Optimization Methods for Robotics

Course Topics

• Formulating robotics problems (planning, control, and state estimation) as optimizations.
• Numerical methods (gradient-based and gradient-free) for solving optimization problems.
• Handling rotations, rigid-body transformations, and constraints.
• Robust optimization under model mismatch and contact.

Course Logistics

Resources

• Course website - all course information and materials will be posted here.
• Ed Discussion forum - for asking and answering questions about the course material.
• Gradescope - for submitting assignments and viewing grades/feedback.
• Canvas - final grades and assignment solutions will be posted here.

Prerequisites

This course assumes the following background:

• Comfortable programming in Python. All assignments will be in Python and will make use of NumPy and JAX. Students with substantial programming experience in another language (e.g. C/C++, MATLAB, Julia) should be able to transition quickly.

• Foundations in linear algebra and calculus. You should be comfortable working with vectors and matrices, and with derivatives and gradients. Familiarity with Hessians will be helpful.

• Basic probability and statistics. You should be familiar with random variables, probability distributions, expectation, variance, and Bayes’ rule.

The following background is helpful but not required:

• Some exposure to optimization concepts, such as gradient descent or convexity.

• Some exposure to robotics, for example kinematics, dynamics, or control.

Students without the recommended background are still encouraged to enroll, but may need to do some independent review during the semester.

Assignments and Grading

Course grades are determined by homework and a final project.

• Homework (50%) Four assignments will be given at roughly three week intervals.
• Final Project (45%) Work may be done individually or in teams of up to three. Projects should investigate a problem related to optimal or learning based control or estimation. Evaluation is divided across a project proposal (5%), a milestone report (10%), and a final report with a three minute video (30%).
• Participation (5%) We will assess participation credit based on engagement in lectures (e.g., answering in-class polling questions), and responding to the intro- and mid-semester surveys.
• Bonus (up to 5%) Students earn 0.5% of extra credit for each staff-endorsed answer on Ed Discussion, up to a total of 5%.

Syllabus

The syllabus for the course can be found here.

Schedule

The tentative schedule for the course can be found here.