| Education | Mathematics and Control |
Michigan Robotics mathematics pathway
ROB 101, ROB 201, and ROB 501.
A connected sequence of open course materials for computational linear algebra, calculus for modern engineering, and graduate mathematics for robotics.
Computational linear algebra for robotics, data, and AI-scale applications.
Calculus as modeling, motion, numerical methods, and control.
Proof, estimation, probability, real analysis, and optimization.
Teaching career
Teaching the mathematics behind robotics.
Bringing an open source mindset to teaching through freely available course notes, textbooks, lectures, and project materials.
A career dedicated to outstanding teaching alongside pioneering research.
Jessy's teaching persona is rigorous but inviting: grounded in robotics and feedback control, serious about mathematical structure, and animated by helping students move from intuition to formal tools.
- Modeling
- Connect physical systems to equations, approximations, and simulation.
- Computation
- Use code and numerical methods to make mathematics operational.
- Control
- Turn models into feedback laws for robots that move through the world.
- Inference
- Give students the proof, estimation, probability, and optimization tools needed for robotics research.
How to learn modeling and feedback control of bipedal locomotion
For students and researchers wanting to learn bipedal locomotion, the materials are best read as a progression: begin with undergraduate bootcamp notes, move into the 2007 monograph, and then continue to later papers and tutorial surveys that extend the method.
Undergraduate bootcamp notes
Dr. Wami Ogunbi's Bipedal Bootcamp is the best starting point for undergraduates who want to learn control of bipedal locomotion before moving into the research monograph.
Research monograph
Feedback Control of Dynamic Bipedal Robot Locomotion, co-authored with Eric R. Westervelt, Christine Chevallereau, Jun-Ho Choi, and Benjamin Morris, was published by Taylor & Francis in June 2007 and is available for free download.
It treats virtual constraints and hybrid zero dynamics for the creation of asymptotically stable periodic motions in hybrid systems.
Methods developed after the monograph
These papers significantly extend virtual constraints and hybrid zero dynamics: Machine Learning, Zero Dynamics and Low-order Models, MPC and Virtual Constraints, Robust Optimization, and Bilinear Matrix Inequalities (BMI).
Review and survey material
For broader orientation, see the 2018 HZD Review paper by Ames and Poulakakis, the Springer reference chapter Humanoid Robotics: A Reference, and the 2015 survey on HZD in Automatica.
Earlier teaching in feedback control and applied mathematics
From 1987 to 2020, Jessy taught courses primarily in feedback control and applied mathematics for engineering. At the University of Michigan EECS Department, these included:
- EECS 216
- Signals and Systems
- EECS 460
- Control Systems Analysis and Design
- EECS 560
- Linear Systems Theory
- EECS 562
- Nonlinear Systems and Control
- EECS 600
- Function Space Methods for Systems Theory
- EECS 662
- Advanced Nonlinear Control
Course notes for the EECS courses have been passed on to Professors Necmiye Ozay and Dimitra (Mika) Panagou.
Resources
Course pages, repositories, and bipedal locomotion materials collected for students and colleagues.
Advanced extensions
Machine learning, low-order models, MPC, robust optimization, and BMI extensions.
Use the learning pathHZD tutorials and surveys
Review, reference chapter, and Automatica survey material.
Use the learning path