⚡ electrical engineering

Hybrid Software Controller for Precise Position and Trajectory Control of Quadcopters

This paper proposes and validates a hybrid control framework that enhances quadcopter trajectory tracking in dynamic environments by integrating a traditional PID controller with real-time reference modulation via Artificial or Deep Neural Networks, demonstrating that the PID+DNN approach outperforms PID+ANN in convergence smoothness and control efficiency.

Original authors: Mayank Sharma, Utkarsh Panth, Shivani Verma, Rachna Jain, Amit Srivastava

Published 2026-08-04

📖 6 min read🧠 Deep dive

CC BY 4.0

Original authors: Mayank Sharma, Utkarsh Panth, Shivani Verma, Rachna Jain, Amit Srivastava

Original paper licensed under CC BY 4.0 (https://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 are trying to teach a clumsy, four-legged robot dog to walk in a straight line while a strong wind blows against it. If you just tell the dog "go forward," it might trip, spin in circles, or get stuck because it doesn't know how to adjust to the wind or its own wobbly legs. This is the world of Unmanned Aerial Vehicles (UAVs), or quadcopters—those cool flying drones we see taking photos and delivering packages. They are tricky to control because they are naturally unstable; if you push them, they wobble, and if the wind hits them, they drift.

To keep these drones steady, engineers usually use a control system called a PID controller. Think of a PID controller as a very strict, by-the-book coach. It constantly checks where the drone is versus where it should be. If the drone is off course, the coach yells, "Move left!" or "Move up!" The coach has three rules: it reacts to the current mistake (Proportional), it remembers past mistakes to fix lingering errors (Integral), and it predicts future mistakes to stop them early (Derivative). However, this coach has a flaw: it's a bit rigid. If the wind is too strong, the drone's motors hit their maximum speed (like a runner hitting a wall), and the coach keeps screaming "Go faster!" even though it can't. This causes the drone to overshoot and wobble wildly, a problem called "wind-up." To fix this, engineers added a "safety brake" (anti-windup) to stop the coach from screaming when the motors are maxed out. But even with the safety brake, the coach still can't learn or adapt to new, tricky situations on the fly.

This brings us to a new idea: what if we gave the coach a brain that could learn? This is where Artificial Neural Networks (ANNs) and Deep Neural Networks (DNNs) come in. Imagine these as a student sitting next to the coach. The student watches the wind and the drone's wobbles, learns from the mistakes, and whispers a tiny correction to the coach's "target" before the coach even yells. This paper, titled "Hybrid Software Controller for Precise Position and Trajectory Control of Quadcopters" by Mayank Sharma and colleagues from Amity University, explores exactly this. The researchers built a simulation to see if combining the strict coach (PID) with a learning student (Neural Network) could make the drone fly smoother and more accurately than the coach working alone.

The Experiment: Teaching the Drone to Dance in the Wind

The researchers set up a virtual 3D world to test their ideas. They created a digital quadcopter that weighed 1.0 kg and had a maximum thrust of 20 N. To make things realistic, they didn't just let the drone fly in a calm room; they blasted it with a wind that pushed and pulled with a strength of 0.3 N, changing direction in a wave pattern every 0.5 seconds (a frequency of 0.5 Hz). The goal was simple: get the drone to fly to a specific spot in the air—2.0 meters forward, 2.0 meters to the side, and 1.5 meters up—and stay there without wobbling.

They tested three different "brains" for the drone:

The Classic Coach: A standard PID controller with the safety brake (anti-windup) to handle the motor limits.
The Coach + The Student (ANN): The PID controller paired with a simple Artificial Neural Network. This student had a "shallow" brain with just two layers of neurons, designed to quickly spot errors and whisper a correction to the target.
The Coach + The Deep Thinker (DNN): The PID controller paired with a Deep Neural Network. This student had a much "deeper" brain with four layers of neurons, including some special filters to ignore noise and handle complex, messy situations better.

What They Found: The Deep Thinker Wins the Race

The results, observed over a 20-second flight simulation, told a clear story. Both the "Coach + Student" teams were much better than the Classic Coach alone, proving that adding a learning layer helps the drone handle the wind. However, the two students had very different personalities.

The ANN (the simple student) was fast but a bit reckless. It reacted quickly to the wind, getting the drone to the target in about 2 seconds. But, it was a bit too eager. When it tried to correct the path, it sometimes pushed the drone too hard, causing it to overshoot the target and wobble a bit before settling down. It was like a sprinter who starts too fast and stumbles at the finish line. The drone's movements were a bit jerky, and it had to work harder (more "control effort") to stay on track.

The DNN (the deep thinker), on the other hand, was a bit more cautious at the start. It took slightly longer to get the drone moving, but once it got going, it was incredibly smooth. It didn't overshoot as much and settled into the target position with very little wobble. The simulation showed that after the first 5 seconds, the DNN was keeping the drone much closer to the perfect path than the ANN. In fact, the final "Root Mean Square" (RMS) error—a fancy way of measuring how far off the drone was on average—was about 0.03 meters for the DNN, compared to 0.05 meters for the ANN.

The difference was also clear in how the drone moved. The ANN made the drone's motors work harder and more erratically, especially in the twisting motions (roll and pitch). The DNN, however, kept the motor commands smooth and steady. It was like the difference between a driver who slams on the brakes and jerks the steering wheel versus a driver who glides smoothly through traffic.

