Applied Control Systems 2: autonomous cars (360 tracking)

About Course

Dive deep into the world of autonomous vehicle control with this free Applied Control Systems 2: Autonomous Cars (360 Tracking) course. Taught by Mark, an Aerospace & Robotics Engineer, this course builds upon the concepts of Applied Control Systems 1: Autonomous Cars: Math + PID + MPC, and dives deeper into the world of autonomous vehicle design and implementation.

Learn how to design and implement control systems for autonomous vehicles using advanced techniques like Model Predictive Control (MPC) and Linear Parameter Varying (LPV) systems. This course will guide you through applying a linear MPC controller to a nonlinear system using the LPV form, enabling your autonomous vehicle to track a general 2D trajectory. You’ll also gain valuable knowledge in using quadratic solvers to apply MPC constraints and keep your system operating within realistic boundaries.

Key topics covered include:

Model Predictive Control (MPC)
Linear Parameter Varying (LPV) systems
Quadratic solvers
Autonomous vehicle control

This free course is available now on Theetay. This course is from Udemy and is part of our collection of free top-rated courses from platforms like Udemy, Udacity, Coursera, MasterClass, NearPeer, and more.

revision of Model Predictive Control for Linear Time Invariant (LTI) systems
mathematical modeling of an autonomous car on a 2D X-Y plane using the bicycle model
going from the vehicle's equations of motion to its state space form
mastering & applying linear Model Predictive Control (MPC) to a nonlinear system using Linear Parameter Varying (LPV) formulation
mastering & applying Model Predictive Control (MPC) constraints to the autonomous car
simulating the control loop for the autonomous car in Python including the Model Predictive Control (MPC) controller and its constraints

Course Content

Revision

Introduction & general instructions

06:24
Equations of motion formulation in the lateral direction

06:53
Going from equations of motion to the state-space equations

06:33
Controller limitations from the small yaw angle assumption 1

05:02
Controller limitations from the small yaw angle assumption 2

08:21
Model Based Control VS PID

05:50
Revision of the plant box equations

04:58
Revision of the MPC basic principle

05:26
Revision of the MPC basic principle

05:26
Revision of the MPC basic principle

05:26
Revision of making the LTI system discrete

11:38
Revising how MPC predicts future states

07:12
Revision of augmenting the LTI state space model – exercise

05:43
Revision of augmenting the LTI state space model – solution

03:32
Revision of MPC cost function reformulation

11:06
Course Material Download Link

00:00

State space equations for the plant

Intro to equations of motion

04:38
Analyzing forces in the longitudinal direction

06:17
Analyzing forces in the lateral direction

06:22
Forming the equations of motion

07:43
Forming the lateral forces 1

03:41
Forming the lateral forces 2

04:32
Forming the lateral forces 3

06:49
Forming the lateral forces 4

07:14
Analyzing net acceleration in a rotating body frame (forces) 1

05:32
Analyzing net acceleration in a rotating body frame (forces) 2

08:04
Analyzing net acceleration in a rotating body frame (forces) 3

07:58
Analyzing net acceleration in a rotating body frame (forces) 4

13:29
Analyzing net acceleration in a rotating body frame (moments)

03:21
Simplifications made in the previous course in the equations of motion

07:56
Going from equations of motion to the state-space equations – exercise

06:17
Going from equations of motion to the state-space equations – solution

13:22
Follow up!

00:37

LPV – MPC – no constraints (Intro to Linear Parameter Varying method)

Intro to Linear Parameter Varying techniques 1

09:41
Intro to Linear Parameter Varying techniques 2

10:04
Intro to Linear Parameter Varying techniques 3

11:36
Intro to Linear Parameter Varying techniques 4

07:43
Converting the car’s state space equations in the LPV form 1

07:30
Converting the car’s state space equations in the LPV form 2

07:38
Converting the car’s state space equations in the LPV form 3

07:47
Choosing the outputs for the car system 1

04:40
Choosing the outputs for the car system 1

04:40
Choosing the outputs for the car system 2

08:47
Choosing the outputs for the car system 3

04:02
Choosing the outputs for the car system 4

06:19
Choosing the outputs for the car system 5

07:05
Revision of the MPC controller application

08:25
Differences in the MPC application 1 LTI vs LPV

10:59
Differences in the MPC application 2 LTI vs LPV

08:00
Differences in the MPC application 3 LTI vs LPV

10:50
Differences in the MPC application 4 LTI vs LPV

08:03
Differences in the MPC application 5 LTI vs LPV

02:28
LPV-MPC simplification in a UAV drone case

13:32
General recommendations for tracking a reference trajectory

04:41
Why MPC constraints & cubic polynomials

11:23

LPV – MPC controller – with constraints + cubic polynomials

Intro to MPC constraints – intuition 1

07:37
Intro to MPC constraints – intuition 2

08:11
Intro to MPC constraints – intuition 3

04:42
Intro to MPC constraints – intuition 4

05:44
Intro to quadratic solvers 1

09:11
Intro to quadratic solvers 2

07:10
Intro to quadratic solvers 3

07:29
The car’s fixed vs changing constraints 1

11:28
The car’s fixed vs changing constraints 2

06:59
Minimum point of a cost function for many dimensions (no constraints)

07:21
Minimum point of a cost function for many dimensions (with constraints)

