1. Sprawl Robots Biomimetic Design Analysis: Simplified Models
Motion Analysis
Performance Testing

2. Design Inspiration Control heirarchy Passive component
Active component

3. Is Passive Enough? Passive Dynamic Stabilization
No active stabilization
Geometry
Mechanical system properties

4. Sprawl 1.0: Biomimetic, not just a copy
Low-Level
Control
MURI
Sprawl 1.0: Biomimetic, not just a copy
- cockroaches don’t attempt to use complicated, high-level control but still outperform robots that do (Dante - very impressive, but took a very long time to cross rough terrain because of footholds), not searching for footholds, no real-time solutions to optimal force vectors, what else?
- sprawled posture and decoupled leg mechanism biologically selected for locomotion - sprawled posture has a lower center of mass which is harder to tip - decoupled mechanism allows for a simplified control - thrust force is the direct result of one actuator instead of a combination of actuators (main power producing muscles have been identified)
- mechanical system rather than high-level control rejects disturbances
Full’s research highlights certain important locomoting components
Power-producing thrust muscles
Supporting/repositioning hip joints

5. Implementation Cockroach Geometry Functional Biomimesis
Shape Deposition
Manufactured Robot
Passive Compliant Hip Joint
Effective Thrusting Force
Rotary Joint
Prismatic Joint
Damped, Compliant Hip Flexure
Embedded Air Piston

6. Sprawlita Mass - .27 kg Dimensions - 16x10x9 cm Leg length - 4.5 cm
Max. Speed - 39cm/s body/sec
Hip height obstacle traversal

7. Mechanical System Properties
Prototype: Empirically tuned properties
Design for behavior
Understanding ?
Mechanical
System
Properties

8. Robot Analysis for Design
Simplified Models
Motion Analysis
Performance Testing
24 deg.
k, b, nom

9. Robot Analysis for Design
Simplified Models
Motion Analysis
Performance Testing
24 deg.
k, b, nom

10. “Simple” Model 18 parameters to tune - TOO MANY! K, B, nom k, b, nom
Full 3D model
Planar model
Symmetry assumption
k, b, nom
Body has 3 planar degrees of freedom
x, z, theta
mass, inertia
3 massless legs (per tripod)
rotating hip joint - damped torsional spring
prismatic leg joint - damped linear spring
6 parameters per leg
18 parameters to tune - TOO MANY!

11. Simplest Locomotion Modelg g
k, b, nom
Biped
Biped
Quadruped
Body has 2 planar degrees of freedom
x, z
mass
4 massless legs
freely rotating hip joint
prismatic leg joint - damped linear spring
3 parameters per leg
6 parameters to tune, assuming symmetry

12. Modeling assumptions g Time-Based Mode Transitions One “reset” mode
Clock-driven motor pattern
“Groucho running”1
One “reset” mode
Two sets of legs - Two modes
Symmetric - treat as one mode
Mode initial conditions
Nominal leg angles
Instant passive component compression
Leg Set 2 1
State
Time x
= state trajectory
Stride Period T
1 McMahon, et al 1987

13. Modeling assumptions t = 2T- g Time-Based Mode Transitions
Clock-driven motor pattern
“Groucho running”1
One “reset” mode
Two sets of legs - Two modes
Symmetric - treat as one mode
Mode initial conditions
Nominal leg angles
Instant passive component compression
t = 2T-
State x
Leg Set
Leg Set
Leg Set
Leg Set 1 2 1 2 T
Time
= state trajectory
Stride Period
1 McMahon, et al 1987

14. Modeling assumptions t = 2T+ g Time-Based Mode Transitions
Leg Set 2 1
State
Time x
= state trajectory
Stride Period
t = 2T+ T g
Time-Based Mode Transitions
Clock-driven motor pattern
“Groucho running”1
One “reset” mode
Two sets of legs - Two modes
Symmetric - treat as one mode
Mode initial conditions
Nominal leg angles
Instant passive component compression
1 McMahon, et al 1987

