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Multi-Agent gatekeeper: Safe Flight Planning and Formation Control for Urban Air Mobility

Thomas Marshall Vielmetti, Devansh R Agrawal, Dimitra Panagou

TL;DR

This work addresses safe flight planning and formation control for urban air mobility by introducing multi-agent gatekeeper, a distributed safety framework that couples a precomputed safe leader trajectory with online formation tracking. Followers compute nominal plans but may switch to a guaranteed-safe backup path along the leader trajectory, ensuring forward invariance safety against static obstacles and inter-agent collisions. The method extends a prior single-agent gatekeeper to multiple agents, proving safety under ideal communications and sequential planning, and demonstrating 100% collision avoidance over 100 randomized 3D urban-like trials, with hardware validation on quadcopters. The empirical results show superior safety performance compared to CBF-QP and NMPC baselines, highlighting the approach\'s practicality for robust, scalable urban drone operations, while acknowledging limitations related to offline computation and communication assumptions.

Abstract

We present Multi-Agent gatekeeper, a framework that provides provable safety guarantees for leader-follower formation control in cluttered 3D environments. Existing methods face a trad-off: online planners and controllers lack formal safety guarantees, while offline planners lack adaptability to changes in the number of agents or desired formation. To address this gap, we propose a hybrid architecture where a single leader tracks a pre-computed, safe trajectory, which serves as a shared trajectory backup set for all follower agents. Followers execute a nominal formation-keeping tracking controller, and are guaranteed to remain safe by always possessing a known-safe backup maneuver along the leader's path. We formally prove this method ensures collision avoidance with both static obstacles and other agents. The primary contributions are: (1) the multi-agent gatekeeper algorithm, which extends our single-agent gatekeeper framework to multi-agent systems; (2) the trajectory backup set for provably safe inter-agent coordination for leader-follower formation control; and (3) the first application of the gatekeeper framework in a 3D environment. We demonstrate our approach in a simulated 3D urban environment, where it achieved a 100% collision-avoidance success rate across 100 randomized trials, significantly outperforming baseline CBF and NMPC methods. Finally, we demonstrate the physical feasibility of the resulting trajectories on a team of quadcopters.

Multi-Agent gatekeeper: Safe Flight Planning and Formation Control for Urban Air Mobility

TL;DR

This work addresses safe flight planning and formation control for urban air mobility by introducing multi-agent gatekeeper, a distributed safety framework that couples a precomputed safe leader trajectory with online formation tracking. Followers compute nominal plans but may switch to a guaranteed-safe backup path along the leader trajectory, ensuring forward invariance safety against static obstacles and inter-agent collisions. The method extends a prior single-agent gatekeeper to multiple agents, proving safety under ideal communications and sequential planning, and demonstrating 100% collision avoidance over 100 randomized 3D urban-like trials, with hardware validation on quadcopters. The empirical results show superior safety performance compared to CBF-QP and NMPC baselines, highlighting the approach\'s practicality for robust, scalable urban drone operations, while acknowledging limitations related to offline computation and communication assumptions.

Abstract

We present Multi-Agent gatekeeper, a framework that provides provable safety guarantees for leader-follower formation control in cluttered 3D environments. Existing methods face a trad-off: online planners and controllers lack formal safety guarantees, while offline planners lack adaptability to changes in the number of agents or desired formation. To address this gap, we propose a hybrid architecture where a single leader tracks a pre-computed, safe trajectory, which serves as a shared trajectory backup set for all follower agents. Followers execute a nominal formation-keeping tracking controller, and are guaranteed to remain safe by always possessing a known-safe backup maneuver along the leader's path. We formally prove this method ensures collision avoidance with both static obstacles and other agents. The primary contributions are: (1) the multi-agent gatekeeper algorithm, which extends our single-agent gatekeeper framework to multi-agent systems; (2) the trajectory backup set for provably safe inter-agent coordination for leader-follower formation control; and (3) the first application of the gatekeeper framework in a 3D environment. We demonstrate our approach in a simulated 3D urban environment, where it achieved a 100% collision-avoidance success rate across 100 randomized trials, significantly outperforming baseline CBF and NMPC methods. Finally, we demonstrate the physical feasibility of the resulting trajectories on a team of quadcopters.

Paper Structure

This paper contains 21 sections, 2 theorems, 21 equations, 5 figures, 1 table, 3 algorithms.

Table of Contents

  1. Nomenclature
  2. Introduction
  3. Preliminaries & Problem Statement
  4. Preliminaries
  5. gatekeeper Preliminaries
  6. Problem Statement
  7. Proposed Solution
  8. Multi-Agent gatekeeper
  9. Formation Control With Multi-Agent gatekeeper
  10. Backup Trajectory Generation and Coordination
  11. Algorithm 2: Construct Candidate
  12. Algorithm 3: Validate Candidate
  13. Implementation Details
  14. Simulation Results
  15. Setup
  16. ...and 6 more sections

Key Result

Lemma 1

Let the leader trajectory $([t_0, t_f], p_L(t), u_L(t))$ be a valid trajectory backup set by def:valid_trajectory_backup_set. Suppose agents $i$ and $j$ begin to execute $\pi^{\rm bak}$ from the leader path at times $t_i$ and $t_j$ respectively, at path parameters $t_{Li}$ and $t_{Lj}$ such that, If the arc-length separation between the agents at time $t_c = \max(t_i, t_j)$ satisfies, i.e. the a

Figures (5)

  • Figure 1: A leader trajectory (red) generated using Dubins RRT* in a 3D environment with cylindrical obstacles. (a) Full 3D perspective. (b) Side profile, demonstrating the path's adherence to pitch constraints. (c) Top-down XY projection. While the leader's path is safe and dynamically feasible, the nominal follower trajectories (blue) , created from a fixed offset , are shown intersecting with obstacles and violating dynamic constraints.
  • Figure 2: Evolution of a sample simulation over time, shown at six distinct time steps. The agents navigate a dense 3D environment with cylindrical obstacles. Agents can be seen deviating from their nominal formation and rejoining the leader's path to safely avoid collisions with obstacles.
  • Figure 3: Trajectory and performance metrics for the simulation scenario shown in \ref{['fig:3d_gk_solution_times']}. (Left) Full 3D agent paths; (Center) 2D projection with static obstacles; (Top-Right) minimum inter-agent distance over time, which remains above the collision threshold; and (Bottom-Right) agent deviation from their nominal reference trajectories.
  • Figure 4: Hardware demonstration of multi-agent gatekeeper with three Crazyflie 2.0 quadcopters navigating through a narrow gate.
  • Figure : Construct Candidate

Theorems & Definitions (21)

  • Definition 1: Agent
  • Definition 2: Trajectory
  • Definition 3: Arc Length
  • Definition 4: Undirected Graph
  • Remark 1
  • Definition 5: Backup Set
  • Definition 6: Nominal Trajectory
  • Definition 7: Backup Trajectory
  • Definition 8: Candidate Trajectory
  • Definition 9: Formation Control
  • ...and 11 more