Vehicle Dynamics and Robot Vehicles

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Vehicle Dynamicsand Robot Vehicles

• Jim Van de Ven
• February 18, 2004

Unless otherwise noted, all images
from Gillespie, Thomas D. Fundamentals of
Vehicle Dynamics
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Outline

• Background
• Robotic Vehicles
• Vehicle Dynamics Basics
• Two Wheel (Bicycle) Model
• Stability
• Steering Control System

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Background Information

• MTS Systems Vehicle Dynamics Division
• SAE Mini-Baja
• Formula SAE Mini-Indy
• Legend Air Suspension
• Robotic Vehicles
• Other

Picture From http//www.legend-airride.com
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Robot Vehicles

• What Distinguishes a Robot?
• Autonomous?
• Intelligent Mechanism?
• Useful Task?

Kodiak- Univ of Alberta
Segway
Cadillac Night Vision System
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Robot Vehicle Examples

• Scout
• Developed by Univ of MN, MTS, Honeywell, and ATC

Video From http//distrob.cs.umn.edu/scout.php
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Robot Vehicle Examples

• Soccer Segway Carnegie Mellon Univ

Video From ftp//brim.coral.cs.cmu.edu/pub/robot/
segway/movies/index.html
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Robot Vehicle Examples

• Intelligent Ground Vehicle Competition
• Collegiate Competition June 12-14, 2004
• Oakland University in Rochester, MI

Picture From http//www.igvc.org/deploy/
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Two Wheel (Bicycle) ModelLow Speed Turning

• R L/? (for small ?)

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Two Wheel (Bicycle) ModelHigh Speed Cornering

• Tires Slip During All Cornering
• Center of Turn Dictated by Front vs. Rear Slip

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Tire Slip Angle

• Difference Between Direction of Travel and
  Direction the Wheel is Pointing
• Torsional Spring- Hand on Table Example

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Tire Slip Angle
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Tire Model

• Tires Behavior is Not Linear

• Camber Creates Lateral Force

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Camber Thrust

• Camber Angle of Tire Lean From Vertical
• Examples
• Motorcycle
• Road Grader
• Tracking Grooves in Road

Picture From http//www.caterpillar.com
Picture From http//www.motorcyclesafety.state.mn
.us
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Stability- Oversteer (Loose)

• Rear Lateral Traction Exceeded
• Vehicle Enters a Spin
• Completely Unstable Above Critical Speed

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Oversteer Video
Video From http//www.esceducation.org/about_esc/
how_esc_works/
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Critical Speed- Equations
WFltWR
?

• ( ) 0

-
Neg
rYaw Rate (deg/sec) ?Steer Angle
(deg) VVelocity (ft/sec) LWheelbase
(ft) KUndersteer Gradient (deg/g) C?Tire
Cornering Stiffness (lb/deg) WWeight (lb)
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Understeer (Push)

• Front Lateral Traction Exceeded
• Vehicle Slides Straight
• Most Production Vehicles are Understeer

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Understeer Video
Video From http//www.esceducation.org/about_esc/
how_esc_works/
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Stability Examples

• Shopping Cart
• Push Forwards Understeer
• Push Backwards Oversteer (No Rear Lateral Force)

• Pulling Emergency Brake
• Oversteer (Low Lateral Force of Sliding Rear
  Tires)

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Bicycle Model

• Inherent Downfalls
• Lateral Weight Transfer
• Steering Geometry
• Camber and Roll Center
• Motorcycle Camber Force

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4 Wheel Model

• Turning Radius
• Ackerman Steering Ideal Steering Geometry
• Inner Tire Turns More than Outer Tire
• Perpendicular Bisectors Meet

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More Advanced Dynamics

• Suspensions
• Tuning Oversteer/Understeer
• Roll Centers
• Camber Change
• Acceleration/Deceleration
• Transient Behavior
• Active Suspensions
• Aerodynamics
• Tire Behavior

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Steering Control System
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Open-Loop Transfer Function

• Physical System
• Free Body Diagrams
• Governing Equations
• Laplace Transform
• Solve Simultaneously

Graph From http//www.ee.usyd.edu.au/tutorials_on
line/matlab/examples/motor/motor.html
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Closed-Loop Block Diagram
G(s)
Y(s)
U(s)
H(s)

• Closed Loop Transfer Function

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P, D, and I Control

• Proportional Control Decreases Rise Time
• Derivative Control Decreases Overshoot
• Integral Control Minimizes St-St Error

Graph From http//web.mit.edu/2.003/www/extra_fil
es/trans.pdf
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P, PD, PI, PID Controllers
Controller
G(s)
Y(s)
U(s)

• Open Loop
• P
• PD
• PI
• PID

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Matlab Controller Tuning