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)

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]

> 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

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!

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

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]

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]

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]

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.

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.

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]

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 … …