#### Course Info:

**Instructor:**Wei Zhang, Innovation Park 7 – 602

**Time:**Tuesday 2- 3:50pm / Thursday 2-3:50 am (odd week)

**Location:**荔园 6栋 403 / 荔园1栋 205

**Webpage:**Blackboard

#### 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.

### Lecture Notes:

**Lecture 1: Introduction****Lecture 2: Rigid Body Configuration and Velocity**[PDF]**Lecture 3: Operation View of Rigid-Body Transformation**[PDF]Rotation Operation, Rigid-Body Transformation Operation **Lecture 4: Exponential Coordinate of Rigid-Body Configuration**[PDF]Exponential Coordinate, Euler Angles and Euler-Like Parameterizations, Instantaneous Velocity of Moving Frames **Lecture 5: Kinematics of Open Chain**[PDF]Forward Kinematics: Product of Exponential Formula, Jacobian, Geometric Jacobian Derivation, Analytic Jacobian **Lecture 6: Rigid Body Dynamics**[PDF]Spatial Acceleration, Spatial Force (Wrench), Spatial Momentum, Newton-Euler Equation using Spatial Vectors **Lecture 7: Dynamics of Open Chains**[PDF]Inverse and Forward Dynamics: Recursive Newton-Euler Algorithm (RNEA), Analytical Form of the Dynamics Model **Lecture 8: Basics of Optimization**[PDF]Linear Algebra, Multivariable Calculus, Sets and Functions, Linear Program, Quadratic Program **Lecture 9: Basic Linear Control Engineering****Lecture 10: Robot Motion Control**[PDF]Motion Control with Velocity/Acceleration as Input, Motion Control with Torque as Input, Task-Space Error in SO(3)/SE(3) **Lecture 11: Elementary Model Predictive Control**[PDF]Formulation of General MPC Problems, Linear MPC Problems **Lecture 12: Basics of Feedback Linearization**[PDF]Input-Output Linearization

#### References:

**"Mathematical introduction to robotic manipulation", R. Murray, Z. Li, S. Sastry****"Modern Robotics: Mechanics, Planning, and Control", Kevin M. Lynch and Frank C. Park, Cambridge University Press, 2017, ISBN 9781107156302**
http://hades.mech.northwestern.edu/index.php/Modern_Robotics
**"Rigid Body Dynamics Algorithms", Roy Featherston**
https://www.springer.com/gp/book/9780387743141
**"Predictive Control for Linear and Hybrid Systems", F. Borrelli, A. Bemporad, M. Morari, Cambridge University Press , July, 2017**
http://www.mpc.berkeley.edu/mpc-course-material
**"Calculus of Variations and Optimal Control Theory: A Concise Introduction", Daniel Liberzon, Princeton University Press, 2011**
http://liberzon.csl.illinois.edu/teaching/cvoc/cvoc.html
**"Convex optimization", Stephen Boyd, Cambridge University Press**
https://web.stanford.edu/~boyd/cvxbook/
**Lecture notes, and papers distributed in class.**