⚡ electrical engineering

Predictive Control over LAWN: Joint Trajectory Design and Resource Allocation

This paper proposes a joint trajectory design and resource allocation framework for low-altitude wireless networks, utilizing model predictive control and finite blocklength transmission to optimize drone paths and power allocation for reliable real-time control of mobile automated guided vehicles through an alternating optimization algorithm validated by simulations and AirSim experiments.

Original authors: Haijia Jin, Jun Wu, Weijie Yuan, Ruizhi Ruan, Jiacheng Wang, Dusit Niyato, Dong In Kim, Abbas Jamalipour

Published 2026-06-02

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CC BY 4.0

Original authors: Haijia Jin, Jun Wu, Weijie Yuan, Ruizhi Ruan, Jiacheng Wang, Dusit Niyato, Dong In Kim, Abbas Jamalipour

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 a busy warehouse floor filled with self-driving carts (AGVs) that need to move precisely along specific paths to deliver packages. Now, imagine a drone flying overhead, acting as a "traffic controller" that talks to these carts via wireless signals, telling them exactly when to speed up, slow down, or turn.

This paper is about making that conversation between the drone and the carts as perfect as possible, even when the wireless connection is shaky or the carts are moving fast.

Here is a breakdown of the paper's ideas using simple analogies:

1. The Problem: A Shaky Walkie-Talkie

In the past, engineers treated the drone's flight path and the wireless signal as two separate jobs. They would plan the drone's route first, then worry about the signal later.

The Flaw: If the signal gets weak (like a walkie-talkie with static), the cart might not get the "turn left" command on time. If the cart doesn't get the command, it might crash or go off-course.
The Reality: In the real world, data packets are short (like quick, urgent whispers), not long, perfect sentences. This is called Finite Blocklength (FBL). It means the signal is more prone to errors if the distance is too far or the power is too low.

2. The Solution: The "Smart Conductor"

The authors propose a system where the drone acts like a smart conductor who doesn't just wave a baton but constantly listens to the orchestra and adjusts the music in real-time.

Model Predictive Control (MPC): Instead of just reacting to what happened now, the drone looks ahead. It's like a chess player thinking three moves ahead. The drone predicts where the carts will be in the next few seconds and calculates the best commands to send now to ensure they stay on track.
The "Outage" Safety Net: The system calculates the "outage probability"—essentially, the chance that the message won't get through. If the drone knows the signal might fail, it adjusts its plan immediately. It might fly closer to a cart or boost its power, just like a speaker leaning in closer to be heard over a loud crowd.

3. The Three-Way Dance

The paper solves a complex puzzle where three things must change together to work best:

The Drone's Path: Where should the drone fly to be closest to the carts?
The Power: How loud should the drone shout (transmit power) to each cart?
The Commands: What specific instructions should the carts follow?

The authors created an algorithm that tweaks all three at the same time. It's like a dance where the drone, the power, and the instructions are all partners; if one partner stumbles, the others adjust instantly to keep the dance smooth.

4. How They Solved the Math

The math behind this is very messy (non-convex), like trying to find the lowest point in a foggy, bumpy landscape.

The Trick: They broke the big, scary problem into three smaller, easier problems and solved them one by one, over and over again (an "Alternating Optimization" framework).
The Tools: They used two mathematical "flashlights":
- Projected Gradient Descent: Like walking downhill step-by-step, checking your footing at every step to ensure you don't fall off a cliff.
- Successive Convex Approximation: Like smoothing out a bumpy road with a roller so you can drive straight over it.

5. The Results: Testing the Theory

The team tested their idea in two ways:

Computer Simulations: They ran thousands of virtual scenarios. They found that their "Smart Conductor" method kept the carts on track much better than older methods (like giving everyone equal power or flying in a straight line). Even when the signal was bad or the carts made sharp turns, their system kept the error low.
AirSim Experiments: They took the code and ran it in a realistic flight simulator (AirSim) that included wind, rain, and fog. Even with these real-world "messy" conditions, the drone successfully guided the carts, proving the math works in a physical-like environment.

Summary

In short, this paper teaches a drone how to be a better boss for self-driving carts. Instead of just flying a pre-set path and shouting orders, the drone constantly calculates the best route, the best volume for its voice, and the best instructions to ensure the carts arrive exactly where they need to go, even if the wireless connection is imperfect.

Technical Summary: Predictive Control over Low-Altitude Wireless Networks

Problem Statement
This work addresses the challenge of real-time wireless control for multiple mobile Automated Guided Vehicles (AGVs) within Low-Altitude Wireless Networks (LAWNs) assisted by an aerial drone. The core problem lies in the tight coupling between communication reliability and control performance in latency-critical scenarios. Traditional approaches often treat communication and control as independent subsystems or assume infinite blocklength (IBL) transmissions, which fail to capture the stringent latency and reliability requirements of real-time control. In such systems, operational periods are segmented into short time slots, necessitating finite blocklength (FBL) transmission. Under FBL, the achievable rate is non-convex and highly sensitive to signal-to-noise ratio (SNR), blocklength, and block error rate (BLER), making the joint optimization of control policy, transmit power, and drone trajectory significantly more complex than in IBL-based systems. Furthermore, existing studies often overlook the intricate interplay between communication outages and the stability of inner-loop control mechanisms, particularly in multi-agent coordinated settings.

