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Chapter 10

Path Following

Beard & McLain, “Small Unmanned Aircraft,” Princeton University Press, 2012, Chapter 10, Slide 1

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Control Architecture

path planner

path manager

path following

autopilot

unmanned aircraft

waypoints

on-board sensors

position error

tracking error

status

destination,�obstacles

servo commands

state estimator

wind

path definition

airspeed,�altitude,

heading,

commands

map

Beard & McLain, “Small Unmanned Aircraft,” Princeton University Press, 2012, Chapter 10, Slide 2

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Path Following

  • For small UAVs, a major issue is wind
    • Always present to some degree
    • Usually significant with respect to commanded airspeed
  • Wind makes traditional trajectory tracking approaches difficult, if not infeasible
    • Have to know the wind precisely at every instant to determine desired airspeed
  • Better approach: path following
  • Rather than “follow this trajectory”, we control UAV to “stay on this path”

Beard & McLain, “Small Unmanned Aircraft,” Princeton University Press, 2012, Chapter 10, Slide 3

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Path Types

  • We will focus on two types of paths to follow:
    • Straight lines between two points in 3-D
      • Inclination of path within climb capabilities of UAV
    • Circular orbits or arcs in the horizontal plane
  • Paths for common applications can be built up from these path primitives
    • Methods for following other types of paths found in literature

Beard & McLain, “Small Unmanned Aircraft,” Princeton University Press, 2012, Chapter 10, Slide 4

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Straight Line Path Description

north

east

Beard & McLain, “Small Unmanned Aircraft,” Princeton University Press, 2012, Chapter 10, Slide 5

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Lateral Tracking Problem

north

east

Beard & McLain, “Small Unmanned Aircraft,” Princeton University Press, 2012, Chapter 10, Slide 6

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Lateral Tracking Problem

north

east

Beard & McLain, “Small Unmanned Aircraft,” Princeton University Press, 2012, Chapter 10, Slide 7

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Lateral Tracking - Vector Field Concept

Beard & McLain, “Small Unmanned Aircraft,” Princeton University Press, 2012, Chapter 10, Slide 8

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Vector Field Tuning

Beard & McLain, “Small Unmanned Aircraft,” Princeton University Press, 2012, Chapter 10, Slide 9

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Lyapunov’s 2nd Method

Beard & McLain, “Small Unmanned Aircraft,” Princeton University Press, 2012, Chapter 10, Slide 10

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Lateral Tracking Stability Analysis

Beard & McLain, “Small Unmanned Aircraft,” Princeton University Press, 2012, Chapter 10, Slide 11

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Longitudinal Tracking Problem

Beard & McLain, “Small Unmanned Aircraft,” Princeton University Press, 2012, Chapter 10, Slide 12

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Longitudinal Tracking Problem

Beard & McLain, “Small Unmanned Aircraft,” Princeton University Press, 2012, Chapter 10, Slide 13

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Longitudinal Guidance Strategy

Beard & McLain, “Small Unmanned Aircraft,” Princeton University Press, 2012, Chapter 10, Slide 14

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Smallest Angle Turn Logic

Beard & McLain, “Small Unmanned Aircraft,” Princeton University Press, 2012, Chapter 10, Slide 15

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Orbit Following

Beard & McLain, “Small Unmanned Aircraft,” Princeton University Press, 2012, Chapter 10, Slide 16

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Orbit Following

Beard & McLain, “Small Unmanned Aircraft,” Princeton University Press, 2012, Chapter 10, Slide 17

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Orbit Following

Beard & McLain, “Small Unmanned Aircraft,” Princeton University Press, 2012, Chapter 10, Slide 18

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Orbit Tracking Stability Analysis

Beard & McLain, “Small Unmanned Aircraft,” Princeton University Press, 2012, Chapter 10, Slide 19

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Orbit Following

Beard & McLain, “Small Unmanned Aircraft,” Princeton University Press, 2012, Chapter 10, Slide 20

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Roll Feedforward: no wind

Beard & McLain, “Small Unmanned Aircraft,” Princeton University Press, 2012, Chapter 10, Slide 21

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Roll Feedforward: wind

Beard & McLain, “Small Unmanned Aircraft,” Princeton University Press, 2012, Chapter 10, Slide 22

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Dubins Airplane Model

Adapted from: Mark Owen, Randal W. Beard, Timothy W. McLain, “Implementing Dubins Airplane Paths on Fixed-wing UAVs,” Handbook of Unmanned Aerial Vehicles, ed. Kimon P. Valavanis, George J. Vachtsevanos, Springer Verlag, Section XII, Chapter 68, p. 1677-1702, 2014.

Flight path projected onto ground

horizontal component

of airspeed vector

Beard & McLain, “Small Unmanned Aircraft,” Princeton University Press, 2012, Chapter 10, Slide 23

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3D Vector Field Path Following

Adapted from: V. M. Goncalves, L. C. A. Pimenta, C. A. Maia, B. C. O. Durtra, G. A. S. Pereira, B. C. O. Dutra, and G. A. S. Pereira, “Vector Fields for Robot Navigation Along Time-Varying Curves in n-Dimensions,” IEEE Transactions on Robotics, vol. 26, pp. 647–659, Aug 2010.

​

Beard & McLain, “Small Unmanned Aircraft,” Princeton University Press, 2012, Chapter 10, Slide 24

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3D Vector Field Path Following

Beard & McLain, “Small Unmanned Aircraft,” Princeton University Press, 2012, Chapter 10, Slide 25

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3D Vector Field Path Following

Beard & McLain, “Small Unmanned Aircraft,” Princeton University Press, 2012, Chapter 10, Slide 26

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3D Vector Field – Straight Line path

Beard & McLain, “Small Unmanned Aircraft,” Princeton University Press, 2012, Chapter 10, Slide 27

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3D Vector Field – Helical Path

Beard & McLain, “Small Unmanned Aircraft,” Princeton University Press, 2012, Chapter 10, Slide 28