Underactuated Robotics
Spring 2022
Robots today move far too conservatively, using control systems that attempt to maintain full control authority at all times. Humans and animals move much more aggressively by routinely executing motions which involve a loss of instantaneous control authority. Controlling nonlinear systems without complete control authority requires methods that can reason about and exploit the natural dynamics of our machines. This course introduces nonlinear dynamics and control of underactuated mechanical systems, with an emphasis on computational methods. Topics include the nonlinear dynamics of robotic manipulators, applied optimal and robust control and motion planning. Discussions include examples from biology and applications to legged locomotion, compliant manipulation, underwater robots, and flying machines.
Spring 2009
Topics
- Nonlinear dynamics of the simple pendulum
- Dynamic programming and value interation: grid world, double integrator, and pendulum examples
- Acrobot and cart-pole: controllability, partial feedback linearization (PFL), and energy shaping
- Acrobot and cart-pole (cont.)
- Policy search: open-loop optimal control, direct methods, and indirect methods
- Policy search (cont.): trajectory stabilization, iterative linear quadratic regulator (iLQR), differential dynamic programming (DDP)
- Simple walking models: rimless wheel, compass gait, kneed compass gait
- Feedback control for simple walking models
- Simple running models: spring-loaded inverted pendulum (SLIP), Raibert hoppers
- Midterm
- Motion planning: Dijkstra’s, A-star
- Randomized motion planning: rapidly-exploring randomized trees and probabilistic road maps
- Feedback motion planning: planning with funnels, linear quadratic regulator (LQR) trees
- Function approximation and system identification
- Model systems with uncertainty: state distribution dynamics and state estimation
- Stochastic optimal control
- Aircraft
- Swimming and flapping flight
- Randomized policy gradient
- Randomized policy gradient (cont.)
- Model-free value methods: temporal difference learning and Q-learning
- Final project presentations
Readings
- Strogatz, Steven H. Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering . Boulder, CO: Westview Press, 2001. ISBN: 9780738204536.
- Slotine, Jean-Jacques E., and Weiping Li. Applied Nonlinear Control . Upper Saddle River, NJ: Prentice Hall, 1991. ISBN: 9780130408907.
- Fantoni, Isabelle, and Rogelio Lozano. Non-linear Control for Underactuated Mechanical Systems . New York, NY: Springer-Verlag, 2002. ISBN: 9781852334239.
- Bertsekas, Dimitri P. Dynamic Programming and Optimal Control . 3rd ed. Vols. I and II. Nashua, NH: Athena Scientific, 2007. ISBN: 9781886529083 (set).
- Bertsekas, Dimitri P., and John N. Tsitsiklis. Neuro-Dynamic Programming . Nashua, NH: Athena Scientific, 1996. ISBN: 9781886529106.
- LaValle, Steven M. Planning Algorithms . New York, NY: Cambridge University Press, 2006. ISBN: 9780521862059.
- Chapter 1 and Appendix A
- SES #: 2 · TOPICS: Nonlinear dynamics of the simple pendulum · READINGS: Chapter 2
- Chapter 9 (cont.)
- SES #: 6 · TOPICS: Acrobot and cart-pole: controllability, partial feedback linearization (PFL), and energy shaping · READINGS: Chapter 3
- SES #: 7 · TOPICS: Acrobot and cart-pole (cont.) · READINGS: Chapter 3 (cont.)
- SES #: 8 · TOPICS: Policy search: open-loop optimal control, direct methods, and indirect methods · READINGS: Chapter 12
- SES #: 9 · TOPICS: Policy search (cont.): trajectory stabilization, iterative linear quadratic regulator (iLQR), differential dynamic programming (DDP) · READINGS: Chapter 12 (cont.)
- SES #: 10 · TOPICS: Simple walking models: rimless wheel, compass gait, kneed compass gait · READINGS: Chapter 5
- SES #: 11 · TOPICS: Feedback control for simple walking models · READINGS: Chapter 5 (cont.)
- SES #: 12 · TOPICS: Simple running models: spring-loaded inverted pendulum (SLIP), Raibert hoppers · READINGS: Chapter 6
- SES #: 13 · TOPICS: Motion planning: Dijkstra’s, A-star · READINGS: Chapter 13
- SES #: 14 · TOPICS: Randomized motion planning: rapidly-exploring randomized trees and probabilistic road maps · READINGS: Chapter 13 (cont.)
- SES #: 15 · TOPICS: Feedback motion planning: planning with funnels, linear quadratic regulator (LQR) trees · READINGS: Chapter 14
- SES #: 16 · TOPICS: Function approximation and system identification · READINGS: Chapter 8 and Appendix B
- SES #: 17 · TOPICS: Model systems with uncertainty: state distribution dynamics and state estimation · READINGS: Chapter 8 (cont.)
- SES #: 18 · TOPICS: Stochastic optimal control · READINGS: Chapter 15
- SES #: 19 · TOPICS: Aircraft · READINGS: Chapter 7
- SES #: 20 · TOPICS: Swimming and flapping flight · READINGS: Chapter 7 (cont.)
- SES #: 21 · TOPICS: Randomized policy gradient · READINGS: Chapter 17
- SES #: 22 · TOPICS: Randomized policy gradient (cont.) · READINGS: Chapter 17 (cont.)
- SES #: 23 · TOPICS: Model-free value methods: temporal difference learning and Q-learning · READINGS: Chapter 16
- CHAPTERS: I. Nonlinear dynamics and control
- CHAPTERS: 4 · TOPICS: Manipulation
- CHAPTERS: 6 · TOPICS: Running
- CHAPTERS: 7 · TOPICS: Flight
- CHAPTERS: 8 · TOPICS: Model systems with stochasticity
- CHAPTERS: II. Optimal control and motion planning
- CHAPTERS: 11 · TOPICS: Analytical optimal control with Pontryagin’s minimum principle
- CHAPTERS: 13 · TOPICS: Feasible motion planning
- CHAPTERS: 14 · TOPICS: Global policies from local policies
- CHAPTERS: 15 · TOPICS: Stochastic optimal control
- CHAPTERS: 16 · TOPICS: Model-free value methods
- CHAPTERS: 18 · TOPICS: Actor-critic methods
- CHAPTERS: IV. Applications and extensions
- CHAPTERS: 19 · TOPICS: Learning case studies and course wrap-up
- CHAPTERS: Appendix
Sources
- Course catalogue ↗Historical OpenCourseWare
- MIT OpenCourseWare ↗Spring 2009
- MIT OCW syllabus ↗
- MIT OCW calendar ↗
- MIT OCW readings ↗
- Historical MIT OpenCourseWare offering. Named reading entries and schedule topics are automatically extracted from the linked source pages.
- Historical MIT OpenCourseWare offering. Named reading entries and schedule topics are automatically extracted from the linked source pages.