The Verdict

The study suggests that while a simple learning network (ANN) can help a drone fly faster initially, a deeper, more complex learning network (DNN) is better at keeping the flight smooth and accurate, especially when the wind is blowing. By letting the DNN gently adjust the target path in real-time based on the errors it sees, the drone doesn't have to fight as hard against the wind.

The authors conclude that this "hybrid" approach—mixing the reliable, old-school PID controller with a modern, learning-based neural network—is a powerful way to make drones smarter. It keeps the stability of the classic system while adding the ability to adapt to the chaos of the real world. While these results were found in a computer simulation with a 20-second flight time, they suggest that future drones could navigate stormy skies with the grace of a dancer rather than the stumble of a clumsy robot.

Technical Summary: Hybrid Software Controller for Precise Position and Trajectory Control of Quadcopters

Problem Statement
Quadcopters, while versatile for applications like surveillance and delivery, present significant control challenges due to their underactuated nature, strong coupling between rotational and translational dynamics, and sensitivity to environmental disturbances such as wind. The industry standard, the Proportional–Integral–Derivative (PID) controller, offers simplicity and stability for linear or mildly nonlinear systems but suffers in dynamic environments. Key limitations include:

Lack of Adaptability: Fixed control gains ( $K_p, K_i, K_d$ ) cannot adjust to changing conditions like wind gusts or payload variations.
Integrator Wind-up: When actuators (motors) reach saturation limits, the integral term accumulates excessive error, leading to overshoot, instability, and slow recovery.
Disturbance Rejection: Classical PID, even with anti-windup and feedforward components, struggles to differentiate error types or adapt to complex, time-varying nonlinearities.

Methodology
The authors propose two hybrid control architectures designed to retain the stability of PID while introducing adaptive intelligence via neural networks. Both methods utilize a real-time reference modulation strategy where a neural network dynamically adjusts the reference trajectory setpoints based on current position and angle errors, rather than directly controlling the actuators.

System Model: A 6-degree-of-freedom (6-DOF) rigid-body quadcopter model is used, incorporating translational dynamics (thrust, gravity, drag, wind) and rotational dynamics (torques, moments of inertia). External wind is modeled as a time-varying sinusoidal force.
Base Controller: A standard PID controller with back-calculation anti-windup logic is employed. This mechanism adjusts the integral term when control outputs (thrust or torque) exceed physical limits, preventing wind-up.
Hybrid Approaches:
- PID + ANN (Artificial Neural Network): A shallow feedforward network (2 hidden layers, 32 neurons each) takes 6 inputs (position and angular errors) and outputs a 3-dimensional reference correction vector ( $\Delta r$ ) for the $x, y, z$ axes. It is trained online using backpropagation to minimize Mean Squared Error (MSE).
- PID + DNN (Deep Neural Network): A deeper architecture (4 hidden layers with 128, 128, 64, and 32 neurons) featuring Dropout for regularization and mixed activation functions (ReLU and Tanh). It processes the same error inputs but aims for better generalization in noisy, complex dynamics. It is trained online using the Adam optimizer.
Control Loop: At each time step, the neural network computes a correction to the nominal reference ( $r_{adj} = r_{nom} + \Delta r$ ). This adjusted reference is fed into the PID controller, which generates the thrust and torque commands.

Key Contributions

Novel Hybrid Architecture: The paper introduces a specific control design where neural networks act as reference modulators rather than direct controllers, preserving the interpretability and robustness of the underlying PID loop.
Comparative Analysis: It provides a direct simulation-based comparison between a shallow ANN and a deep DNN in the context of quadcopter trajectory tracking under wind disturbances.
Integration of Anti-Windup: The work explicitly combines anti-windup strategies with neural reference adaptation to address both saturation issues and dynamic adaptability simultaneously.

Results
Simulations conducted over a 20-second period with sinusoidal wind disturbances ($0.5$ Hz, $0.3$ N) yielded the following findings:

Convergence: PID+ANN demonstrated faster initial convergence (approx. 2 seconds) but exhibited higher overshoot and oscillations in the X and Y axes. PID+DNN showed a slightly slower initial rise but a smoother, more stable settling behavior.
Tracking Accuracy: While PID+ANN performed well initially, PID+DNN achieved superior long-term precision. The final Root Mean Square (RMS) error for PID+DNN was approximately 0.03 m, compared to 0.05 m for PID+ANN.
Control Effort: PID+DNN generated smoother control inputs (torques and thrust) with fewer aggressive oscillations, particularly in the roll and pitch axes. This indicates lower control stress and more efficient actuation.
Disturbance Rejection: The DNN-based approach demonstrated better handling of nonlinear disturbances, resulting in a more direct and compact 3D trajectory compared to the wider initial arcs observed with the ANN.

Significance and Claims
The paper claims that combining classical control with neural network-based reference adaptation offers a "powerful and adaptable method" for intelligent UAV navigation. The authors assert that while the PID+ANN approach is effective for simple nonlinearity compensation, the PID+DNN configuration provides superior generalization and flexibility due to its deeper network structure.

The study concludes that this hybrid approach successfully addresses the rigidity of fixed-gain PID controllers without sacrificing stability. By allowing the system to learn optimal corrections in real-time based on error dynamics, the proposed methods enable quadcopters to maintain precise trajectory tracking and reject disturbances more effectively than traditional anti-windup PID controllers alone. The work positions this architecture as a lightweight yet robust solution for real-time control of nonlinear aerial systems.

The Experiment: Teaching the Drone to Dance in the Wind

What They Found: The Deep Thinker Wins the Race

The Verdict

Technical Summary: Hybrid Software Controller for Precise Position and Trajectory Control of Quadcopters

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