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Multi-goal Rapidly Exploring Random Tree with Safety and Dynamic Constraints for UAV Cooperative Path Planning

Thu Hang Khuat, Duy-Nam Bui, Hoa TT. Nguyen, Mien L. Trinh, Minh T. Nguyen, Manh Duong Phung

TL;DR

The paper tackles cooperative path planning for multiple UAVs by extending RRT into a multi-goal framework (MultiRRT) that respects UAV dynamics and safety constraints. It introduces a dynamic-constrained expansion, a node reduction mechanism, and Bezier-based path smoothing, with formal guarantees that interpolated paths remain collision-free and dynamically feasible. Empirical results show that MultiRRT delivers shorter, smoother paths and faster planning than several state-of-the-art RRT variants, validated through simulations and real UAV experiments, and accompanied by public source code. The work advances real-time, multi-UAV coordination in cluttered environments, with practical impact for missions requiring synchronized arrivals and robust safety margins.

Abstract

Cooperative path planning is gaining its importance due to the increasing demand on using multiple unmanned aerial vehicles (UAVs) for complex missions. This work addresses the problem by introducing a new algorithm named MultiRRT that extends the rapidly exploring random tree (RRT) to generate paths for a group of UAVs to reach multiple goal locations at the same time. We first derive the dynamics constraint of the UAV and include it in the problem formulation. MultiRRT is then developed, taking into account the cooperative requirements and safe constraints during its path-searching process. The algorithm features two new mechanisms, node reduction and Bezier interpolation, to ensure the feasibility and optimality of the paths generated. Importantly, the interpolated paths are proven to meet the safety and dynamics constraints imposed by obstacles and the UAVs. A number of simulations, comparisons, and experiments have been conducted to evaluate the performance of the proposed approach. The results show that MultiRRT can generate collision-free paths for multiple UAVs to reach their goals with better scores in path length and smoothness metrics than state-of-the-art RRT variants including Theta-RRT, FN-RRT, RRT*, and RRT*-Smart. The generated paths are also tested in practical flights with real UAVs to evaluate their validity for cooperative tasks. The source code of the algorithm is available at https://github.com/duynamrcv/multi-target_RRT

Multi-goal Rapidly Exploring Random Tree with Safety and Dynamic Constraints for UAV Cooperative Path Planning

TL;DR

The paper tackles cooperative path planning for multiple UAVs by extending RRT into a multi-goal framework (MultiRRT) that respects UAV dynamics and safety constraints. It introduces a dynamic-constrained expansion, a node reduction mechanism, and Bezier-based path smoothing, with formal guarantees that interpolated paths remain collision-free and dynamically feasible. Empirical results show that MultiRRT delivers shorter, smoother paths and faster planning than several state-of-the-art RRT variants, validated through simulations and real UAV experiments, and accompanied by public source code. The work advances real-time, multi-UAV coordination in cluttered environments, with practical impact for missions requiring synchronized arrivals and robust safety margins.

Abstract

Cooperative path planning is gaining its importance due to the increasing demand on using multiple unmanned aerial vehicles (UAVs) for complex missions. This work addresses the problem by introducing a new algorithm named MultiRRT that extends the rapidly exploring random tree (RRT) to generate paths for a group of UAVs to reach multiple goal locations at the same time. We first derive the dynamics constraint of the UAV and include it in the problem formulation. MultiRRT is then developed, taking into account the cooperative requirements and safe constraints during its path-searching process. The algorithm features two new mechanisms, node reduction and Bezier interpolation, to ensure the feasibility and optimality of the paths generated. Importantly, the interpolated paths are proven to meet the safety and dynamics constraints imposed by obstacles and the UAVs. A number of simulations, comparisons, and experiments have been conducted to evaluate the performance of the proposed approach. The results show that MultiRRT can generate collision-free paths for multiple UAVs to reach their goals with better scores in path length and smoothness metrics than state-of-the-art RRT variants including Theta-RRT, FN-RRT, RRT*, and RRT*-Smart. The generated paths are also tested in practical flights with real UAVs to evaluate their validity for cooperative tasks. The source code of the algorithm is available at https://github.com/duynamrcv/multi-target_RRT

Paper Structure

This paper contains 17 sections, 2 theorems, 34 equations, 17 figures, 3 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. UAV dynamic model and constraint analysis
  4. Dynamic model
  5. Dynamic constraint analysis
  6. MultiRRT for cooperative path planning
  7. Multi-goal RRT with dynamic constraint
  8. Node reduction mechanism
  9. Path smoothing using Bezier curves
  10. Results and Discussion
  11. Scenario setup
  12. Node reduction evaluation
  13. Comparison with other RRT variants
  14. Comparison with other approaches
  15. Scalability analysis
  16. ...and 2 more sections

Key Result

Theorem 1

The second order Bezier curve $B_k\left(\tau\right)$ defined in eqn:bezier always lies within the safe zone at point $P_k$. That is, the distance from any point $B_j$ on $B_k\left(\tau\right)$ to $P_k$ is always less than or equal to the radius of the safe zone at $P_k$:

Figures (17)

  • Figure 1: A cooperative path planning task where multiple UAVs need to reach different target locations at the same time
  • Figure 2: UAV model and its turning angle
  • Figure 3: Illustration of the enhanced RRT algorithm with the constraint on the turning angle
  • Figure 4: Illustration of redundant node reduction using the triangle inequality
  • Figure 5: The safe zone and its intersection with path segments
  • ...and 12 more figures

Theorems & Definitions (7)

  • Definition 1
  • Theorem 1
  • proof
  • Theorem 2
  • proof
  • Remark 1
  • Remark 2