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Longitudinal and Lateral Vehicle Longitudinal and Lateral Vehicle Velocity Estimation with aVelocity Estimation with a

Nonlinear ObserverNonlinear Observer

An Example of Using TruckSim in Developing Vehicle Control Algorithms

Ragnar LedesmaCVS Advanced Engineering

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Background

• Current dynamic vehicle control systems include the following sensors:• Wheel rotation rates, steering angle, lateral and longitudinal

accelerometers, yaw rate

• Advanced control systems require time-varying parameters or states that can not be measured directly:• Vehicle velocity, vehicle slip angle, spindle loads, friction

coefficient, roll angles, etc.

• Need estimators (state observers) to provide reliable real-time estimates, subject to: • Model uncertainty, external disturbances, uncertainty in

measurements, changes in operating conditions

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Overview: Vehicle Velocity / Side Slip Estimation

Variables to estimate:• Longitudinal velocity vx

• Lateral velocity vy

• (Vehicle side slip angle

Secondary variables:• Maximum friction coefficient H

• Road bank angle

Sensors• Lateral/longitudinal acceleration ay/ax

• yaw rate r• wheel speed i and steering angle i

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Vehicle Model for Nonlinear Observer• Simplified vehicle model:

• Measurement variables:• Steering angles

• Wheel speeds

• Yaw rate

• Accelerations

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Proposed Nonlinear Observer

• Tire-ground friction model required• Restrictions are imposed on observer gains to assure

convergence of the estimates to the actual states

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Example 1: Sinusoidal Steering

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Example 1: Sinusoidal Steering

vehicle side slip angle

lateral speed

longitudinal speed

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Example 2: Constant Radius Test on Low Friction Surface

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Example 2: Constant Radius Test on Low Friction Surface

vehicle side slip angle

lateral speed

longitudinal speed

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Example 3: Braking in a Turn

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Example 3: Braking in a Turn

vehicle side slip angle

lateral speed

longitudinal speed

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Example 4: Split- Braking (with ABS)

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Example 4: Split- Braking (with ABS)

longitudinal speed

lateral speed

vehicle side slip angle

wheel speeds

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Example 5: Double Lane Change at 80 Km/Hr

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Example 5: Double Lane Change at 80 Km/Hr

longitudinal speed

lateral speed

vehicle side slip angle

yaw rate

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Example 6: Double Lane Change on a Split- Surface

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Example 6: Double Lane Change on a Split- Surface

longitudinal speed

lateral speed

vehicle side slip angle

yaw rate

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Next Step: Adaptive Nonlinear Observer

• Nonlinear observer relies on tire-ground friction model

• Friction model is characterized by “maximum friction coefficient”,

• Difficult to measure ground friction

• Need on-line adaptation model for