Data-Driven MPC for Quadrotors (2102.05773v2)

Abstract: Aerodynamic forces render accurate high-speed trajectory tracking with quadrotors extremely challenging. These complex aerodynamic effects become a significant disturbance at high speeds, introducing large positional tracking errors, and are extremely difficult to model. To fly at high speeds, feedback control must be able to account for these aerodynamic effects in real-time. This necessitates a modelling procedure that is both accurate and efficient to evaluate. Therefore, we present an approach to model aerodynamic effects using Gaussian Processes, which we incorporate into a Model Predictive Controller to achieve efficient and precise real-time feedback control, leading to up to 70% reduction in trajectory tracking error at high speeds. We verify our method by extensive comparison to a state-of-the-art linear drag model in synthetic and real-world experiments at speeds of up to 14m/s and accelerations beyond 4g.

• The paper presents a novel GP-augmented MPC framework that reduces quadrotor trajectory errors by up to 70% in high-speed maneuvers.
• It leverages Gaussian Process models to predict residual dynamics and compensate for unmodeled aerodynamic forces in real time.
• Extensive tests in simulations and real-world scenarios demonstrate improved performance and robustness over traditional linear drag models.

Insights into Data-Driven MPC for Quadrotors

The paper, "Data-Driven MPC for Quadrotors," presents a methodology aimed at improving quadrotor performance in high-speed and high-acceleration flight regimes by integrating Gaussian Process (GP)-based correction with Model Predictive Control (MPC). The primary challenge addressed by the paper is the modeling of complex aerodynamic forces, which introduce significant positional tracking errors during high-speed operations. By leveraging a data-driven approach, the authors propose a system that enhances real-time control precision and reduces trajectory tracking errors by up to 70%.

Methodology

This research introduces a novel control system structure that incorporates GP models to compensate for the unmodeled aerodynamic effects. The MPC framework is augmented using learned residual dynamics, which refine the control accuracy during agile maneuvers. The GP models predict the residual dynamics by augmenting a nominal model of the quadrotor, thereby addressing discrepancies caused by aerodynamic disturbances.

Key Elements of Implementation

• Gaussian Processes: The GPs are employed to learn the residual errors of a simplified quadrotor model. The training of GPs is based on a dataset collected from flights under nominal control, capturing velocity-related dynamic disturbances.
• Model Predictive Control: The controller operates by solving an optimization problem using a sequential quadratic programming (SQP) approach, integrating the augmented dynamics. Notably, the controller was designed to consider real-time constraints and platform-specific limitations by utilizing a Runge-Kutta method for dynamic propagation.
• Data Collection and Experimentation: Extensive tests were conducted in both simulations and real-world scenarios, emphasizing various trajectory types, such as circular and lemniscate maneuvers, to validate the proposed model's robustness and generalizability.

Results and Implications

The experimental results underscore the approach's ability to reduce positional tracking errors significantly compared to a state-of-the-art linear drag model baseline (RDRv). Specifically, the paper highlights the GP-MPC's superior performance at speeds up to 14 m/s and accelerations beyond 4g in real-world tests.

1. Performance Improvement: The GP-augmented MPC consistently outperformed the RDRv model, especially at higher speeds, indicating its effectiveness in handling nonlinear aerodynamic effects that linear models fail to capture.
2. Model Generalization: The method demonstrated strong generalization to new trajectories not encountered during training, which is indicative of the approach's potential for broad applicability in various operational contexts.

Future Directions

The research opens several avenues for future exploration:

• Real-Time Adaptive Control: The potential to integrate real-time learning capabilities that adapt to dynamic environmental changes, such as wind gusts or varying battery levels, could enhance operational robustness.
• Safety and Obstacle Avoidance: Using the uncertainty estimates inherent to GPs could be exploited in safety-critical applications, allowing quadrotors to perform agile maneuvers near obstacles with improved reliability.

Conclusion

This work delivers a meaningful contribution to the field of autonomous quadrotor flight by presenting a viable solution to the challenges posed by high-speed trajectory tracking and complex aerodynamic disturbances. The GP-augmented MPC framework demonstrates considerable advancements over traditional linear models, offering robust and efficient control solutions that align well with the evolving demands of autonomous drone applications across various sectors. The insights gleaned from this research are poised to inform subsequent developments in adaptive control mechanisms for UAVs.