metastable legged- robot locomotion katie byl robot locomotion group june 21, 2007
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Metastable Legged-Robot Locomotion
Katie Byl Robot Locomotion GroupJune 21, 2007
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MIT Computer Science & Artificial Intelligence Laboratory
Overview
Background Past projects and degree work
PhD Work Stability metrics for locomotion on rough terrain:
mean first-passage time (MFPT) Metastable (long-living) dynamics Compass-gait biped simulations LittleDog Phase 1 (static) and 2 (dynamic) motions
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MIT Computer Science & Artificial Intelligence Laboratory
Background: Past MIT Projects
2.70 (now 2007) “Intro to Design” / 6.270 Lego/LOGO instructor at Museum of Science MIT Blackjack Team 6.302 lost-cost maglev lab kit various UROPS and MATLAB-coding jobs
2.706.270
MIT BJ 6.302
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MIT Computer Science & Artificial Intelligence Laboratory
Background: Past MIT Projects
2.70 (now 2007) “Intro to Design” / 6.270 Lego/LOGO instructor at Museum of Science MIT Blackjack Team 6.302 lost-cost maglev lab kit various UROPS and MATLAB-coding jobs
2.706.270
MIT BJ 6.302
![Page 5: Metastable Legged- Robot Locomotion Katie Byl Robot Locomotion Group June 21, 2007](https://reader035.vdocuments.us/reader035/viewer/2022062321/56649f115503460f94c24360/html5/thumbnails/5.jpg)
MIT Computer Science & Artificial Intelligence Laboratory
Background
Bachelor’s thesis * Dynamic Signal Analyzer (DSA)
• to obtain empirical transfer function for a system
• Simulink/MATLAB block for dSPACE controller
Master’s thesis * 2.003 lab creation Inverted pendulum (segway-type)
TA appointments 2.14 (Controls); 2.670 and 2.29 (MATLAB);
2.003 (Modeling Dynamics and Control)
*Precision Motion Control Lab, Prof. Dave Trumper
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MIT Computer Science & Artificial Intelligence Laboratory
Bachelor’s Thesis
Dynamic Signal Analyzer (DSA) Goal: integrated system ID for real-time controllers Simulink/MATLAB block for dSPACE boards MATLAB code to get empirical transfer function
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MIT Computer Science & Artificial Intelligence Laboratory
Master’s Thesis ActivLab labware for 2.003:
Modeling Dynamics and Control 1 1st-order dynamics
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MIT Computer Science & Artificial Intelligence Laboratory
Master’s Thesis 2nd- and 4th-order dynamics
Timeresponse
Freq.response
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MIT Computer Science & Artificial Intelligence Laboratory
Master’s Thesis Segway-style inverted pendulum
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MIT Computer Science & Artificial Intelligence Laboratory
PhD: Legged Locomotion
Mean first-passage time (MFPT) Goal: Exceptional performance most of the time,
with rare failures (falling) Metric: maximize distance (or time) between failures
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MIT Computer Science & Artificial Intelligence Laboratory
PhD: Legged Locomotion
Metastability Fast mixing-time dynamics Rapid convergence to long-living (metastable) limit-
cycle behavior
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MIT Computer Science & Artificial Intelligence Laboratory
PhD: Legged Locomotion
Compass gait: optimal vs one-step control
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MIT Computer Science & Artificial Intelligence Laboratory
PhD: Legged Locomotion
LittleDog: Phase 1 (static crawl) results
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MIT Computer Science & Artificial Intelligence Laboratory
PhD: Legged Locomotion
LittleDog Phase 2: dynamic, ZMP-based gaits
All 6 teams passed Phase 1 metrics (below) 3 teams (at most) can pass Phase 2
Phase 1: 1.2 cm/sec, 4.8 cm [step ht] Phase 2: 4.2 cm/sec, 7.8 cm
Fastest recorded run, with NO COMPUTATION:
- about 3.4 cm/sec
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MIT Computer Science & Artificial Intelligence Laboratory
PhD: Legged Locomotion
LittleDog Phase 2: dynamic, ZMP-based gaits
All 6 teams passed Phase 1 metrics (below) 3 teams (at most) can pass Phase 2
Phase 1: 1.2 cm/sec, 4.8 cm [step ht] Phase 2: 4.2 cm/sec, 7.8 cm
Fastest recorded run, with NO COMPUTATION:
- about 3.4 cm/sec
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MIT Computer Science & Artificial Intelligence Laboratory
Sequencing motions: Funnels
R. R. Burridge, A. A. Rizzi, and D. E. Koditschek. Sequential composition of dynamically dexterous robot behaviors. International Journal of Robotics Research, 18(6):534-555, June 1999.
