CS 5757

Optimization Methods for Robotics

Course Description

Course information provided by the 2025-2026 Catalog.

Robotics requires translating high-level goals into precise physical motion under real-world dynamics, sensing, and constraints. Optimization offers a principled mathematical framework for this challenge, unifying methods for planning, control, and state estimation. This course develops the theory and practice of numerical optimization, spanning sampling-based methods, Newton-style algorithms, and constrained nonlinear programming. Students will implement these methods in core robotics applications such as trajectory optimization and state estimation on manifolds. Coursework will emphasize hands-on experience: problem sets will guide students through implementing core algorithms and applying them to realistic robotics tasks, while a semester-long project allows students to explore the application of optimization-based techniques in robotics, AI, or other domains of interest.

Enrollment Priority Strong familiarity with linear algebra (e.g., MATH 2940) and vector calculus (e.g., MATH 1920). Proficiency in Python. Familiarity with basic probability theory (e.g., ENGRD 2700) recommended. Enrollment limited to: CS MEng only with waitlist for others.

Last 4 Terms Offered (None)

Learning Outcomes

• 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.

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