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title: Gaits and Functions

Minutae

Agenda

  • HW2P1 Released
    • around 75% average
    • almost everyone got Problem 1.3 wrong
    • People who came to office hours performed better.
  • HW2P2 grading in progress - will be released before midterm
  • HW3 will probably not be released in time
  • Attendance will be updated soon
  • Remember to join groups
  • Final part of Pendulum extensions
    • controller
    • get force
    • sensors and sites
  • Today's lecture
  • Practical exercise: code up a simple robot in Mujoco

Attendance

Biomechanics II

What is a "Gait"

Different Animals

Elephant walking Muybridge buffalo galloping Gait of healthy hamster

Gaits

Two-legged

  • Walk
  • Run

Four-legged (horse)

  • walk
  • trot
  • canter
  • gallop
  • pronk

Six-legged

  • Alternating Tripod
  • ...many others

Pronking

https://www.youtube.com/watch?v=jMIiB9DnRXg

Alternating Tripod

https://upload.wikimedia.org/wikipedia/commons/transcoded/6/61/Alternating_Tripod_Gait.webm/Alternating_Tripod_Gait.webm.720p.vp9.webm

Representations

Footprints

Footfall Patterns

Stills

Biomechanics Studies

Biomechanics Studies

Biewener, a a. “Biomechanics of Mammalian Terrestrial Locomotion.” Science (New York, N.Y.) 250, no. 4984 (1990): 1097–1103. https://doi.org/10.1126/science.2251499.

Biomechanics Studies

Fujita, M., K. Kawakami, and H. Higuchi. “Hopping and Climbing Gait of Japanese Pygmy Woodpeckers (Picoides Kizuki).” Comparative Biochemistry and Physiology. Part A, Molecular & Integrative Physiology 148, no. 4 (2007): 802–10. https://doi.org/10.1016/j.cbpa.2006.06.048.

Muscle Activation Patterns

Reproduction

CPGs

Ijspeert, Auke Jan. “Central Pattern Generators for Locomotion Control in Animals and Robots: A Review.” Neural Networks 21, no. 4 (May 2008): 642–53. https://doi.org/10.1016/j.neunet.2008.03.014.

Periodic Functions

\[y = A\sin(t)\]

Additional parameters

\[y = A\sin(2\pi(ft-l)) + b\]
  • \(f\): frequency (Hz)
  • \(b\): vertical offset
  • \(t\): time
  • \(l\): percentage of cycle

Amplitude

Frequency

Offset

Time Offset

inverse dynamics

Time Offset

Superposition

Practical Examples

  • beetle
  • spherical four-bar -- chapter 35 in textbook -- simulation section
  • contact
  • inverse dynamics