GO-Flock: Goal-Oriented Flocking in 3D Unknown Environments with Depth Maps

TL;DR

GO-Flock addresses deadlocks and local minima in 3D obstacle-rich flocking by coupling a depth-map–driven Perception Module with a downstream APF-based Collective Navigation Module. The perception component identifies an intermediate waypoint $w_1$ and obstacle-related virtual agents, feeding a velocity command $\mathbf{v}_{i}^{des} = \mathbf{v}_{i}^{goal} + \tilde{\mathbf{v}}_{i}^{neigh} + \mathbf{v}_{i}^{obs}$ that is rescaled to $[-\phi^{max}, \phi^{max}]$, while safety is ensured by removing problematic components near obstacles. The approach is validated through simulations and hardware-in-the-loop experiments involving 9 drones (6 real, 3 virtual) in forest-like environments, showing improved cohesion, higher velocity alignment (Cosine Similarity around 0.9), and faster time-to-goal compared with baselines. This work demonstrates a practical, scalable path to robust, depth-sensor–driven flocking in unknown 3D settings, though it notes limitations such as incomplete drone masking and limited real-world testing for broader deployment.

Abstract

Artificial Potential Field (APF) methods are widely used for reactive flocking control, but they often suffer from challenges such as deadlocks and local minima, especially in the presence of obstacles. Existing solutions to address these issues are typically passive, leading to slow and inefficient collective navigation. As a result, many APF approaches have only been validated in obstacle-free environments or simplified, pseudo 3D simulations. This paper presents GO-Flock, a hybrid flocking framework that integrates planning with reactive APF-based control. GO-Flock consists of an upstream Perception Module, which processes depth maps to extract waypoints and virtual agents for obstacle avoidance, and a downstream Collective Navigation Module, which applies a novel APF strategy to achieve effective flocking behavior in cluttered environments. We evaluate GO-Flock against passive APF-based approaches to demonstrate their respective merits, such as their flocking behavior and the ability to overcome local minima. Finally, we validate GO-Flock through obstacle-filled environment and also hardware-in-the-loop experiments where we successfully flocked a team of nine drones, six physical and three virtual, in a forest environment.

Figures (6)

• Figure 1: Hardware-in-the-loop flocking test: (A) and (B) show six physical drone flights captured from the drone's perspective and a bottom-up view. (C) and (D) show the corresponding simulated cluttered environment where the drones navigate through tight gaps and around foliage using depth image input.
• Figure 2: The color-filled circles represent the waypoint and virtual agents $w_1$ to $w_4$. The dotted arrows represent the potential vectors utilized from Eqn. \ref{['eqn:neighbours']} to \ref{['eqn:final_eqn']}. The dotted purple circle concentric to the obstacle represents the inflation to account for the drone's volume and safety. $w_1$ is thus chosen to be the tangent to the inflated obstacle, which minimizes deviation from the direct path to $g$. Note that $\textbf{v}_{ij}^{neigh}$ if applied naively to Eqn. 1, would have result in $v_{i}^{des}$ having vector components that drive Agent i towards the obstacle. To improve safety, Eqn \ref{['eqn:final_eqn']} and hence, $\tilde{\textbf{v}}_{ij}^{neigh}$, sought to remove such effects. Note that $\tilde{\textbf{v}}_{ij}^{neigh}$ would eventually lie on the left half plane of $\textbf{p}_{w_1 - i}$
• Figure 3: Hardware-in-the-loop system diagram for conducting real-world flocking experiments. Each drone's flocking algorithm is run as a separate process on the same workstation. The green, yellow and blue arrows represent communication flow. For example, velocity commands (blue arrows) are sent from the flocking algorithm and received by the real and virtual drones.
• Figure 4: The white rectangle represents an obstacle in the environment. Each multi-colored path shows the past trajectory of an agent, illustrating where it has moved over time. The red dots indicate the agents' current positions at the moment captured in the snapshot. (A) A sample run using GO-Flock showing the separation of a flock into 2 subgroups as well as its corresponding $D(t)$ and $CS(t)$ metrics. (B) A typical run using Maguire et al.'s showing the siphoning effect of the algorithm and it corresponding $D(t)$ and $CS(t)$ metrics. (C) Increasing $\varphi_n^{ref}$ and thus inter-agent cohesion factor could reduce stray agent incidents from occurring. Instead of being attracted to the target waypoint $w_1$, the green agent opted to move in cohesion with the rest of the group. (D) A sample run showing Maguire et al.'s method resulting in separation of the flock. Since $\textbf{C}_{siphon}$ (the blue arrow pointing from the stuck agent to the nearest free agent) was directed toward the obstacle—because the free agent had already moved ahead—the stuck agents ended up colliding with the obstacle.
• Figure 5: Orange lines show the path undertaken by the agents from Experimental Group 2 (Panel A) and 3 (Panel B). The purple square shows an infinitely tall cuboid obstacle. (A) As the agents split into 2 subgroups, the cohesive effects drew the smaller subgroup into obstacle. (B) Both subgroups were able to circumnavigate the obstacle successfully and rejoined.