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Anchor synthesis via template composition

Avik De
June 30, 2015
22

Anchor synthesis via template composition

This talk was given at AMAM 2015 in Cambridge, MA.

Avik De

June 30, 2015
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  1. Anchor synthesis via template composition
    Avik De and Daniel E. Koditschek
    Electrical & Systems Engineering, University of Pennsylvania
    ARL/GDRS RCTA W911NF-1020016
    NSF 1028237
    AFOSR MURI FA9550-10-1-0567
    NSF CABiR (CDI 1028237)

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  2. Asada [5]
    >
    Kim [7]
    >
    Toward a family of direct-drive robots: genealogy
    [1] M. Raibert, “Legged Robots that Balance,” 1986.
    [2] M. Ahmadi and M. Buehler, "The ARL monopod II running robot: control and energetics," ICRA 1999.
    [3] D. Papadopoulos and M. Buehler, "Stable running in a quadruped robot with compliant legs," ICRA 2000.
    [4] U. Saranli, M Buhler and D. E. Koditschek, “RHex: A Simple and Highly Mobile Hexapod Robot,” IJRR 2001.
    [5] H. Asada and K. Youcef-Toumi, “Direct-Drive Robot: Theory and Practice.”
    [6] J. K. Salisbury, and M. A. Srinivasan, "Phantom-based haptic interaction with virtual objects," CG&A 1997.
    [7] S. Seok, A. Wang, M. Y. Michael Chuah, D. J. Hyun, J. Lee, D. M. Otten, J. H. Lang, and S. Kim, “Design Principles for
    Energy-Efficient Legged Locomotion and Implementation on the MIT Cheetah Robot,” IEEE/ASME Transactions on
    Mechatronics, 2015.
    [8] G. Kenneally and D. E. Koditschek, “Kinematic Leg Design in an Electromechanical Robot,” Submitted.
    [9] G. Kenneally, A. De and D. E. Koditschek, “Design Principles for a Family of Direct-Drive Legged Robots,” in prep.
    Buehler et. al. ’99-’01 [2-4]
    Raibert ’86 [1]
    Asada ’87 [5]
    Kim ’15 [7]
    Kenneally ’15 [8]
    Salisbury ’97 [6]
    3.5 Nm motor (250 g)
    ~0.7 KW Motor controller+encoder (~30 g)
    “Computer”+IMU (~20 g)
    [9]

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  3. >
    A family of direct-drive robots [1]
    • Motors: select by thermal specific
    torque
    • Legs: motors in parallel (add force),
    task-optimized infinitesimal
    kinematics [2], minimal passive
    compliance (tunable)
    • Construction: 40-50% motor mass
    • Control bandwidth: >1KHz
    • New measure:
    [1] G. Kenneally, A. De and D. E. Koditschek, “Design Principles for a Family of Direct-Drive Legged Robots,” in prep.
    [2] G. Kenneally and D. E. Koditschek, “Kinematic Leg Design in an Electromechanical Robot,” Submitted.
    [3] A. De and D. E. Koditschek, “The Penn Jerboa: A Platform for Exploring Parallel Composition of Templates,” arXiv:1502.05347 [cs.RO].
    [4] A. Brill, A. De, A. Johnson and D. E. Koditschek, “Tail-Assisted Rigid and Compliant Legged Leaping,” submitted.
    Legs 2
    Actuated DOFs /
    leg
    1
    Tail DOFs 2
    Mass (Kg) 2.4
    MCVA 1.2
    Legs 1
    Actuated
    DOFs / leg
    3
    Mass (Kg) 1.9
    MCVA 1.45
    Legs 4
    Actuated
    DOFs / leg
    2
    Mass (Kg) 5
    MCVA 1.47
    Delta hopper
    Jerboa [3,4] Minitaur

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  4. Anchor synthesis via template composition
    Synthetic viewpoint:
    1. reference plant; map controllers T→A
    2. anchoring multiple templates simultaneously without
    interaction (“parallel composition”) [3]
    3. sufficient conditions for correctness [4]
    [1] R. J. Full and D. E. Koditschek, “Templates and anchors: neuromechanical hypotheses of legged locomotion on land,” JEB 1999.
    [2] M. Raibert, “Legged Robots that Balance,” 1986.
    [3] A. De and D. E. Koditschek, “Parallel Composition of Templates for Tail-Energized Planar Hopping,” ICRA 2015.
    [4] A. De and D. Koditschek, “Averaged Anchoring of Decoupled Templates in a Tail-Energized Monoped,” submitted.
    [1]
    [2]
    CLASSICAL (ANALYTICAL) VIEW PROPOSED “SYNTHETIC” VIEW
    • relation between closed-loop
    systems
    • good for analyzing animals, and
    the end result on robots
    Anchors can be synthesized by composing templates
    Get a notion of modularity
    Explore a
    suite/family/palette
    (>2) of templates!