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MIT Computer Science & Artificial Intelligence Laboratory
Double-support gait creation
3 possible leg-pairing types Pacing left vs right Bounding fore vs rear Trot diagonal pairings
ZMP method: Aim for COP near “knife-edge” Not simply planning leg-contacts… Plan [model] COB accelerations and ground forces directly
Pacing
Trotting
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MIT Computer Science & Artificial Intelligence Laboratory
Double-support gait creation
Pacing
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MIT Computer Science & Artificial Intelligence Laboratory
Double-support gait creation
Trotting
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MIT Computer Science & Artificial Intelligence Laboratory
Questions?
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MIT Computer Science & Artificial Intelligence Laboratory
ZMP pacing – with smoothing
Smoothing requested ZMP reduces overshoot
square wave smoothed input
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MIT Computer Science & Artificial Intelligence Laboratory
Phase 2: dynamic gaits
Control of ZMP using method in Kajita03 S. Kajita, F. Kanehiro, K. Kaneko, K. Fujiware, K. Harada, K. Yokoi, and H. Hirukawa.
Biped walking pattern generation by using preview control of zero-moment point. In ICRA IEEE International Conference on Robotics and Automation, pages 1620-1626. IEEE, Sep 2003.
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MIT Computer Science & Artificial Intelligence Laboratory
Markov Process The transition matrix for a stochastic system prescribes state-to-state
transition probabilities
For metastable systems, the first (largest) eigenvalue of its transpose is 1, corresponding to the absorbing FAILURE state
The second largest eigenvalue is the inverse MFPT, and the corresponding vector gives the metastable distribution
F
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MIT Computer Science & Artificial Intelligence Laboratory
MFPT and Metastability Fast mixing-time dynamics Rapidly either fails (falls) or converges to long-living (metastable)
limit-cycle behavior
add Gaussian noise; sigma=.2
Deterministic return map Stochastic return map
MFPT as fn of init. cond.
Metastable basin of attraction
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MIT Computer Science & Artificial Intelligence Laboratory
MFPT and Metastability Example for a DETERMINISTIC system with high sensitivity to initial
conditions (as shown by steep slope of the return map)
Green shows where the “metastable basin” is developing
MFPT and density of metastable basin give us better intuition for the system dynamics (where the exact initial state is not known)
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MIT Computer Science & Artificial Intelligence Laboratory
Compass Gait
Limit cycle analysis
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MIT Computer Science & Artificial Intelligence Laboratory
Motivation – Phase 2
Opportunity for science in legged robots Dynamic gaits [Phase 2]
• Speed
• Agility
Precision motion planning (vs CPG)• Optimal to respond to variations in terrain
Wheeled locomotion analogy: Tricycle = static stability [Phase 1] Bicycle = dynamic and fast Unicycle = dynamic and agile
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MIT Computer Science & Artificial Intelligence Laboratory
Double-support results to date
Bounding – currently quite heuristic… Plan a “step” in COP, to REAR legs for Δt At start of Δt, tilt body up Push down-and-back with rear legs Simultaneously extend fore legs Recover a zero-pitch 4-legged stance Plan a “step” in COP, to FORE legs
Intended “lift” of rear legs - actually dragged
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MIT Computer Science & Artificial Intelligence Laboratory
Where to go next…
Optimization of double-support Gradient methods, in general Actor-critic, in particular
Attempt “unipedal” support? Is there a practical use in Phase 2? Is this interesting science?
Potential for significant airborne phase Plan now for 5x more compliant BDI legs
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MIT Computer Science & Artificial Intelligence Laboratory
Master’s Thesis Inverted pendulum dynamics
Bandwidth = 0.5 Hz
ζ= 0.25(damping ratio)
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MIT Computer Science & Artificial Intelligence Laboratory
Murphy Video
Goals: Identify gait characteristics Speculate on forces and timing
Questions relevant to LittleDog gaits What is being optimized? (If anything?) How important is ankle torque? How/why do different motions segue well
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MIT Computer Science & Artificial Intelligence Laboratory
Dog gaits
Trotting - Efficient; most-common; rear feet follow fore feet
Gallop - Fast; 1-2-1 support; pole-vault with front
Pacing - Asymmetric; low lateral accelerations; push-pull
Crawl - Not common; used to amble or to step carefully
Leap - used to clear obstacles; practiced often (in play)
Bound - uncommon; gallop-like except pairwise rear and front
Weave - example of learning to do a motion efficiently
video to follow…
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MIT Computer Science & Artificial Intelligence Laboratory
Video list
trot_waterprints_withpan gallop_tri_1 pacing_3 crawl_waterprints leap_from_trot bound_uphill_snow dbbound_slide_snow weave_hops agility_frontcross