15. Modeling assumptions t = 2T + 1/3T g Time-Based Mode Transitions
Leg Set 2 1
State
Time x
= state trajectory
Stride Period
t = 2T + 1/3T T g
Time-Based Mode Transitions
Clock-driven motor pattern
“Groucho running”1
One “reset” mode
Two sets of legs - Two modes
Symmetric - treat as one mode
Mode initial conditions
Nominal leg angles
Instant passive component compression
1 McMahon, et al 1987

16. Modeling assumptions t = 2T + 2/3T g Time-Based Mode Transitions
Leg Set 2 1
State
Time x
= state trajectory
Stride Period
t = 2T + 2/3T T g
Time-Based Mode Transitions
Clock-driven motor pattern
“Groucho running”1
One “reset” mode
Two sets of legs - Two modes
Symmetric - treat as one mode
Mode initial conditions
Nominal leg angles
Instant passive component compression
1 McMahon, et al 1987

17. Modeling assumptions t = 3T- g Time-Based Mode Transitions
Leg Set 2 1
State
Time x
= state trajectory
Stride Period
t = 3T- T g
Time-Based Mode Transitions
Clock-driven motor pattern
“Groucho running”1
One “reset” mode
Two sets of legs - Two modes
Symmetric - treat as one mode
Mode initial conditions
Nominal leg angles
Instant passive component compression
1 McMahon, et al 1987

18. Modeling assumptions t = 3T+ g Time-Based Mode Transitions
Leg Set 2 1
State
Time x
= state trajectory
Stride Period
t = 3T+ T g
Time-Based Mode Transitions
Clock-driven motor pattern
“Groucho running”1
One “reset” mode
Two sets of legs - Two modes
Symmetric - treat as one mode
Mode initial conditions
Nominal leg angles
Instant passive component compression
1 McMahon, et al 1987

19. Modeling assumptions t = 3T + 1/3T g Time-Based Mode Transitions
Leg Set 2 1
State
Time x
= state trajectory
Stride Period
t = 3T + 1/3T T g
Time-Based Mode Transitions
Clock-driven motor pattern
“Groucho running”1
One “reset” mode
Two sets of legs - Two modes
Symmetric - treat as one mode
Mode initial conditions
Nominal leg angles
Instant passive component compression
1 McMahon, et al 1987

20. Non-linear analysis tools
Discrete non-linear system
Fixed points
numerically integrate to find
exclude horizontal position information
= state trajectory
= fixed points
xk+1 = xk = x*
Leg Set 2 1
State
Time x
= state trajectory
Stride Period T

21. Non-linear analysis tools
Floquet technique
Analyze perturbation response
Digital eigenvalues via linearization - examine stability
Use selective perturbations to construct M matrix
= nominal trajectory
Numerically
Integrate

22. Analysis trends Relationships Use for design
6.5 7
7.5 8
8.5 9
9.5 10
1.2
1.4
1.6
1.8 2
2.2
2.4
2.6
2.8
0.04
0.045
0.05
0.055
0.06
0.065
0.07
0.075
Damping (N-s/m)
Recovery Rate
Horizontal
Velocity
X_dot (m/s)
1/max[eig(M)]
Relationships
damping vs. speed and “robustness”
stiffness, leg angles, leg lengths, stride period, etc
Use for design
select mechanical properties
select other parameters
Insight into the mechanism of locomotion

23. Locomotion Insight Body tends towards equilibrium point
Parameters and mechanical properties determine how

24. Design Procedure Find parameter set that will yield fixed points
Establish trends by varying one parameter
Perturb and integrate
Build the M matrix
Find eigenvalues and performance index
Select new parameter value
Iterate

25. Design Example Robustness Speed Damping Damping Damping Stiffness
Notice that with the damper there is a tradeoff btw speed and robustness, but hat tradeoff does not exist by changing the springs
In other words, you sacrifice speed for robustness and vice versa in the trends with the dampers, while this is not true when changing the spring rates.
Stiffness
Stiffness
Stiffness
Speed = 0
Speed = 13 cm/s
Speed = 23.5 cm/s

