 • Feb , 2023

## Course Info

Instructor:     Wei Zhang, College of Engineering North Tower 519
Time:              Monday 10:20- 12:10am / Wednesday 14:00-15:50 pm (odd week)
Location:       一教 503
TAs:                Linfang Zheng, Yongjian Su, Ronghan Xu
Recordings:   https://space.bilibili.com/474380277/channel/collectiondetail?sid=1129069&ctype=0

## Description

The objective of this course is for students to develop the ability to recognize, formulate, and solve control problems within the context of robotic applications. We will introduce important concepts and tools for design and analysis of advanced robotic control systems. Topics include advanced rigid body kinematics and dynamics using product of exponentials, screw theory, and spatial vectors, nonlinear dynamical systems, Lyapunov stability, feedback linearization, optimal control and trajectory optimization, model predictive control, among others. An emphasis will be placed on developing competency in control and optimization theory and on applications within robotics.

## Objectives

• Develop solid analytical skills to conduct cutting edge research in control theory and robotics
• Train the student’s ability in formulating robotic control problems through optimization
• Develop advanced understanding in multibody dynamics using product of exponential, spatial vectors, and screw theory
• Develop good theoretic foundations on advanced control methods that are commonly used in robotics, including feedback linearization, optimal control, trajectory optimization, DDP, reachability, and MPC
• Use the theory learned in class to solve research problems of interest

## Lecture Notes

• Lecture 1: Linear Differential Equations and Matrix Exponential [PDF][Noted]
​Linear System Model, Matrix Exponential, Solution to Linear Differential Equations
• Lecture 2: Rigid Body Configuration and Velocity[PDF][Noted]
Rigid Body Configuration, Rigid Body Velocity(Twist), Geometric Aspect of Twist: Screw Motion
• Lecture 3: Operator View of Rigid-Body Transformation[PDF][Noted]
Rotation Operation with Rotation Matrix, Rigid-Body Operation with Homogeneous Transformation Matrix
• Lecture 4: Exponential Coordinate of Rigid Body Configuration [PDF][Noted]
Exponential Coordinate of SO(3), Euler Angles and Euler-Like Parameterizations, Exponential Coordinate of SE(3)
• Lecture 5: Instantaneous Velocity of Moving Frames [PDF][Noted]
Instantaneous Velocity of Rotating Frames, Instantaneous Velocity of Moving Frames
• Lecture 6: Product of Exponential and Kinematics of Open Chain [PDF][Noted]
Kinematics Background, Product of Exponential Formula Derivations
• Lecture 7: Velocity Kinematics: Geometric and Analytic Jacobian of Open Chain [PDF][Noted]
Velocity Kinematics Background, Geometric Jacobian Derivations, Analytic Jacobian
• Lecture 8: Rigid Body Dynamics [PDF][Noted]
Spatial Acceleration, Spatial Force (Wrench), Spatial Momentum, Newton-Euler Equation using Spatial Vectors
• Lecture 9: Dynamics of Open Chains [PDF][Noted]
Inverse Dynamics: Recursive Newton-Euler Algorithm (RNEA), Analytical Form of the Dynamics Model, Forward Dynamics Algorithms
• Lecture 10: Basics of Optimization [PDF][Noted]
Some Linear Algebra, Sets and Functions, Optimizaiton Inctroduction, Linear Program, and Quadratic Program
• Lecture 11: Differential Inverse Kinematics[PDF][Noted]
Differential IK
• Lecture 12: Robot Motion Control[PDF][Noted]
Basic Linear Control Design, Motion Control Problems, Motion Control with Velocity/Acceleration as Input, Motion Control with Torque as Input and Task Space Inverse Dynamics

Homework                         20%
Mini-Project                       15%
Quiz                                   10%
Midterm                              25%
Final Exam                         30%

## Supporting Materials

Tutorial for Python Numpy and Matplotlib:  [file]

## References

1. “Mathematical introduction to robotic manipulation”, R. Murray, Z. Li, S. Sastry
https://www.cds.caltech.edu/~murray/books/MLS/pdf/mls94-complete.pdf
2. “Modern Robotics: Mechanics, Planning, and Control”, Kevin M. Lynch and Frank C. Park, Cambridge University Press, 2017, ISBN 9781107156302