Sprawl Robots

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

• Fulls 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

• Damped, Compliant Hip Flexure
• Embedded Air Piston

• Rotary Joint
• Prismatic Joint

6
Sprawlita

• Mass - .27 kg
• Dimensions - 16x10x9 cm
• Leg length - 4.5 cm
• Max. Speed - 39cm/s 2.5 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

9
Robot Analysis for Design

• Simplified Models
• Motion Analysis
• Performance Testing

10
Simple Model
K, B, ?nom
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 Model
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

• Time-Based Mode Transitions
• Clock-driven motor pattern
• Groucho running1
• 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
13
Modeling assumptions

• Time-Based Mode Transitions
• Clock-driven motor pattern
• Groucho running1
• 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
0
Leg Set
Leg Set
Leg Set
Leg Set
2
1
2
1
Time
Stride Period
1 McMahon, et al 1987
14
Modeling assumptions

• Time-Based Mode Transitions
• Clock-driven motor pattern
• Groucho running1
• 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

• Time-Based Mode Transitions
• Clock-driven motor pattern
• Groucho running1
• 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

• Time-Based Mode Transitions
• Clock-driven motor pattern
• Groucho running1
• 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

• Time-Based Mode Transitions
• Clock-driven motor pattern
• Groucho running1
• 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

• Time-Based Mode Transitions
• Clock-driven motor pattern
• Groucho running1
• 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

• Time-Based Mode Transitions
• Clock-driven motor pattern
• Groucho running1
• 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

21
Non-linear analysis tools

• Floquet technique
• Analyze perturbation response
• Digital eigenvalues via linearization - examine
  stability
• Use selective perturbations to construct M matrix

Numerically Integrate
22
Analysis trends

• 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 towardsequilibrium point
• Parameters andmechanical propertiesdetermine 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
Damping
Damping
Damping
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!

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

30
Robot Analysis for Design

• Simplified Models
• Motion Analysis
• Performance Testing

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)
7.7 Hz
-0.088
-0.09
-0.092
-0.094
12.5 Hz
-0.096
-0.098
0
0.05
0.1
0.15
0.2
0.25
horizontal position (m)
37
Motion Analysis

• Integrate motion data with on-board
  instrumentation

(O)
38
Robot Analysis for Design

• Simplified Models
• Motion Analysis
• Performance Testing

39
Work to DateMeasurements 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
• 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

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