Accurate Tracking of Aggressive Quadrotor Trajectories using Incremental Nonlinear Dynamic Inversion and Differential Flatness (1809.04048v2)

Abstract: Autonomous unmanned aerial vehicles (UAVs) that can execute aggressive (i.e., high-speed and high-acceleration) maneuvers have attracted significant attention in the past few years. This paper focuses on accurate tracking of aggressive quadcopter trajectories. We propose a novel control law for tracking of position and yaw angle and their derivatives of up to fourth order, specifically, velocity, acceleration, jerk, and snap along with yaw rate and yaw acceleration. Jerk and snap are tracked using feedforward inputs for angular rate and angular acceleration based on the differential flatness of the quadcopter dynamics. Snap tracking requires direct control of body torque, which we achieve using closed-loop motor speed control based on measurements from optical encoders attached to the motors. The controller utilizes incremental nonlinear dynamic inversion (INDI) for robust tracking of linear and angular accelerations despite external disturbances, such as aerodynamic drag forces. Hence, prior modeling of aerodynamic effects is not required. We rigorously analyze the proposed control law through response analysis, and we demonstrate it in experiments. The controller enables a quadcopter UAV to track complex 3D trajectories, reaching speeds up to 12.9 m/s and accelerations up to 2.1g, while keeping the root-mean-square tracking error down to 6.6 cm, in a flight volume that is roughly 18 m by 7 m and 3 m tall. We also demonstrate the robustness of the controller by attaching a drag plate to the UAV in flight tests and by pulling on the UAV with a rope during hover.

• The paper introduces an innovative INDI control law that integrates differential flatness to enable aggressive, high-precision quadrotor tracking.
• It achieves a root-mean-square tracking error of 6.6cm at speeds up to 12.9m/s while effectively compensating for aerodynamic disturbances.
• The controller’s design obviates complex aerodynamic modeling, offering a robust framework for advanced UAV trajectory tracking.

Overview of Quadrotor Trajectory Tracking using Incremental NDI and Differential Flatness

The paper "Accurate Tracking of Aggressive Quadrotor Trajectories using Incremental Nonlinear Dynamic Inversion and Differential Flatness" by Ezra Tal and Sertac Karaman explores the elaborate construction and experimental validation of a sophisticated control system for autonomous UAVs, specifically quadrotors, designed to perform aggressive maneuvers. The research addresses critical aspects such as tracking position, yaw, and their respective high-order derivatives including velocity, acceleration, jerk, and snap, using advanced control methodologies.

Key Contributions

The paper introduces a novel control law that effectively applies Incremental Nonlinear Dynamic Inversion (INDI) combined with Differential Flatness, allowing robust tracking of dynamic UAV trajectories. A noteworthy contribution is the emphasis on tracking jerk and snap, which are typically overlooked in conventional flight controls, particularly under high-speed conditions where aerodynamic drag becomes a significant factor. The tracking of snap is innovatively handled using direct body torque control facilitated by closed-loop motor speed regulation, employing optical encoders for precision measurements.

The proposed system successfully circumvents the necessity of intricate aerodynamic modeling, which is often required in scenarios of high-speed flight with considerable aerodynamic disturbances. This robustness is achieved through the INDI approach, which compensates for the disturbances without relying on detailed prior modeling.

Experimental Validation

The experimental resolutions demonstrated the controller's capabilities in maintaining precision tracking of intricate 3D trajectories, reaching speeds of up to 12.9 m/s and achieving accelerations up to 2.1g. Remarkably, the system maintained a root-mean-square tracking error of 6.6 cm within a controlled flight environment. Further validations included stress tests with external disturbances such as drag plates and dynamic tension-applied forces, proving the system's proficiency in maintaining aerodynamic stability even under perturbative conditions.

Numerical Analysis and Implications

Numerical results underpin the paper's findings, showcasing how the controller's incremental nature inherently improves robustness against unpredictable external forces and moments, compared to traditional non-incremental systems. The comparative analysis further elucidates the advantages introduced by tracking higher-order derivatives such as jerk and snap, contributing to significantly enhanced trajectory tracking performance.

Practical and Theoretical Impact

The implications of this research are substantial both in practical and theoretical domains. Practically, the controller's robustness negates the dependence on exhaustive aerodynamic models, allowing for greater adaptability in varying operational contexts without degradation of task performance. Theoretically, the use of differential flatness and incremental control as a unified framework showcases potential evolution paths in UAV control design, facilitating more responsive and adaptive systems capable of high precision in conditions previously deemed challenging.

Future Directions

Given the promising results, future research could explore extending this control strategy to larger classes of UAVs or integrating with more complex environmental interactions. Furthermore, advancements in sensor technology could refine the precision of real-time feedback, further minimizing tracking errors and optimizing energy consumption during high-agility maneuvers. Overall, this paper adds significant value to the trajectory tracking discourse, providing a solid foundation for ongoing innovations in UAV control systems.