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  5. Outline
    • Same template; different bodies and anchors
    • Same body, behavior; different composition
    (alternate “solutions”)
    • The price of modularity
    • (Near) future

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  6. Same template, different bodies: vertical hopping
    [1] M. Raibert, “Legged Robots that Balance,” 1986.
    [2] G. Zeglin, “Uniroo: A One Legged Dynamic Hopping Robot,” B.S., MIT Dept. of Mechanical Engineering, 1991.
    [3] A. De and D. Koditschek, “Parallel composition of templates for tail-energized planar hopping,” ICRA 2015.
    • Restore
    vertical
    momentum
    lost to gravity
    • With or
    without a
    physical
    spring!
    [1]
    [3]
    Vertical height
    Raibert planar hopper [1]
    • Analytical result:
    stable limit cycle
    Delta hopper
    Jerboa tail-energized VH [3]
    Zeglin Uniroo [2]

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  7. Same template, different bodies: “stepping” speed control
    • “Active” rimless wheel to
    adapt to different slopes
    (forward speeds)
    • Raibert stepping controller [3]
    (servo around neutral)
    • Assume known stance time
    Forward speed
    [1] J. Bhounsule, J. Cortell, and A. Ruina, “Design and control of ranger: an energy-efficient, dynamic walking robot,” in Proc. CLAWAR, pp. 441–448, 2012.
    [2] A. De and D. Koditschek, “Averaged Anchoring of Decoupled Templates in a Tail-Energized Monoped,” submitted.
    [3] M. Raibert, “Legged Robots that Balance,” 1986.
    [1] Minitaur bound ~3.5 BL/s
    Jerboa [1]
    Minitaur pronk 1.5-2 BL/s
    [2]

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  8. Same template, different bodies: attitude control in stance
    Body attitude
    Minitaur yaw control
    Minitaur attitude control
    [1] M. Raibert, “Legged Robots that Balance,” 1986.
    [2] M. A. Sharbafi, C. Maufroy, M. N. Ahmadabadi, M. J. Yazdanpanah, and A. Seyfarth, “Robust hopping based on virtual pendulum posture control,” B&B 2013.
    [3] I. Poulakakis and J. W. Grizzle, “The Spring Loaded Inverted Pendulum as the Hybrid Zero Dynamics of an Asymmetric Hopper,” TAC 2009.
    Minitaur “crabbing”
    • Use available actuation
    to servo to to desired
    angle [1]
    • Roll, pitch controlled using
    differential vertical forces
    • Yaw controlled using
    differential tangential forces
    at the toe
    • Roll bias introduced
    VPP-based attitude control [2]
    • trials to
    come…
    ASLIP [3]

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  9. Same body; different composition: Minitaur
    Bound
    or
    Pronk
    Add vertical energy for a single stance
    Bound leap Pronk leap
    Vertical leap
    Pronk
    Bound
    decoupled
    Only coordination through physical body
    ✓ REUSE
    ✓ GENERATE
    [1] I. Poulakakis, “On the Stability of the Passive Dynamics of Quadrupedal Running with a Bounding Gait,” IJRR 2006.
    [2] K. Murphy and M. Raibert, “Trotting and bounding in a planar two-legged model,” in Theory and Practice of Robots and Manipulators, Springer, 1985, pp. 411–420.

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  10. Same body; different composition: Jerboa [2]
    [1] A. De and D. E. Koditschek, “Parallel composition of templates for tail-energized planar hopping,” in ICRA 2015.
    [2] A. De and D. E. Koditschek, “The Penn Jerboa: A Platform for Exploring Parallel Composition of Templates,” arXiv:1502.05347 [cs.RO].
    Tail-energized hopping
    ✓ Good for traction
    [2]
    Hip-energized hopping
    • 2Kg robot with 4
    motors that can
    (could) sit, stand,
    walk, hop, run,
    skip, turn,
    ✓ Good for speed
    …or
    CT-SLIP
    HipSLIP,
    TD-SLIP,
    etc.

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  11. Price of modularity
    DESIGN COMPROMISES
    (SIMPLE)
    PERFORMANCE (SUBTLE)
    [1] M. Raibert, “Legged Robots that Balance,” 1986.
    [2] H-W. Park, S. Park and S. Kim, “Variable-speed Quadrupedal Bounding Using Impulse Planning: Untethered High-speed 3D Running of MIT Cheetah 2,” ICRA 2015.
    6.4 BL/s (8 BL/s now?)
    3.5 BL/s (2 months)
    • Appears that body should
    be designed to minimize
    coupling interactions
    • Delta hopper: massless
    toe
    • heavy toe couples
    stepping to pitch
    • Jerboa: light tail
    • heavy tail causes
    Coriolis forces due to
    moving CoM
    [2]
    Raibert planar hopper [1]

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  12. Conclusions and the near future
    ❑ formalize averaging result and
    complete proofs for the current
    empirical results
    ❑ coupling through phases
    ❑ program using these symbols
    (sequential+parallel composition)
    ❑ more general classes of steady
    state compositions
    ❑ abstraction is useful
    ❑ anchors can be synthesized from templates
    ❑ not immutable “bodies”
    ❑ combinatorial choices from template “palette”
    ❑ same template; different anchors/bodies
    ❑ same body/behavior; different compositions
    ❑ different vision than optimization (synthetic but not generative)
    ❑ take a performance hit (?); gain reuse
    ❑ friendly to learning
    ❑ learning templates (in signal space)
    ❑ template-based learning (in symbol space)
    SUMMARY FUTURE WORK
    http://rosettacode.org/wiki/Sorting_algorithms/Bubble_sort
    Bubble sort in C
    Bubble sort in 360 asm
    … …

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