Methodology
The authors propose a communication-assisted Model Predictive Control (MPC) framework where a drone serves multiple AGVs via FBL transmission. The methodology proceeds through the following steps:

System Modeling:
- Communication: The air-to-ground (A2G) channel is modeled using Nakagami-m fading to account for both Line-of-Sight (LoS) and Non-Line-of-Sight (NLoS) conditions. The achievable rate is derived using FBL theory, incorporating SNR, blocklength, and BLER constraints.
- Control: The AGVs are modeled as linear discrete-time systems. To ensure smooth actuation, the system is reformulated using an augmented state vector that includes the previous control input. The control objective is to minimize trajectory tracking error and control effort over a finite prediction horizon.
- Integration: The framework explicitly models transmission reliability via outage probability ( $P_k[n]$ ). The system dynamics are reformulated to account for the probability of control command failure; during an outage, the AGV evolves based on intrinsic dynamics without external input. This outage probability is integrated directly into the MPC cost function.
Problem Formulation:
A joint optimization problem is formulated to minimize the expected control cost by simultaneously optimizing the control input sequence, transmit power allocation, and drone trajectory. The problem is subject to constraints on total transmit power, maximum drone speed, flight boundaries, and control input limits. The resulting problem is non-convex due to the coupling of variables and the complex nature of the FBL rate expression.
Solution Algorithm:
- Closed-Form Derivation: The authors first derive a closed-form expression for the outage probability under FBL transmission.
- Reformulation: Using this expression, the original problem is recast into a Quadratic Programming (QP) structure.
- Alternating Optimization (AO): An AO framework is developed to solve the non-convex problem by decomposing it into three tractable sub-problems:
  - Control Strategy: Solved as a standard QP using convex optimization techniques.
  - Power Allocation: Solved using the Projected Gradient Descent (PGD) method with backtracking line search to handle the non-convex objective.
  - Drone Trajectory: Solved using Successive Convex Approximation (SCA) to linearize non-convex terms via first-order Taylor expansions.
- The algorithm iteratively updates these variables until convergence. The paper provides a rigorous analysis of the algorithm's convergence properties and computational complexity.

Key Contributions

Novel Framework: Development of a wireless control framework for drone-assisted LAWNs that enables real-time remote trajectory tracking of multiple AGVs under FBL transmission, explicitly coupling communication reliability (via outage probability) with MPC-based control.
Joint Optimization Formulation: Formulation of a joint optimization problem that minimizes total control cost by optimizing control inputs, power allocation, and drone trajectory. This formulation explicitly captures the impact of communication disruptions on control performance, subject to physical mobility and power constraints.
Algorithmic Solution: Derivation of a closed-form outage probability expression and the subsequent transformation of the non-convex problem into a QP structure. The development of an AO framework utilizing PGD and SCA techniques to achieve computationally efficient sub-optimal solutions, accompanied by convergence and complexity analysis.
Validation: Extensive simulations and AirSim-based experiments validating the approach against baseline schemes (Predictive PID, Predictive LQR, Equal Power Allocation, and Straight Flight).

Results

Convergence: Simulations demonstrate that the proposed algorithm converges rapidly (within a few iterations) to a stable control cost across different time slots.
Robustness: The proposed method maintains lower Root Mean Square Error (RMSE) in trajectory tracking compared to benchmarks, even under imperfect channel state information (CSI) and varying power budgets. It shows slower degradation in performance as channel estimation errors increase.
Impact of Parameters:
- Power Budget: Higher power budgets lead to improved control accuracy. The proposed joint optimization significantly outperforms Equal Power Allocation (EPA), especially in low-reliability scenarios.
- Rate Threshold: As the required data rate threshold increases, control cost rises due to higher outage probabilities. The proposed method manages this trade-off more effectively than baselines.
- Blocklength: Control cost decreases as blocklength increases, converging toward the IBL case. The proposed method consistently outperforms static allocation and fixed-trajectory baselines.
Trajectory Adaptation: In multi-AGV scenarios, the drone dynamically adjusts its trajectory to prioritize areas with complex AGV movements (e.g., sharp turns), whereas baseline schemes (like EPA) result in longer, less efficient trajectories and higher tracking deviations.
AirSim Validation: Experiments on the AirSim platform, incorporating realistic environmental disturbances (rain, wind, fog), confirm the method's practicality. While physical constraints introduce more deviation than ideal simulations, the drone still successfully hovers near high-complexity regions to support AGVs, demonstrating robustness.

Significance
The paper claims that its primary significance lies in addressing the gap between communication reliability and control stability in real-time, latency-critical IoT systems. By moving beyond the assumption of infinite blocklength and treating communication and control as a unified system, the proposed framework offers a more realistic and effective approach for drone-assisted LAWNs. The work provides a practical solution for coordinating multiple mobile agents in dynamic environments, demonstrating that joint optimization of trajectory, power, and control policy is essential for maintaining high-performance tracking under strict communication constraints. The validation via AirSim further underscores the practical applicability of the theoretical model in physically grounded, disturbance-prone environments.