Description

• Course Title: Nonlinear Control and Planning in Robotics
• Course Number: EN530.678
• Time: MW 3:00-4:15
• Location: Hodson 316
• Professor: Marin Kobilarov
  • Contact: marin(at)jhu.edu, Hackerman 117
  • Office Hours: Monday 12:00-1:00, Hackerman 117
• Teaching Assistants
  • Gabe Baraban (gbaraba1(at)jhu.edu), Rajni Bansal (rbansal3(at)jhu.edu), Tianqi Zheng (tzheng8(at)jhu.edu)
  • TA Office Hours: Monday 11:00-12:00 and Friday 11:00-12:00, Hackerman 111
• Course material (homeworks/projects) can be submitted using the file upload form 

The course starts with a brief introduction to nonlinear systems and covers selected topics related to model-based trajectory planning and feedback control. Focus is on applications to robotic systems modeled as underactuated mechanical systems subject to constraints such as obstacles in the environment. Topics include: nonlinear stability, controllability, stabilization, trajectory tracking, systems with symmetries, differential flatness, backstepping, probabilistic roadmaps, stochastic optimization. Recommended Course Background: multi-variable/differential calculus, differential equations, linear algebra, undergraduate linear control, basic probability theory, programming in MATLAB; an introductory robotics course is useful but not required.

Objectives

• Basic analysis and stability of nonlinear systems
• Controllability of nonholonomic systems
• Stabilization and tracking of underactuated/nonholonomic systems
• Trajectory generation using differential flatness/symmetries
• Optimal trajectory generation: gradient/gradient-free methods
• Motion planning with complex constraints
• Combining trajectory generation and feedback control: receding horizon control

Reading

There is no required textbook for the course. A list of relevant textbooks is provided below.

• Textbooks: General Nonlinear Control
  • Sastry, “Nonlinear Systems: Analysis, Stability, and Control, 1999
  • Khalil, “Nonlinear Systems, 1991
  • Slotine, Li, “Applied Nonlinear Control, 1991

• Textbooks: Robot Control and Planning
  • Murray, Li, Sastry, “Mathematical Introduction to Robotic Manipulation, 1994, Chapters 7,8 (available online)
  • Choset, Lynch, Hutchinson, Kantor, Burgard, Kavraki and Thrun, “Principles of Robot Motion: Theory, Algorithms, and Implementations, 2006
  • Lavalle, “Planning Algorithms, 2006, Chapters 14, 15 (available online)
  • Spong, Hutchinson, Vidyasagar, “Robot Modeling and Control, 2005
  • edited by Laumond, “Robot motion planning and control, 1998
  • Canudas de Wit, Siciliano, Bastin, “Theory of Robot Control, 1996

• Textbooks for additional/advanced background:
  • Manifolds/Basics:
    • “Calculus on manifolds”, Spivak, 1965
  • Differential Geometry:
    • “A Comprehensive Introduction to Differential Geometry”, Spivak
    • “An Introduction to Differentiable Manifolds and Riemannian Geometry”, Boothby
  • Mechanics
    • “Mathematical Methods of Classical Mechanics”, Arnold, 1987
    • “Introduction to Mechanics and Symmetry”, Marsden and Ratiu, 1999
    • “Nonholonomic Mechanics and Control”, Bloch, 2003
    • “Geometric Control of Mechanical Systems”, Bullo, Lewis, 2004

Schedule (tentative — check often!)

Week	Topic	Lecture Notes	Code	Assignments
1/27/2020	Introduction, preliminaries, system models	Intro Lecture #1 Lecture #2
2/3/2020	Nonlinear Stability	Lecture #3	lecture3_1.m lecture3_2.m hw1_lyapunov_example.m	Homework #1 due Feb 12
2/12/2020	Nonlinear Stability (cont'd)		hw2_example.m	Homework #2 due Feb 19
2/17/2020	Manifolds and Vector Fields	Lecture #4	lecture4_1.m
2/24/2020	Controllability and Nonholonomy	Lecture #5		Homework #3 due Mar 4
2/26/2020	Stabilizability and Nonholonomic Steering	Lecture #6
3/2/2020	Differential Flatness	Lecture #7	uni_flat_care.m arm_test.m	Homework #4 due Mar 11
3/4/2020	Feedback Linearization	Lecture #8	uni_flat_fl.m	Homework #5 due 3/25
3/30/2020	Backstepping	Lecture #9	unit_flat_bs.m	Homework #6 due 4/8

Grading Policy

There will be homeworks given every week and due one week later (on Wednesday before class). There will be a midterm and a final covering the first half and second half of the semester, and a project involving both analys and implementation (e.g. in MATLAB). Grades will be determined according to:

Homeworks	30%
Midterm	25%
Final	25%
Project	20%

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Ethics

You can work together with other students to study the material related to homeworks/tests but the submitted work must be entirely your own. For more information, see the guide on “Academic Ethics for Undergraduates” and the Ethics Board web site (http://ethics.jhu.edu).

Late homework will not be accepted without a prior approval from the instructor.