Optimization Methods for Robotics
Robotics requires translating high-level goals into precise physical motion under real-world dynamics, sensing, and constraints. Optimization offers a unified framework for this challenge, and by exploiting problem structure, the same numerical methods can solve planning, estimation, and control problems in milliseconds on real robots. This course teaches students to recognize that structure and to build the solvers that exploit it, from the linear algebra up. Following an introduction to numerical linear algebra and unconstrained optimization, the course covers constrained optimization, dynamic programming, trajectory optimization, and model predictive control (MPC). Topics include least squares, Newton-type methods, KKT conditions, the linear quadratic regulator, and sampling-based MPC. Applications include kinematic retargeting, trajectory planning, and state estimation for robot arms, cars, quadrotors, and humanoids.
Topics
- Formulate planning, control, and estimation tasks as well-posed optimization problems, and identify the structure that determines how they should be solved.
- Implement zero-, first-, and second-order optimization methods from their derivations, using numerical linear algebra and automatic differentiation, and predict their behavior on a given problem from its conditioning and structure.
- Derive and implement the core algorithms of optimal control, including dynamic programming, LQR, trajectory optimization, and model predictive control, and understand their relationship to one another.
- Solve a realistic robotics problem online, in a receding-horizon loop, and explain the method and its limitations.
- Formulate planning, control, and state estimation tasks in robotics as well-posed numerical optimization problems, specifying objectives, constraints, and problem structure.
- Implement and compare zero-, first-, and second-order optimization methods, and evaluate their convergence properties, computational tradeoffs, and suitability for different classes of problems.
- Apply optimization algorithms to robotics research problems and analyze how system dynamics, constraints, and geometric structure influence solvability and efficiency.
Official roster learning outcomes
Prerequisites & course information
background equivalent to: MATH 2940; MATH 1920; CS 1110 or CS 1112.
Sources
- Course catalogue ↗2026-2027
- Catalogue entry ↗
Catalogue variants
- Optimization Methods for Robotics · 3.0 · Graduate