Nonlinear Model Predictive Control for Leaderless UAV Formation Flying with Collision Avoidance under Directed Graphs

TL;DR

The paper tackles leaderless UAV formation flying with collision avoidance under directed communication by proposing a distributed NMPC method grounded in the Model Reference Adaptive Consensus (MRACon) framework. A linear discrete double-integrator reference model generates formation references, which each UAV tracks using a nonlinear NMPC that enforces obstacle and reciprocal collision constraints as well as actuator limits; stability is established for sufficiently large horizon $N$. The approach operates over directed graphs with a spanning tree, leveraging relative measurements to achieve consensus without a central leader. Validation includes simulations in cluttered environments with fixed and transforming formations and hardware experiments on seven Crazyflie drones, demonstrating safe trajectories, formation maintenance, and prescribed velocity tracking. The work provides a scalable, communication-efficient solution for distributed, collision-free formation control in realistic multi-UAV scenarios.

Abstract

This paper studies the leaderless formation flying problem with collision avoidance for a group of unmanned aerial vehicles (UAVs), which requires the UAVs to navigate through cluttered environments without colliding while maintaining the formation. The communication network among the UAVs is structured as a directed graph that includes a directed spanning tree. A novel distributed nonlinear model predictive control (NMPC) method based on the model reference adaptive consensus (MRACon) framework is proposed. Within this framework, each UAV tracks an assigned reference output generated by a linear reference model that utilizes relative measurements as input. Subsequently, the NMPC method penalizes the tracking error between the output of the reference model and that of the actual model while also establishing constraint sets for collision avoidance and physical limitations to achieve distributed and safe formation control. Finally, simulations and hardware experiments are conducted to verify the effectiveness of the proposed method.

Figures (11)

• Figure 1: Block diagram of a multi-UAV formation flying system with the MRACon-based distributed NMPC algorithm.
• Figure 2: (Left) The $j$th neighboring UAV's predicted trajectory $\hat{\boldsymbol{p}}^j[k+l]$ and spherical error boundary $\boldsymbol{B}^j[k+l]$. (Right) Collision model $\boldsymbol{C}^{ij}$, spherical error boundary $\boldsymbol{B}^j[k+l]$, and outer ellipsoid $\boldsymbol{E}^{ij}[k+l]$.
• Figure 3: Directed communication topologies with corresponding geometric shapes, from left to right: a hexagon used in the fixed formation experiment; followed by the letters "M", "A", and "S" used in the formation transformation experiment.
• Figure 4: Formation trajectories of the UAVs flying from the left side to the right side. The black symmetrical shapes represent the UAVs, the blue columns represent obstacles, and the thick light blue lines represent the edges of the UAV formation. The upper graph displays the result of a hexagon-shaped UAV formation flying through a cluttered environment. The below shows the result of UAV formation transformation during the flight through the environment with formation shapes like the letters "M", "A", and "S".
• Figure 5: The upper graph shows the minimum relative distance among all UAVs, and the below shows the minimum distance between all UAVs and the surface of obstacles.

Theorems & Definitions (2)

• proof
• proof