[Paper Review] Quadrotor Formation Flying Resilient to Abrupt Vehicle Failures via a Fluid Flow Navigation Function

Matthew Romano, Harshvardhan Uppaluru+2 more|arXiv (Cornell University)|Mar 3, 2022

Distributed Control Multi-Agent Systems4 citations

TL;DR

This paper proposes a real-time, fluid flow-based navigation function for quadrotor formation flight that ensures safety during abrupt vehicle failures by modeling healthy drones as particles in an ideal fluid flow with failed vehicles as excluded singularity points. The Containment Exclusion Mode (CEM) algorithm dynamically adjusts sliding speed along streamlines to maintain minimum separation, validated experimentally with two and six quadrotors achieving safe, real-time avoidance of failed agents while tracking velocity commands within 0.4ms runtime at 100Hz.

ABSTRACT

This paper develops and experimentally evaluates a navigation function for quadrotor formation flight that is resilient to abrupt quadrotor failures and other obstacles. The navigation function is based on modeling healthy quadrotors as particles in an ideal fluid flow. We provide three key contributions: (i) A Containment Exclusion Mode (CEM) safety theorem and proof which guarantees safety and formally specifies a minimum safe distance between quadrotors in formation, (ii) A real-time, computationally efficient CEM navigation algorithm, (iii) Simulation and experimental algorithm validation. Simulations were first performed with a team of six virtual quadrotors to demonstrate velocity tracking via dynamic slide speed, maintaining sufficient inter-agent distances, and operating in real-time. Flight tests with a team of two custom quadrotors were performed in an indoor motion capture flight facility, successfully validating that the navigation algorithm can handle non-trivial bounded tracking errors while guaranteeing safety.

Motivation & Objective

• To address the challenge of ensuring safety and mission continuity in multi-quadrotor formations after abrupt vehicle failures.
• To develop a computationally efficient, real-time navigation algorithm that guarantees collision avoidance without relying on centralized control or complex potential field optimization.
• To formally prove safety conditions for quadrotor formations under failure scenarios using fluid dynamics principles.
• To validate the proposed CEM navigation algorithm through both simulation and real-world flight experiments with indoor motion capture systems.

Proposed method

• Model healthy quadrotors as particles in an ideal fluid flow, with failed vehicles treated as singularity points excluded from the flow domain.
• Define desired trajectories as streamlines of the fluid flow that naturally avoid the excluded failure zones, ensuring safe partitioning.
• Introduce a dynamic sliding speed control mechanism via a phase variable φ that adjusts Δφ iteratively to track a 1.0 m/s maximum velocity command.
• Implement a Containment Exclusion Mode (CEM) navigation algorithm that computes real-time trajectories using a modified harmonic potential field with saddle-point escape guarantees.
• Formally prove two safety theorems: Theorem 1 ensures minimum safe distance in multi-obstacle scenarios, and Theorem 2 provides safety bounds for single-failure cases.
• Use a rotation matrix extension to generalize the 2D navigation solution to arbitrary flight directions in the x-y plane.

Experimental results

Research questions

• RQ1 How can a multi-quadrotor formation maintain safety and continue its mission after an abrupt failure of one or more vehicles?
• RQ2 What mathematical framework enables real-time, computationally efficient trajectory generation that avoids failed vehicles without local minima?
• RQ3 Can a fluid flow-based navigation function guarantee minimum inter-agent separation under bounded controller errors?
• RQ4 How does dynamic adjustment of the phase variable φ enable accurate velocity tracking while maintaining safety in the presence of saddle points?
• RQ5 To what extent can the CEM algorithm be scaled to larger teams with multiple failures?

Key findings

• The CEM navigation algorithm achieved real-time performance with runtimes of 0.2ms, 0.4ms, and 1ms for K=1, 2, and 5 respectively, all within the 10ms hard limit for 100Hz operation.
• Flight tests with two quadrotors demonstrated that controller errors remained bounded within δ=40cm, and Q2 maintained a safe distance from the failed Q1’s exclusion zone.
• In the six-quadrotor simulation, all agent pairs maintained at least 2(δ+ε) separation, confirming the formal safety theorem.
• The algorithm successfully navigated Q2 around saddle points near the exclusion zone, with Δφ decreasing significantly at these points to enable rapid motion.
• Velocity tracking was most accurate with K=2, achieving a maximum speed error lower than K=1 and K=5, while maintaining acceptable computational cost.
• Theoretical analysis confirmed that the fluid flow-based navigation function has only saddle points as local minima, enabling reliable escape and safe trajectory generation.