1. Can We Figure Out What Algorithms Are Used For Balance and Gait in Biological Systems?
Chris Atkeson
CMU

2. Goals What features can be used for standing balance and control?
What experiments would distinguish between these approaches in humans, animals, and robots?
Collaborative Research in Computational Neuroscience (CRCNS) program. Nov. 2.
Humans and cats.
Are there perturbations we can apply that can distinguish these approaches?
Are there relevant motor illusions?
How are quantities like COM position and velocity computed or perceived, if COM is used in control?
Are there different learning effects?
DARPA wants to know: how evaluate robot balance and walking?

3. Alternatives at CMU
Map from muscle variables (length, velocity, force) to muscle activation, with minimal cross muscle activity (Geyer).
Map from body parts (primarily torso position, orientation, angle, and angular velocity) to joint torque (Hodgins).
Map from center of mass (COM) position and velocity to foot (and other contact) forces. Maybe regulate body angular momentum (Stephens).
Map full state (all joint positions and velocities and root position, orientation, and corresponding velocities) to joint torques (Atkeson).

4. Neuromuscular Models (Geyer)

6. Local Feedback Am = g*Lm (g<0: springlike)
Am = g*Fm (g>0: positive force feedback)
Some coupling
ATA = g*LTA – gFSOL
AHFL = g*LHFL – g*LHAM

8. Issues Sparse interactions: Mostly homonymous feedback.
Some antagonistic feedback.
No synergistic feedback?
Contralateral force feedback to initiate swing.
Adapts to unknown slopes and steps.
How launch, stop, turn (3D)?
Relationship to CPG? What happens when feedback distorted or removed?
Vestibular input: trunk uses vertical reference.
Vision input? Foot placement?
Anticipation? Planning?

9. A Possible Signature: Positive Force Feedback
Can we test for sign of force feedback (GTO to extensor reflexes)?
Need to disassociate from length or velocity feedback, joint feedback.
What stabilizes positive force feedback?

10. Control at the level of body parts
Raibert 3 part running control:
Actual or virtual telescoping leg.
Hopping height: more push off if low, …
Attitude: Hip pitch torque on stance leg to level body (based on vestibular input)
Τ = -g1*(θ – θd) – g2*θvel
Foot placement: Cartesian step size based on desired velocity and velocity error:
s = g3*Vd – g4*(V – Vd)

11. Hodgins Hodgins, Biped Gait Transitions ICRA 91

12. Wisse

13. Wisse

14. Modern Versions: Big Dog, Petman, Simbicon
Pointer to Big Dog goes here
Pointer to Petman, Atlas goes here
Pointer to Simbicon goes here

15. Issues
Global inputs: measuring height/energy, forward velocity, body angle with respect to vertical.
Virtual model: telescoping leg, Cartesian foot placement.
Adapts to unknown slopes and steps.
How launch, stop, turn (3D)?
Foot placement? Vision input?
Relationship to CPG? What happens when feedback distorted or removed?
Joint torques to muscle activations?

16. COM-based control
Stephens, 19

17. Balance Recovery Strategies
Ankle Strategy – single link inverted pendulum
Hip Strategy – torso as flywheel
Squat Strategy – change height of COM
Step Strategy – change polygon of support
Righting Reflex – arm as flywheel
Grasp Strategy – change polygon of support ….

18. Approach
Plan each strategy at COM level for N seconds ahead using trajectory optimization.
Each different number of steps a distinct plan
Multiple internal simulations.
Pick best option.
Do it for a fraction of a second.
Repeat.
Input is COM position and velocity.
Outputs are contact forces and torques (COP)

19. COM-Level Stepping Optimization
Choose step locations for particular feet.
Timing, number of steps, initial stance foot fixed.
Optimize closeness of COM and foot step locations to goals for these.
Minimize COM velocity, COP velocity.

20. An Example Plan Double support Take step Stop Take step Push left
Start falling forward

21. Full Body Control: Weighted Objective Optimization
Objectives:
Dynamics
Task Objectives
COM Acceleration
Torque About COM
Reference Pose Tracking
Minimize Controls
Constraints:
Center of Pressure
Friction Cone
Joint Torque Limits
Stephens
M. de Lasa, I. Mordatch, and A. Hertzmann, “Feature-Based Locomotion Controllers,” ACM Transactions on Graphics, vol. 29, 2010.

