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Safe Reference Tracking and Collision Avoidance for Taxiing Aircraft Using an MPC-CBF Framework

Brooks A. Butler, Zarif Cabrera, Andy Nguyen, Philip E. Paré

TL;DR

A high-level path-planning algorithm is implemented that models taxiway intersections as nodes in an undirected graph, algorithmically constructs a directed graph according to the physical limitations of the aircraft, and finds the shortest valid taxi path through the directed graph using Dijkstra’s algorithm.

Abstract

In this paper, we develop a framework for the automatic taxiing of aircraft between hangar and take-off given a graph-based model of an airport. We implement a high-level path-planning algorithm that models taxiway intersections as nodes in an undirected graph, algorithmically constructs a directed graph according to the physical limitations of the aircraft, and finds the shortest valid taxi path through the directed graph using Dijkstra's algorithm. We then use this shortest path to construct a reference trajectory for the aircraft to follow that considers the turning capabilities of a given aircraft. Using high-order control barrier functions (HOCBFs), we construct safety conditions for multi-obstacle avoidance and safe reference tracking for simple 2D unicycle dynamics with acceleration control inputs. We then use these safety conditions to design an MPC-CBF framework that tracks the reference trajectory while adhering to the safety constraints. We compare the performance of our MPC-CBF controller with a PID-CBF control method via simulations.

Safe Reference Tracking and Collision Avoidance for Taxiing Aircraft Using an MPC-CBF Framework

TL;DR

A high-level path-planning algorithm is implemented that models taxiway intersections as nodes in an undirected graph, algorithmically constructs a directed graph according to the physical limitations of the aircraft, and finds the shortest valid taxi path through the directed graph using Dijkstra’s algorithm.

Abstract

In this paper, we develop a framework for the automatic taxiing of aircraft between hangar and take-off given a graph-based model of an airport. We implement a high-level path-planning algorithm that models taxiway intersections as nodes in an undirected graph, algorithmically constructs a directed graph according to the physical limitations of the aircraft, and finds the shortest valid taxi path through the directed graph using Dijkstra's algorithm. We then use this shortest path to construct a reference trajectory for the aircraft to follow that considers the turning capabilities of a given aircraft. Using high-order control barrier functions (HOCBFs), we construct safety conditions for multi-obstacle avoidance and safe reference tracking for simple 2D unicycle dynamics with acceleration control inputs. We then use these safety conditions to design an MPC-CBF framework that tracks the reference trajectory while adhering to the safety constraints. We compare the performance of our MPC-CBF controller with a PID-CBF control method via simulations.
Paper Structure (16 sections, 2 theorems, 36 equations, 5 figures)

This paper contains 16 sections, 2 theorems, 36 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Notation
  3. Preliminaries
  4. Control Barrier Functions
  5. High-Order Control Barrier Functions
  6. Path Planning for Taxiing Aircraft
  7. Reference Trajectory Generation
  8. Safety Framework Using MPC-CBF
  9. Collision Avoidance
  10. Safe Reference Tracking
  11. MPC-CBF Framework
  12. PID-CBF Framework
  13. Simulations
  14. Parameterization
  15. Simulation Results
  16. ...and 1 more sections

Key Result

Lemma 1

ames2016control Consider a CBF $h(x)$. Then, any locally Lipschitz controller $u(x): \mathbb{R}^n \rightarrow \mathbb{R}^m$ such that will render the set $\mathcal{C}$ forward invariant for system eq:dyn_gen.

Figures (5)

  • Figure 1: Undirected graph representation of Purdue University Airport (LAF) for autonomous aircraft navigation, illustrating runways and taxiways as nodes and edges for control module integration.
  • Figure 2: A directed graph representation of Purdue University Airport's taxiways and gates, with edges representing possible aircraft movement paths for autonomous navigation systems.
  • Figure 3: Comparison of the performance for the PID controller (blue solid) with the MPC controller (black dotted) in tracking the runway reference trajectory (red dashed) without external disturbances or obstacles. Note that the MPC controller outperforms the tuned PID controller at tracking the reference trajectory over time.
  • Figure 4: An example of the MPC-CBF framework (blue solid) under the external disturbance of a constant crosswind compared with the MPC controller without safe reference tracking (black dotted). Note that, without the reference tracking CBF active, the system is pushed outside of the defined safe region for the reference trajectory.
  • Figure 5: An example of the MPC-CBF framework controlled aircraft (blue solid) under the external disturbance of a constant crosswind while avoiding obstacles placed along the reference trajectory (red dashed). Note that, even under external disturbances, the MPC-CBF controller is capable of satisfying both the obstacle avoidance and safe reference tracking conditions for all time.

Theorems & Definitions (5)

  • Definition 1
  • Lemma 1
  • Definition 2
  • Definition 3
  • Lemma 2