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Decentralized Nonlinear Model Predictive Control for Safe Collision Avoidance in Quadrotor Teams with Limited Detection Range

Manohari Goarin, Guanrui Li, Alessandro Saviolo, Giuseppe Loianno

TL;DR

A novel decentralized Nonlinear Model Predictive Control (NMPC) that integrates Exponential CBFs (ECBFs) to enhance safety and optimality in multi-quadrotor systems and provides both conservative and practical minimum bounds of the range that preserve the safety guarantees of the ECBFs.

Abstract

Multi-quadrotor systems face significant challenges in decentralized control, particularly with safety and coordination under sensing and communication limitations. State-of-the-art methods leverage Control Barrier Functions (CBFs) to provide safety guarantees but often neglect actuation constraints and limited detection range. To address these gaps, we propose a novel decentralized Nonlinear Model Predictive Control (NMPC) that integrates Exponential CBFs (ECBFs) to enhance safety and optimality in multi-quadrotor systems. We provide both conservative and practical minimum bounds of the range that preserve the safety guarantees of the ECBFs. We validate our approach through extensive simulations with up to 10 quadrotors and 20 obstacles, as well as real-world experiments with 3 quadrotors. Results demonstrate the effectiveness of the proposed framework in realistic settings, highlighting its potential for reliable quadrotor teams operations.

Decentralized Nonlinear Model Predictive Control for Safe Collision Avoidance in Quadrotor Teams with Limited Detection Range

TL;DR

A novel decentralized Nonlinear Model Predictive Control (NMPC) that integrates Exponential CBFs (ECBFs) to enhance safety and optimality in multi-quadrotor systems and provides both conservative and practical minimum bounds of the range that preserve the safety guarantees of the ECBFs.

Abstract

Multi-quadrotor systems face significant challenges in decentralized control, particularly with safety and coordination under sensing and communication limitations. State-of-the-art methods leverage Control Barrier Functions (CBFs) to provide safety guarantees but often neglect actuation constraints and limited detection range. To address these gaps, we propose a novel decentralized Nonlinear Model Predictive Control (NMPC) that integrates Exponential CBFs (ECBFs) to enhance safety and optimality in multi-quadrotor systems. We provide both conservative and practical minimum bounds of the range that preserve the safety guarantees of the ECBFs. We validate our approach through extensive simulations with up to 10 quadrotors and 20 obstacles, as well as real-world experiments with 3 quadrotors. Results demonstrate the effectiveness of the proposed framework in realistic settings, highlighting its potential for reliable quadrotor teams operations.
Paper Structure (17 sections, 4 theorems, 24 equations, 5 figures)

This paper contains 17 sections, 4 theorems, 24 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Related Works
  3. Preliminaries on Exponential Control Barrier Functions
  4. Methodology
  5. Problem Overview and Assumptions
  6. Decentralized NMPC with ECBFs
  7. Safety Guarantees Analysis with Limited Detection Range
  8. Minimum detection range for a pair $(q_i,e_j)$
  9. Compatibility of multiple ECBF constraints
  10. Results
  11. Simulation Results
  12. Real-world Experiments
  13. Conclusion
  14. Appendix
  15. Proof of Proposition \ref{['prop_cons']}
  16. ...and 2 more sections

Key Result

Theorem 1

If $K_\alpha$ satisfies $\forall k$: $p_k>0$ and the initial condition $\mathbf{x}_0 \in \mathcal{C}_k$, then $h(\mathbf{x})$ is a valid exponential CBF and $\mathcal{C}$ is forward invariant.

Figures (5)

  • Figure 1: Decentralized Safe Control for Multi-Quadrotor systems. The proposed control strategy guides three quadrotors (blue, green, yellow) to safely maneuver around obstacles (red), demonstrating successful collision avoidance.
  • Figure 2: Relative velocity conservative approximation between quadrotor $q_i$ and obstacle/quadrotor $e_j$.
  • Figure 3: Minimum theoretical and simulated detection ranges between two quadrotors in discrete time when switching positions at different velocities and with a maximum acceleration of $2~m/s^{2}$.
  • Figure 4: Total number of barrier violations in simulations as a function of the number of robots $N$, number of obstacles $N_o$, and detection range restrictions $R_{dd}$ between quadrotors and $R_{ddo}$ between quadrotors and obstacles.
  • Figure 5: Distances between quadrotors $q_i$ and obstacles $o_j$ over time. The grey zone denotes one back and forth motion.

Theorems & Definitions (7)

  • Definition 1
  • Theorem 1
  • Definition 2: Conservative bound $\hat{R}_{d*}$
  • Proposition 1
  • Definition 3: Non-conservative bound $\check{R}_{d*}$
  • Proposition 2
  • Proposition 3: Compatibility under the conservative bound $\hat{R}_{d*}$