Differential Flatness-based Fast Trajectory Planning for Fixed-wing Unmanned Aerial Vehicles

2024-12-02

arXiv.org

AI Summary

To address the low computational efficiency and difficulty in ensuring physical feasibility when optimizing trajectories for fixed-wing UAVs under strongly nonlinear, nonholonomic dynamics, this paper proposes a rapid, unconstrained trajectory optimization method grounded in differential flatness. The approach innovatively integrates differential flatness with Bézier or polynomial parameterization to implicitly satisfy dynamical constraints. An integral-type performance objective is formulated, and its analytical gradient is derived, reducing optimization complexity to linear time. Implemented on a standard desktop CPU, the method generates trajectories in sub-second time—accelerating computation by several orders of magnitude over state-of-the-art methods. It enables real-time generation of smooth, collision-free, dynamically feasible trajectories even in environments with randomly distributed obstacles.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Constraint Satisfaction and Optimization: Constraint Optimization
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

Due to the strong nonlinearity and nonholonomic dynamics, despite the various general trajectory optimization methods presented, few of them can guarantee efficient computation and physical feasibility for relatively complicated fixed-wing UAV dynamics. Aiming at this issue, this paper investigates a differential flatness-based trajectory optimization method for fixed-wing UAVs (DFTO-FW). The customized trajectory representation is presented through differential flat characteristics analysis and polynomial parameterization, eliminating equality constraints to avoid the heavy computational burdens of solving complex dynamics. Through the design of integral performance costs and derivation of analytical gradients, the original trajectory optimization is transcribed into a lightweight, unconstrained, gradient-analytical optimization with linear time complexity to improve efficiency further. The simulation experiments illustrate the superior efficiency of the DFTO-FW, which takes sub-second CPU time (on a personal desktop) against other competitors by orders of magnitude to generate fixed-wing UAV trajectories in randomly generated obstacle environments.

Problem

• Efficient trajectory planning for nonlinear fixed-wing UAVs
• Reducing computational burden in complex dynamics optimization
• Ensuring physical feasibility in obstacle-rich environments

Innovation

• Differential flatness-based trajectory optimization method
• Polynomial parameterization eliminates equality constraints
• Lightweight unconstrained gradient-analytical optimization