movement and found something surprising: A robot's power usage today is almost entirely determined by what it was doing a split-second ago.

Imagine you are listening to a song. The note you hear right now isn't random; it's a direct echo of the note that came before it. The researchers found that the robot's energy consumption behaves exactly like that song.

The Math: They found a correlation of 0.95. In plain English, this means if you know what the robot's battery usage was one second ago, you can predict what it will be next second with 95% accuracy.
The Surprise: Knowing how fast the robot is moving (speed) only helped predict the future by 16%. The "echo" of the past was 6 times more important than the current speed!

The Solution: A Tiny Crystal Ball

To use this discovery, they built a very small, smart computer program (an AI model) that acts like a crystal ball.

Instead of asking, "How fast are you going?", the crystal ball asks, "What were you doing just now?"

It looks at the last few seconds of power usage.
It also glances at the speed (just in case).
It then predicts the next second's power usage.

This model is incredibly lightweight. It's so small (only about 7,000 "neurons") that it could run on a simple computer chip inside the robot without slowing it down. In fact, it's 150 times faster than the robot's own control system. It's like having a weather forecaster who can predict the rain in 224 microseconds—faster than you can blink.

Does It Work on Strangers? (The "Zero-Shot" Test)

The real test came when they took this crystal ball, which was trained on one specific robot, and gave it to seven different robots it had never met before.

These new robots had slightly different motors, batteries, and electronics. Usually, a model trained on one machine fails on another. But because this model learned the rhythm of power usage (the "echo") rather than the specific details of one robot, it worked perfectly.

The Result: It predicted the energy usage of these strangers with 87% accuracy.
The Analogy: It's like teaching a chef to cook a perfect steak using one specific cow. You then send that chef to a different farm with different cows, and they can still cook a perfect steak because they learned the technique, not just the specific animal.

Why Does This Matter?

This is a game-changer for robot swarms.

No More Surprises: Robots can now plan their missions knowing exactly when they will run out of battery.
Smarter Simulations: Before sending robots out, engineers can simulate missions in a computer to see if the robots will survive, without worrying about the simulation being wrong about energy.
Real-Time Decisions: Because the prediction is so fast, robots can make split-second decisions to save energy, like slowing down or taking a shortcut, to ensure they make it home.

The Bottom Line

The researchers realized that to predict a robot's energy, you shouldn't look at where it's going; you should look at where it just was. By building a tiny, super-fast AI that listens to this "energy echo," they created a tool that helps robots stay alive longer and work smarter, all while sharing their data so other scientists can build even better robots in the future.

1. Problem Statement

Multi-robot coordination algorithms (e.g., coverage control, task allocation, reinforcement learning) increasingly require energy-awareness to manage battery constraints effectively. However, existing power consumption models rely heavily on kinematic approximations (polynomial functions of velocity or motor commands). These models fail in real-world scenarios because they ignore:

Complex thermal dynamics of motors.
Transient behaviors during acceleration/deceleration.
Wireless communication overhead.
Sensor duty cycles and other hardware-specific effects.

Consequently, kinematic models produce large prediction errors when applied to real telemetry data, leading to unexpected battery failures in physical deployments. The paper addresses the need for a lightweight, accurate, and generalizable power predictor for the GTernal mobile robot platform.

2. Methodology

A. Data Collection

The authors collected a dataset of 48,000 samples from a single GTernal robot in the Georgia Tech Robotarium.

Hardware: GTernal robots (differential-drive, 11cm × 9.5cm) equipped with INA260 power monitors (10 mW precision).
Sampling Rate: Synchronized telemetry at 30 Hz (velocity commands) and 10 Hz (power polling).
Protocols: Six complementary motion trials covering the operational envelope, including structured motion (circles, figure-eights), goal navigation, acceleration variations, extremes (max/min velocity), random walks, and steady-state operation.
Data Scope: 26.5 minutes of continuous operation with power ranging from 3,000 to 8,450 mW.

B. Statistical Analysis & Insight

Before modeling, the authors analyzed the statistical structure of the data:

Temporal Autocorrelation: Power consumption exhibits extremely strong lag-1 autocorrelation ( $\rho_1 \approx 0.95$ ) across all motion patterns.
Feature Dominance: A model using only velocity features explained only 16% of the variance ( $R^2=0.16$ ). In contrast, a model using just the previous power reading explained 90% of the variance.
Theoretical Ceiling: For an AR(1) process with $\rho_1 = 0.95$ , the theoretical maximum $R^2$ is $\approx 0.90$ . This suggests that power dynamics are governed by latent hardware states (thermal inertia, WiFi transients) rather than instantaneous kinematics.

