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Sampling-Based Hierarchical Trajectory Planning for Formation Flight (2407.17392v1)

Published 24 Jul 2024 in cs.RO, cs.SY, and eess.SY

Abstract: Formation flight of unmanned aerial vehicles (UAVs) poses significant challenges in terms of safety and formation keeping, particularly in cluttered environments. However, existing methods often struggle to simultaneously satisfy these two critical requirements. To address this issue, this paper proposes a sampling-based trajectory planning method with a hierarchical structure for formation flight in dense obstacle environments. To ensure reliable local sensing information sharing among UAVs, each UAV generates a safe flight corridor (SFC), which is transmitted to the leader UAV. Subsequently, a sampling-based formation guidance path generation method is designed as the front-end strategy, steering the formation to fly in the desired shape safely with the formation connectivity provided by the SFCs. Furthermore, a model predictive path integral (MPPI) based distributed trajectory optimization method is developed as the back-end part, which ensures the smoothness, safety and dynamics feasibility of the executable trajectory. To validate the efficiency of the developed algorithm, comprehensive simulation comparisons are conducted. The supplementary simulation video can be seen at https://www.youtube.com/watch?v=xSxbUN0tn1M.

Summary

  • The paper presents a two-part approach that integrates sampling-based formation configuration with distributed MPPI trajectory optimization to improve UAV formation safety.
  • It leverages safe flight corridors and cost functions to dynamically generate optimal configurations and assign tasks for collision-free navigation.
  • Simulation results demonstrate enhanced obstacle avoidance, improved formation similarity, and strong adaptability in complex, narrow environments.

Sampling-Based Hierarchical Trajectory Planning for Formation Flight

This paper introduces a novel methodology for addressing the challenges associated with unmanned aerial vehicles (UAVs) performing formation flight within dense obstacle environments. Formation flight involves maintaining a desired geometric arrangement while avoiding collisions with both static and dynamic obstacles. Traditional approaches to UAV formation generally utilize control-theoretic methods, such as position-based, displacement-based, and distance-based controls, but these often lead to rigid formations unsuitable for complex environments. This paper proposes a two-part hierarchical solution to this challenge, combining both front-end sampling-based path generation and back-end distributed trajectory optimization.

Methodological Innovations

The research addresses the need for a coordinated trajectory planning strategy that synergizes formation configuration and obstacle avoidance. The proposed method is built around two core components:

  1. Sampling-Based Formation Path Generation:
    • Formation Configuration Sampling: The method begins by sampling formation configurations based on potential center positions and scale factors within a predefined safe region. This is accomplished by leveraging a safe flight corridor (SFC) for each UAV, which defines the local region free of obstacles.
    • Sequence Optimization: These sampled configurations are evaluated using a set of cost functions that ensure safety, maintain formation, and minimize path deviation. A heuristic search identifies the optimal sequence of formation configurations, subsequently transformed into continuous formation guidance paths.
    • Task Assignment Optimization: A distributed optimization approach, such as the auction algorithm, is used to assign tasks among UAVs, thus reducing the likelihood of collision among agents and optimizing resource allocation.
  2. Trajectory Optimization with Model Predictive Path Integral Control (MPPI):
    • Dynamic Constraints: The method employs MPPI for trajectory optimization to ensure dynamic feasibility and smooth transitions between waypoints along the guidance path.
    • Stochastic Control Framework: The strategy incorporates stochastic inputs to account for and adapt to uncertainties in real time, improving robustness across various conditions.

Numerical Results and Validation

The evaluation of the proposed methodology involves simulations under different conditions, exploring environments with varying obstacle densities and configurations. The results highlight the following key improvements:

  • Achieving high success rates in obstacle avoidance and formation integrity across varied and challenging environments.
  • Superior performance in maintaining formation similarity, with significant reductions observed in average and maximum formation similarity errors when compared to prior methods ([e.g., Zhou et al., 2018], [Quan et al., 2022]).
  • Demonstrated adaptability to environments requiring scale adjustments, such as narrow corridors, where other methods often struggle or fail to maintain cohesive UAV formations.

Implications and Future Directions

The implications of this research extend to both theoretical and practical domains. Theoretically, the integration of a sampling-based approach with trajectory optimization lends itself to more flexible and adaptive formation control strategies. Practically, the methods proposed offer significant advancements in UAV coordination, with potential applications in surveillance, search and rescue, environmental monitoring, and beyond.

Looking ahead, further research could enhance this methodology by developing fully distributed algorithms capable of operating efficiently in real-time with minimal centralized control, broadening its applicability to emergency response scenarios and dynamic environments in real-world operations. Additionally, incorporating machine learning techniques could improve decision-making processes in formation configuration sampling and task assignment under even higher degrees of uncertainty and obstacle density.

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