Real-time Neural-MPC: Deep Learning Model Predictive Control for Quadrotors and Agile Robotic Platforms (2203.07747v5)

Abstract: Model Predictive Control (MPC) has become a popular framework in embedded control for high-performance autonomous systems. However, to achieve good control performance using MPC, an accurate dynamics model is key. To maintain real-time operation, the dynamics models used on embedded systems have been limited to simple first-principle models, which substantially limits their representative power. In contrast to such simple models, machine learning approaches, specifically neural networks, have been shown to accurately model even complex dynamic effects, but their large computational complexity hindered combination with fast real-time iteration loops. With this work, we present Real-time Neural MPC, a framework to efficiently integrate large, complex neural network architectures as dynamics models within a model-predictive control pipeline. Our experiments, performed in simulation and the real world onboard a highly agile quadrotor platform, demonstrate the capabilities of the described system to run learned models with, previously infeasible, large modeling capacity using gradient-based online optimization MPC. Compared to prior implementations of neural networks in online optimization MPC we can leverage models of over 4000 times larger parametric capacity in a 50Hz real-time window on an embedded platform. Further, we show the feasibility of our framework on real-world problems by reducing the positional tracking error by up to 82% when compared to state-of-the-art MPC approaches without neural network dynamics.

• The paper presents a novel Neural MPC framework that integrates high-capacity neural networks into the MPC loop for real-time control of agile quadrotors.
• It employs local approximations and a modified RTI scheme to reduce computational load while maintaining accurate dynamic modeling.
• Experiments demonstrate significant tracking improvements, with up to 82% error reduction compared to nominal controllers in simulations and real-world tests.

Real-Time Neural MPC: Deep Learning Model Predictive Control for Quadrotors and Agile Robotic Platforms

The paper "Real-time Neural MPC: Deep Learning Model Predictive Control for Quadrotors and Agile Robotic Platforms" presents a novel framework for incorporating complex neural network models within the Model Predictive Control (MPC) paradigm for real-time applications. The paper emphasizes the challenge of balancing accurate dynamics modeling and real-time computational feasibility, especially for highly agile systems such as quadrotors.

Key Contributions and Methodology

The primary contribution of this research is the introduction of Real-time Neural MPC (Neural MPC), an efficient approach that enables embedding high-capacity neural network models into the MPC framework without violating real-time constraints. The framework was rigorously tested through simulations and real-world experiments involving a quadrotor, demonstrating effective incorporation of large neural networks for dynamic modeling within an MPC loop.

The approach revolves around overcoming the computational bottlenecks associated with integrating neural networks into real-time MPC. Traditional first-principle models used in MPC often fall short in accurately representing complex dynamic effects. Neural networks offer a solution by capturing these intricate dynamics but suffer from high computational complexity, which hinders their real-time applicability.

Local Approximation Strategy

One of the key innovations in the Neural MPC framework is the use of local approximations. The authors approximate the complex neural network dynamics model locally around the current state and control inputs. By doing so, the heavy computations related to neural network evaluations are significantly reduced within the optimization process. This approximation involves linearizing the neural network model and leveraging efficient parallelization on CPU or GPU, enhancing computational speed without sacrificing model accuracy.

Real-Time Iteration (RTI) Scheme

The paper employs a real-time iteration (RTI) scheme modified to handle neural network dynamics efficiently. The RTI scheme divides the optimization process into three phases: QP Preparation, Data-Driven Dynamics Preparation, and Feedback Response. This division allows for pre-computation and efficient handling of the model's computational load using parallelized operations for neural network evaluations, ensuring the controller can operate at high frequencies required for agile platforms.

Experiments and Results

The efficacy of the proposed Neural MPC framework was validated through extensive experiments in both simulation and real-world settings.

Simplified Simulation

In a simplified quadrotor simulation, the authors compared Neural MPC against conventional MPC with Gaussian Processes (GP) for residual modeling and naive implementations of neural network-based MPC. The results demonstrated that even with moderate-sized neural networks, the Neural MPC framework achieved significant improvements in tracking performance, reducing positional errors substantially more than GP-based approaches. Importantly, the framework maintained real-time computational efficiency, with optimization runtimes well within the required control frequency.

BEM Quadrotor Simulation

A more realistic Blade-Element-Momentum (BEM) simulation was used to further test the framework's capability in handling highly accurate aerodynamic models. Here, Neural MPC continued to show superior performance with larger and more complex models, achieving tracking accuracy unattainable by traditional methods while maintaining high control frequencies.

Real-World Experiments

The real-world evaluations involved flying a quadrotor along predefined high-speed trajectories. The results were impressive, with Neural MPC significantly reducing positional tracking errors up to 82% compared to the nominal controller and up to 55% compared to GP-based methods. Notably, the framework enabled the successful real-time operation of models that caused instability when naively integrated, showcasing the practical viability of the proposed approach.

Implications and Future Directions

The implications of this work span both practical and theoretical domains. Practically, the ability to integrate large, powerful neural network models into real-time MPC directly enhances the performance and safety of autonomous systems operating under high-speed and highly dynamic conditions. Theoretically, the framework paves the way for future developments in learning-based control systems that can leverage large-scale, data-driven models without compromising computational feasibility.

The promising results suggest several avenues for future exploration. One significant direction is extending the framework to incorporate temporal models, such as LSTMs or TCNs, which could provide even richer dynamics representations. Additionally, adapting the framework for other robotic platforms and control tasks could broaden its applicability and impact.

In conclusion, the Real-time Neural MPC framework represents a substantial advancement in embedded control systems, bringing the computational power of deep learning to real-time MPC and opening new possibilities for highly agile and autonomous robotic applications. This work underscores the potential of combining machine learning and control theory to address complex, real-world challenges in robotics.