Anchor synthesis via template composition

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

Transcript

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)
   

   View Slide

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]
   

   View Slide

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
   

   View Slide

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!
   

   View Slide

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

   View Slide

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]
   

   View Slide

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]
   

   View Slide

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]
   

   View Slide

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.
   

   View Slide

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.
    

    View Slide

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]
    

    View Slide

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
    … …
    

    View Slide