08:14
Formulating the constraints for the MPC control inputs 1

09:17
Formulating the constraints for the MPC control inputs 2

06:35
Formulating the constraints for the states 1

14:07
Formulating the constraints for the states 2

11:13
Formulating the constraints for the states 3

04:32
Formulating the constraints for the states 4

07:14
Formulating the constraints for the states 5

06:15
Formulating the constraints for the states 6

05:52
Application & results of the MPC constraints

10:09
The case of no solutions in the optimization control problem 1

07:06
The case of no solutions in the optimization control problem 2

09:20
The case of no solutions in the optimization control problem 3

12:55
The positive definite matrix requirement 1

07:17
The positive definite matrix requirement 2

04:11
The positive definite matrix requirement 2

04:11
The positive definite matrix requirement 3

08:17
Small comment about MPC weights

03:24
The positive definite matrix requirement 4

03:11
Designing trajectories with cubic polynomials 1

00:48
Designing trajectories with cubic polynomials 2

06:20
Designing trajectories with cubic polynomials 3

10:37
Designing trajectories with cubic polynomials 4

03:02
Designing trajectories with cubic polynomials 5

05:50
Designing trajectories with cubic polynomials 6

05:38
Designing trajectories with cubic polynomials 7

07:58
Improving 360 tracking with MPC weights

03:14

The Python code implementation of the LPV-MPC controller with the constraints

General instructions for the code explanation section

03:44
Launching Python files in Windows cmd & UbuntuMacOS terminal

12:54
Ubuntu installation instructions (Py

06:01
Ubuntu installation instructions (Qpsolvers)

02:14
Windows 10 installation instructions (Py

06:01
Windows 10 installation instructions (Qpsolvers)

04:21
MacOS Big Sur installation instructions (Py

08:04
MacOS Big Sur installation instructions (Qpsolvers)

02:56
Python code explanation 1

12:15
Python code explanation 2

05:22
Python code explanation 3

17:19
Python code explanation 4

08:36
Python code explanation 5

09:49
Python code explanation 6

08:08
Python code explanation 7

08:44
Python code explanation 8

12:41
Python code explanation 9

08:54
Python code explanation 10

12:02
Python code explanation 11

08:48
Python code explanation 12

07:12
Python code explanation 13

03:26
Python code explanation 14

05:54

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About Course

What Will You Learn?

Course Content

Revision

Introduction & general instructions

Equations of motion formulation in the lateral direction

Going from equations of motion to the state-space equations

Controller limitations from the small yaw angle assumption 1

Controller limitations from the small yaw angle assumption 2

Model Based Control VS PID

Revision of the plant box equations

Revision of the MPC basic principle

Revision of the MPC basic principle

Revision of the MPC basic principle

Revision of making the LTI system discrete

Revising how MPC predicts future states

Revision of augmenting the LTI state space model – exercise

Revision of augmenting the LTI state space model – solution

Revision of MPC cost function reformulation

Course Material Download Link

State space equations for the plant

Intro to equations of motion

Analyzing forces in the longitudinal direction

Analyzing forces in the lateral direction

Forming the equations of motion

Forming the lateral forces 1

Forming the lateral forces 2

Forming the lateral forces 3

Forming the lateral forces 4

Analyzing net acceleration in a rotating body frame (forces) 1

Analyzing net acceleration in a rotating body frame (forces) 2

Analyzing net acceleration in a rotating body frame (forces) 3

Analyzing net acceleration in a rotating body frame (forces) 4

Analyzing net acceleration in a rotating body frame (moments)

Simplifications made in the previous course in the equations of motion

Going from equations of motion to the state-space equations – exercise

Going from equations of motion to the state-space equations – solution

Follow up!

LPV – MPC – no constraints (Intro to Linear Parameter Varying method)

Intro to Linear Parameter Varying techniques 1

Intro to Linear Parameter Varying techniques 2

Intro to Linear Parameter Varying techniques 3

Intro to Linear Parameter Varying techniques 4

Converting the car’s state space equations in the LPV form 1

Converting the car’s state space equations in the LPV form 2

Converting the car’s state space equations in the LPV form 3

Choosing the outputs for the car system 1

Choosing the outputs for the car system 1

Choosing the outputs for the car system 2

Choosing the outputs for the car system 3

Choosing the outputs for the car system 4

Choosing the outputs for the car system 5

Revision of the MPC controller application

Differences in the MPC application 1 LTI vs LPV

Differences in the MPC application 2 LTI vs LPV

Differences in the MPC application 3 LTI vs LPV

Differences in the MPC application 4 LTI vs LPV

Differences in the MPC application 5 LTI vs LPV

LPV-MPC simplification in a UAV drone case

General recommendations for tracking a reference trajectory

Why MPC constraints & cubic polynomials

LPV – MPC controller – with constraints + cubic polynomials

Intro to MPC constraints – intuition 1

Intro to MPC constraints – intuition 2

Intro to MPC constraints – intuition 3

Intro to MPC constraints – intuition 4

Intro to quadratic solvers 1

Intro to quadratic solvers 2

Intro to quadratic solvers 3

The car’s fixed vs changing constraints 1

The car’s fixed vs changing constraints 2

Minimum point of a cost function for many dimensions (no constraints)

Minimum point of a cost function for many dimensions (with constraints)

Formulating the constraints for the MPC control inputs 1

Formulating the constraints for the MPC control inputs 2

Formulating the constraints for the states 1

Formulating the constraints for the states 2

Formulating the constraints for the states 3

Formulating the constraints for the states 4

Formulating the constraints for the states 5