22. Pushing: Ankle, Hip, and Stepping Strategies
No Stepping
Stepping
Stephens

23. Pushing While Stepping In Place
Stephens

24. Pushing: Moving Floor
Stephens

25. Pushing While Doing A Task
Stephens

26. Stephens

27. Human-like walking: Planning
Plan for heel strike, push off on toe only.
Plan for fully coupled swing leg and whole body dynamics. Only approach that does this now is trajectory optimization (trajectory library: Liu).
Use torso and arms more effectively: pitch, roll, and yaw motions.

28. Human-like walking: Impacts
Optimize contact initiation (impact).
Very small Fx, Fy, Mx, My, Mz initially, low impedance in these directions.
Avoid bounce, gradual increase in Fz, right vertical impedance.
Stiffen after contact when know terrain height and slope.

29. Human-like walking: Foot forces and torques
Optimize swing leg and whole body trajectories to:
Min Fx/Fz, Fy/Fz for each foot to avoid slip
Min Mx/Fz, My/Fz for each foot to avoid tipping
Min Mz for each foot to avoid twist, and keep COP near center of foot (small Mx, My)
Compliant ankles (small Mx, My, and Mz)

30. Human-like walking: Reflexes
Limit Fx, Fy, Mx, My, and Mz based on Fz, COP on each foot in real time.
Use grip like reflexes to detect and stop slipping, tripping, and twist on each foot.

31. Issues
Body level inputs: COM XYZ location and velocity, body angle with respect to vertical.
Body level outputs: Foot forces/COP
COM is gateway/bottleneck. Expect synergies.
Optimization allocates activation to muscles.
Adapts to unknown slopes and steps.
How launch, stop, turn (3D)?
Foot placement easy.
Relationship to CPG? What happens when feedback distorted or removed?
Joint torques to muscle activations? More optimization.

32. Body-Level Control: Dynamic Programming
Whitman

33. Full State Control: Trajectory Library
Biped Walking Control Using a Trajectory Library
Liu, Atkeson, Su; Robotica in press.
Library for 10 dimensional walking
Test set

34. Standing Balance Implementation

35. Pushing The Robot Push Size (N) Ankle Pos Hip Pos Ankle Torque
Hip Torque

36. Push Estimation On Robot

37. Planar Walking Library (left) and Simulated Push Perturbations (right)

38. Simulated 16 Ns Impulse

39. Planar Walking Simulation
“Instantaneous” and continuous pushes
Pushes of different sizes, time varying pushes.
Inclines
Model perturbations (wrong mass)
Ground model variations (ground stiffness)

40. Issues Memory intensive.
Not clear how much memory load can be reduced by online optimization or learning.
Can generate any behavior, so hard to explore experimentally.
COM is NOT gateway/bottleneck. Synergies?
DBFC allocates activation to muscles.
Adapts to unknown slopes and steps.
How launch, stop, turn (3D): Separate learned behaviors
Foot placement easy.
Relationship to CPG? What happens when feedback distorted or removed?
Joint torques to muscle activations? More optimization.

41. Overall Issues Do these approaches have a “signature”?
No perturbation – probably not.
Perturbation?
Need for feedback (CPG debate)
Locality of feedback (Vibrate a tendon?)
Synergies? (factor analysis)
How does vision impact walking? (synergies again)
How does vestibular system impact walking? (synergies again)

42. Detailed Numerical Modeling
Match kinematics
Match contact forces (GRF)
Match inverse dynamics.This is really matching kinematics in a different coordinate system.
Match EMG
Match perturbation kinematics
Match perturbation GRF
Match perturbation EMG
Match decision boundaries where strategies change

43. Perturbation Tests
Moving terrain (“bus”) (Equitest platform, Stewart platform)
Pushes (instantaneous and continuous)
Slips (change terrain material properties)
Trips (unexpected terrain obstacles)
Unknown terrain shape (slopes, ripples, stairs, holes and poles).
Varying terrain material properties (loose soil, sand, gravel, hard dirt, fixed and loose rocks, mud)

44. Control tests Foot placement targets
Avoid no-go ground regions (at footstep scale and at vehicle scale)
Follow velocity trajectories
Follow desired paths (turning)
Traverse known rough terrain

45. State Estimation Need to focus on sensor fusion
Which way is up, angular velocity with respect to vertical (vestibular, optical, proprioception)
Where is COM relative to COP and vertical?
Body angular velocity
Contact and ground conditions.

46. Other Approaches: ZMP