C. Model Architecture

Based on the autocorrelation analysis, the authors designed a lightweight Autoregressive Multi-Layer Perceptron (MLP):

Input Vector (11 dimensions):
- 6 Kinematic features: Linear velocity ( $v$ ), angular velocity ( $\omega$ ), their derivatives ( $\dot{v}, \dot{\omega}$ ), and absolute values ( $|v|, |\omega|$ ).
- 5 Power history lags: The 5 most recent normalized power readings ( $\hat{P}_{t-1} \dots \hat{P}_{t-5}$ ).
Network Structure:
- Three hidden layers with dimensions 64, 64, and 32.
- Activation: Gaussian Error Linear Unit (GELU) for smooth gradients.
- Regularization: Dropout (0.1 probability).
- Output: Single scalar prediction ( $\hat{P}_t$ ), denormalized to milliwatts.
Parameters: Only 7,041 parameters, making it suitable for edge deployment.
Training: Adam optimizer, learning rate $10^{-3}$ , batch size 256, 100 epochs. Data split: Trials 1–4 (Train), Trial 5 (Validation), Trial 6 (Test).

3. Key Contributions

Empirical Characterization: Demonstrated that power consumption on physical differential-drive robots is dominated by temporal persistence (autoregressive dynamics) rather than kinematic state, challenging the standard physics-based modeling approach.
Lightweight Predictor: Developed a 7,041-parameter MLP that achieves near-theoretical prediction accuracy ( $R^2 \approx 0.90$ ) by conditioning on recent power history.
Zero-Shot Transfer: Validated the model on seven unseen robots performing a collision avoidance task (a motion pattern not seen during training) without retraining, proving robustness to hardware variations and new behaviors.
Open Source Release: Released the trained model, dataset, and deployment code to facilitate energy-aware algorithm development.

4. Results

Single-Robot Validation

Accuracy: Achieved $R^2 = 0.92$ on the held-out test trial (steady-state patterns) and a mean $R^2 = 0.90$ across all trials.
Error Metrics: Mean Absolute Error (MAE) of 31.5 mW (0.86% MAPE relative to mean power).
Residuals: The prediction error distribution is approximately Gaussian with a mean of 1.3 mW (unbiased). 90% of errors fall within $\pm 50$ mW.
Performance: The model successfully tracks rapid transitions and steady states with minimal lag, outperforming purely kinematic predictors.

Multi-Robot Physical Validation (Zero-Shot)

Scenario: Deployed on 7 distinct GTernal robots executing a random walk with collision avoidance.
Performance: Achieved a mean $R^2 = 0.87$ across all robots (standard deviation 0.018).
Robustness: Despite manufacturing variations causing systematic shifts in absolute power levels (some robots consumed more power than the training unit), the temporal dynamics remained consistent, allowing the autoregressive model to generalize effectively.
Cumulative Error: Total energy prediction error remained below 2.3% for all robots, sufficient for battery state-of-charge estimation and mission planning.

Deployment Efficiency

Inference Speed: 224 $\mu$ s per inference on GPU (4,500 Hz throughput).
Real-Time Capability: This is 150 $\times$ faster than the Robotarium's 30 Hz control rate, allowing ample computational budget for higher-level planning.
Edge Compatibility: The model runs on the GTernal's Raspberry Pi using NumPy without requiring PyTorch.

5. Significance

This work fundamentally shifts the paradigm for robot energy modeling from kinematic physics-based approximations to data-driven autoregressive modeling.

Algorithmic Impact: Enables multi-robot planners and reinforcement learning agents to reason about battery depletion with high fidelity in both simulation and physical hardware.
Practicality: The model's small size and high inference speed make it deployable on resource-constrained edge devices (e.g., Raspberry Pi) without external dependencies.
Generalization: Proves that a single model trained on one robot can effectively predict power for an entire fleet of heterogeneous units performing unseen tasks, a critical requirement for scalable swarm robotics.

The paper concludes that for mobile robots, recent power history is a far more predictive feature than current velocity, and leveraging this temporal dependency allows for highly accurate, low-cost energy prediction.