Lecture 15: MIT 6.832 Underactuated Robotics (Spring 2022) | "Simple Models of Walking"

This lecture is a masterclass in the fundamentals of legged locomotion, delivered by Russ Tedrake, a leading expert in the field. The content is rigorous and mathematically precise, yet presented in an accessible manner for advanced students. The lecture excels in its clear exposition of the concept of limit cycle stability, which is crucial for understanding periodic motions in robotics. The introduction of the Poincaré map as a tool to reduce the stability analysis of a cycle to that of a fixed point is elegantly explained, and the instructor carefully addresses potential pitfalls, such as the non-uniqueness of the surface of section. The use of the rimless wheel as a canonical example is particularly effective, as it allows for a complete analytical treatment while capturing the essential dynamics of walking. The lecture also touches on important practical considerations, such as the choice of Poincaré section and the computation of the Jacobian, which are often glossed over in textbooks. The historical context provided, including references to McGeer and the Cornell walker, adds depth and illustrates the evolution of ideas. The lecture is well-structured, building from simple to more complex concepts, and the instructor’s enthusiasm is contagious. The only minor criticism is that the lecture assumes prior knowledge of Lyapunov stability and hybrid systems, which may be challenging for those without a strong background in dynamical systems. However, for the target audience, this is not a drawback. Overall, this is an outstanding educational resource that provides a solid foundation for understanding the principles of dynamic walking.

The title accurately reflects the content, which focuses on simple models of walking and their stability analysis.

9/10

Lecture from MIT OpenCourseWare by a leading expert in robotics, based on established theory and research, with clear mathematical derivations and references to seminal work.

Markers derived by PSI from the transcript: the creator did not define chapters.

• 00:00Introduction to the lecture and motivation for studying walking robots.
• 02:00Discussion of passive dynamic walkers, including Tad McGeer's work and the Cornell walker.
• 05:00Introduction of the rimless wheel as the simplest model of walking.
• 10:00Explanation of limit cycle stability and the need for orbital stability.
• 15:00Introduction of the Poincaré map and its role in analyzing limit cycles.
• 20:00Derivation of the Poincaré map for the rimless wheel and computation of its Jacobian.
• 30:00Discussion of hybrid dynamics and impact events in walking.
• 40:00Extension to more complex models and the concept of zero dynamics.
• 50:00Conclusion and summary of key takeaways.

• Tad McGeer's passive dynamic walker — Historical example of a passive walker.
• Cornell passive dynamic walker — Impressive passive walker built by Andy Ruina and Steve Collins.
• Art Kuo's rendition of the McGeer walker — Simplified model of passive walking.

• Underactuated Robotics course materials — Course website with additional resources and lecture notes.