Feedback Linearization for Quadrotors with a Learned Acceleration Error Model (2105.13527v1)

Abstract: This paper enhances the feedback linearization controller for multirotors with a learned acceleration error model and a thrust input delay mitigation model. Feedback linearization controllers are theoretically appealing but their performance suffers on real systems, where the true system does not match the known system model. We take a step in reducing these robustness issues by learning an acceleration error model, applying this model in the position controller, and further propagating it forward to the attitude controller. We show how this approach improves performance over the standard feedback linearization controller in the presence of unmodeled dynamics and repeatable external disturbances in both simulation and hardware experiments. We also show that our thrust control input delay model improves the step response on hardware systems.

• The paper demonstrates integration of a learned acceleration error model within feedback linearization to improve quadrotor tracking accuracy.
• The method mitigates thrust input delays, reducing oscillations and ensuring robust control during aggressive maneuvers.
• Experimental results show reduced position error and enhanced stability, supporting high-precision deployment in autonomous flight applications.

Feedback Linearization for Quadrotors with a Learned Acceleration Error Model: An Overview

This paper presents a series of enhancements to feedback linearization controllers for quadrotors, specifically targeting the challenges posed by unmodeled dynamics and external disturbances. The authors propose integrating a learned acceleration error model alongside a thrust input delay mitigation framework, aiming to preserve the theoretical appeal of feedback linearization while improving its robustness in real-world scenarios.

Methodology Summary

The traditional feedback linearization approach to quadrotor control is renowned for its theoretical simplicity, offering linear error responses that facilitate straightforward tuning and exponential convergence. However, its brittleness in the face of imperfectly modeled dynamics has limited its practical applicability. To address this, the authors have devised a method that incorporates learned disturbance models to accommodate the unmodeled dynamics associated with quadrotors in flight.

1. Acceleration Error Model Integration: The authors develop a learned model that captures the discrepancies between the anticipated and actual accelerations encountered by the quadrotor. This model becomes instrumental in improving the feedback linearization by offering compensatory adjustments during control execution. The model is updated in real-time, leveraging incremental sparse spectrum Gaussian process regression (ISSGPR) to predict force disturbances within the quadrotor's operational space.
2. Thrust Input Delay Mitigation: The second component of the proposed advancement lies in accounting for the thrust input delay, an often-overlooked aspect that can degrade system performance. The authors introduce a delayed thrust model within the feedback linearization framework, effectively rendering the control scheme more resilient to intrinsic delays in actuation, especially during aggressive maneuvers.
3. Implementation Strategy: The methodology is validated both in simulation and hardware implementations. Feedback linearization was enhanced with both learned acceleration error models and an amended system model to include delay dynamics, ensuring that theoretical assumptions were better aligned with real operational environments.

Results

The experimental results showcase marked improvements across several scenarios:

• Step Response Analysis: The proposed methodology demonstrated a reduction in position error compared to traditional cascaded approaches, especially during significant step changes in state inputs. This supports the claim that the enhanced feedback linearization controller retains stability and performance in the presence of large tracking errors.
• Delay Mitigation Efficacy: Implementations including a modeled thrust delay showed reduced oscillations and an overall better handling of transient dynamics, mitigating the adverse effects typically induced by unmodeled input delays.
• Data-Driven Disturbance Correction: The integration of learned models was shown to lead to a substantial decrease in tracking error, pointing to improved handling of environmental and dynamical disturbances. The predictive capacity of the model was notably advantageous in circumstances where the disturbance had a known dependency on state variables.

Applications and Future Work

The immediate implications of this research are evident in applications demanding high precision and robustness, such as autonomous drone navigation and aerial inspection tasks. By enabling feedback linearization controllers to adaptively correct model inaccuracies and anticipate disturbances, this work significantly broadens the scope of control strategies viable for deployment in dynamic environments.

Future directions may encompass several key areas: refinement of disturbance learning algorithms through the integration of more advanced machine learning methodologies such as deep learning, exploration of further mitigations for additional delays (such as those affecting angular feedback), and theoretical analysis to precisely quantify the performance gains under varying conditions. As these methodologies evolve, the potential for truly autonomous operation in complex, unpredictable environments becomes increasingly feasible.

In summary, the paper presents a sophisticated step forward in feedback linearization for quadrotors by harnessing learning-based model corrections. These innovations offer the promise of improved reliability and performance in navigating the intricacies of real-world dynamics.