Aerobatic Trajectory Generation for a VTOL Fixed-Wing Aircraft Using Differential Flatness (2207.03524v1)

Abstract: This paper proposes a novel algorithm for aerobatic trajectory generation for a vertical take-off and landing (VTOL) tailsitter flying wing aircraft. The algorithm differs from existing approaches for fixed-wing trajectory generation, as it considers a realistic six-degree-of-freedom (6DOF) flight dynamics model, including aerodynamics equations. Using a global dynamics model enables the generation of aerobatics trajectories that exploit the entire flight envelope, enabling agile maneuvering through the stall regime, sideways uncoordinated flight, inverted flight etc. The method uses the differential flatness property of the global tailsitter flying wing dynamics, which is derived in this work. By performing snap minimization in the differentially flat output space, a computationally efficient algorithm, suitable for online motion planning, is obtained. The algorithm is demonstrated in extensive flight experiments encompassing six aerobatics maneuvers, a time-optimal drone racing trajectory, and an airshow-like aerobatic sequence for three tailsitter aircraft.

• The paper presents a novel algorithm that leverages differential flatness to simplify 6DOF dynamics for aggressive VTOL aerobatic maneuvers.
• It minimizes snap to optimize control inputs, achieving precise tracking for complex maneuvers like inverted flight, knife-edge, and loops.
• Extensive flight experiments validate the method's robust performance in time-optimal racing trajectories and real-world flight conditions.

Aerobatic Trajectory Generation for VTOL Fixed-Wing Aircraft: An Exploration of Differential Flatness

The paper tackles the nuanced problem of aerobatic trajectory generation for VTOL (Vertical Take-Off and Landing) tailsitter aircraft, using a framework grounded in differential flatness. The research distinguishes itself by proposing an algorithm that marries the mathematical elegance of differential flatness with the practical considerations of a six-degree-of-freedom (6DOF) dynamics model. This model incorporates realistic aerodynamics, thus broadening the maneuverability of the vehicle across its full flight envelope, allowing for complex maneuvers such as stall regime, knife-edge, and inverted flight.

Methodological Innovations

The proposed algorithm utilizes the differential flatness property of the tailsitter flying wing dynamics. The flatness property simplifies the complex relationship between the state variables and the input space by expressing the system in terms of a single flat output and its derivatives. In this context, trajectory generation becomes a problem of output space manipulation, making the process computationally efficient enough for potential online applications.

Distinct from existing methods which often resort to kinematics models due to computational constraints, this approach embraces the comprehensive dynamics of the aircraft. The core computational strategy revolves around minimizing snap (the fourth derivative of position), which is analogously employed in quadcopter trajectory generation. This minimization reduces requirements on control inputs, enhancing the feasibility of aggressive maneuvers by adhering to the realistic dynamic capabilities of the aircraft.

Experimental Validation

The research showcases extensive flight experiments validating the viability of this approach across multiple aerobatic maneuvers, including loops, knife-edge flights, Climbing Turns, and Split-S maneuvers. These tests affirm the method's robustness, with trajectory tracking accuracy revealing that the flatness-based predictions closely parallel the vehicle's actual performance.

A notable aspect of these experiments is the clear verification of the algorithm's capability to efficiently generate trajectories that are dynamically feasible while supporting a swift operational speed—essential for applications such as drone racing, as one case paper included a time-optimal racing trajectory through gates.

Theoretical and Practical Implications

From a theoretical standpoint, this paper contributes a substantial layer to UAV trajectory generation research, demonstrating that differential flatness can be extended beyond rotorcraft to fixed-wing aircraft with significant aerodynamic complexities. Practically, it implies that more agile and safer flight paths can be manufactured even in constrained environments, such as urban areas or inside buildings.

This work could have several implications for the future developments in AI and autonomous navigation systems. Real-time adaptive flight planning could be a viable next step, given this computational efficiency. Furthermore, this algorithm can serve as a groundwork for further exploration into collaborative multi-UAV operations, potentially allowing for complex formations and swarm behaviors.

Conclusion

In summary, this paper illuminates the potential for differential flatness to serve as a scalable, reliable framework for aerobatic VTOL trajectory generation. While further work may be required to fully integrate and optimize this approach for live dynamic environments, the principles and outcomes showcased here offer a promising direction for UAV autonomy and operational safety. Future explorations could delve into broader flight condition simulations or the integration of this trajectory planning into machine-learning-based navigational adjustments, thus paving the way for more advanced autonomous systems.