26. Results and Future Work
“Biomimetic” locomotion
Feedforward motor program
Preflexes
Geometry
Good biomimetic locomotion is more subtle
Speed without sacrificing robustness
Robustness without sacrificing efficiency
Adaptation useful
Changes in “global” conditions
Fast and Robust

27. Good biomimetic locomotion
Comparing detailed results to cockroach locomotion data
Ground reaction forces
Leg workloops
Efficiency
3 legged model
Different than 2 legs – more freedom!
Faster &
More
Efficient

28. Good biomimetic locomotion
Comparing detailed results to cockroach locomotion data
Ground reaction forces
Leg workloops
Efficiency
3 legged model
Different than 2 legs – more freedom!
Time (seconds)
Vertical Displacement
Vertical Displacement
Time (seconds)
Middle leg = 72.5 degrees
Middle leg = 70 degrees

29. Need for Adaptation Robustness, speed, and efficiency are sensitive
Model parameters
Geometry (leg angles, lengths)
Relative stiffnesses
Number of legs
Environment
Slope
Slope
Leg angle
Velocity

30. Robot Analysis for Design
Simplified Models
Motion Analysis
Performance Testing
24 deg.
k, b, nom

31. Motion Analysis Compare simple models to cockroach kinematic data
Horizontal plane
model
(O)

32. Motion Analysis
Experiments in finding model parameters to match kinematic data
(O)

33. Motion Analysis Extract passive stabilizing properties
Horizontal plane
model

34. Motion Analysis
Different set of model parameters will result in different performance
(O)
(O)

35. Motion Analysis
Hi-speed motion capture of robot to qualify performance
(O)

36. Motion Analysis
Results show effect of system parameters in resulting motion
Center of Mass Sagittal Trajectories
-0.08
4.35 Hz
-0.082
-0.084
-0.086
vertical (m)
-0.088
7.7 Hz
-0.09
-0.092
-0.094
12.5 Hz
-0.096
-0.098
0.05
0.1
0.15
0.2
0.25
horizontal position (m)

37. Motion Analysis Integrate motion data with on-board instrumentation

38. Robot Analysis for Design
Simplified Models
Motion Analysis
Performance Testing
24 deg.
k, b, nom

39. Work to Date Measurements of:
Maximum Velocity
Maximum Obstacle Clearance

40. Reasons for Testing Measure performance of system while varying:
System parameters
Terrain properties
Understand locomotion
Adapt to environment
Long-term durability

41. Testing Conditions Vary Terrain Properties Slope Roughness Properties
Smooth
Fractal
Properties
Packed Dirt
Gravel
Sand

42. Velocity vs. Slope

43. Multivariable Testing
Many Parameters affect Performance
Duty Cycle
Gait Period
Front Leg Angles
Middle Leg Angles
Back Leg Angles
Center of Mass
Pressure
Mass
Compliance
Leg Length
Body Length
Etc.

44. Velocity vs. Slope and Gait Period

45. Velocity vs. Slope and Gait Period

46. Velocity vs. Slope and Gait Period

47. Velocity vs. Slope and Duty Cycle

48. Velocity vs. Slope and Duty Cycle

49. Leg Testing
Performance is heavily dependent on the combination of leg angles
Therefore, the leg angles cannot be independently examined.
Begun Factorial Testing
Test relationships between various parameters
Leg Angles, Duty Cycle, Gait Period
Compliance
Define Factorial Testing while talking
Mention that FT is not yet complete. It “will allow us to” …

50. Future Work Test other parameters for maximum velocities
Analyze data for effect
Incorporate findings
Table of best conditions
Adaptive code
Progress to other terrains

51. Lessons Thus Far Ideal parameters change with slope
Performance is dependent on the parameters and their interactions
Adaptation increases capability