Live Modular Robots. Dfki Bremen 2009
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Live modular Robots!
Dr. Houxiang Zhang Faculty of Mathematics, Informatics and Natural Sciences University of Hamburg
Dr. Juan González-Gómez School of Engineering Universidad Autonoma de Madrid
DFKI Bremen – Robotics Innovation Center. Jun, 16th, 2009
Outline
Outline 1.
Introduction
2. Locomotion in 1D 3. Locomotion in 2D 4. Minimal configurations 5. Cube-M modules 6. Conclusions and current work
Live modular Robots!
DFKI Bremen – Robotics Innovation Center. Jun, 16th, 2009
2
The Locomotion Problem Classic approach
Bio-inspired approach
CMU Ambler
Aramies
Dante II
Big Dog
Modular approach
Polybot 3
Modular Robotics
●
Two important aspects: ●
Robot morphology
●
Controller 4
Morphology Modular Robot classification 1D Topology
2D Topology
3D Topology
1D topology sub-classification Pitch-Pitch
Yaw-yaw
Pitch-yaw
5
Controller ●
Coordination problem: Calculation of the joint's angles to realize a gait: i t
●
Classic approach: Mathematical modeling ● Calculation by inverse kinematics ● Disadvantages: The equations are only valid for an specific morphology
CPG ●
CPG
CPG
Bio-inspired controllers: CPGs ● Central Pattern Generators ● CPGs control the rhythmic activities ● Ej. The locomotion of the lamprey
6
Hypothesis: Sinusoidal oscillators
●
CPGs are replaced by a Simplified model CPG
●
CPG
CPG
Sinusoidal oscillators:
2 i t=A i sin i O i T
●
Advantages: ● Few resources required
7
Outline
Outline 1.
Introduction
2. Locomotion in 1D 3. Locomotion in 2D 4. Minimal configurations 5. Cube-M modules 6. Conclusions and current work
Live modular Robots!
DFKI Bremen – Robotics Innovation Center. Jun, 16th, 2009
8
Y1 Modules
●
One degree of freedom
●
Easy to build
●
Cheap
●
Open and “Free”
9
Electronics & control
10
Cube Revolutions (I)
●
Videos
Morphology: 8 modules with pitch-pitch connection
●
Controller: ● ●
8 equal oscillators Parameters:
A , ,T
11
Locomotion mechanism
Locomotion performed by the body wave propagation ●
●
Step: x
V=
●
Mean Speed:
●
Serpenoid curve
●
Step calculation:
x T
l
l 2 k x= −∫0k cos cos sds k l
12
Outline
Outline 1.
Introduction
2. Locomotion in 1D 3. Locomotion in 2D 4. Minimal configurations 5. Cube-M modules 6. Conclusions and current work
Live modular Robots!
DFKI Bremen – Robotics Innovation Center. Jun, 16th, 2009
13
Hypercube (I)
●
Demo
Morphology 8 modules with pitch-yaw connection
●
Controller: ● ● ●
4 vertical oscillators 4 horizontal oscillators Parameters:
A h , A v , h , v , vh ,T 14
Locomotion gaits
●
Searching: Genetic algorithms
●
5 categories of gaits
●
Characterized by the 3D body wave
15
Locomotion mechanism ●
3D Body wave propagation
●
Linear Step: r
●
Angular Step:
●
Dimensions: width (w) x length (lx) x heigth (h)
16
Outline
Outline 1.
Introduction
2. Locomotion in 1D 3. Locomotion in 2D 4. Minimal configurations 5. Cube-M modules 6. Conclusions and future work
Live modular Robots!
DFKI Bremen – Robotics Innovation Center. Jun, 16th, 2009
17
Minimal configurations ●
Configurations with the minimal number of modules that are able to move
●
Searching the control space using genetic algorithms
●
Straight line
●
5 gaits
18
Minicube-I
●
Demo
Morphology 2 modules with a Pitchpitch connection
●
Controller: ●
Two generators
●
Parameters:
A , , T
19
Minicube-II
Demo
Morphology:
●
3 modules with Pitch-yawpitch connection
●
Controller: ●
3 oscillators
●
Parameters:
A v ,A h , v , vh , T 20
Locomotion gaits Forward
Av =40, Ah=0 v =120
Lateral shifting
Av = Ah40 vh =90, v=0 Av = Ah60
Turning Rotating
Av =40, Ah=0 Oh =30, v =120
Rolling
Av =10, Ah=40 vh =90, v=180
vh =90, v=0
21
Outline
Outline 1.
Introduction
2. Locomotion in 1D 3. Locomotion in 2D 4. Minimal configurations 5. Cube-M modules 6. Conclusions and current work
Live modular Robots!
DFKI Bremen – Robotics Innovation Center. Jun, 16th, 2009
22
Cube-M module(I) ●
●
●
Low cost mechanical design Simple robust modules assembling manually and int a quick-to-build, easy-tohandle design Onboard electronics and sensors
23
Cube-M module (II)
Demo
24
Software ● ● ●
Demo
1D topology simulator (Based on Open Dynamics Engine [ODE]) Generics algorithms: PGAPack Mathematical models in Octave/Matlab
25
Outline
Outline 1.
Introduction
2. Locomotion in 1D 3. Locomotion in 2D 4. Minimal configurations 5. Cube-M modules 6. Conclusions and current work
Live modular Robots!
DFKI Bremen – Robotics Innovation Center. Jun, 16th, 2009
26
Conclusions
The controller based on sinusoidal oscillators is valid for the locomotion of the 1D-topology modular robots
● ● ●
Very few resources are required for its implementation The locomotion gaits are very smooth and natural At least 5 different gaits can be achieved
i t =Ai sin
2 i Oi T 27
Current work Locomotion of 2D Topology modular robots
Modular grasping
Climbing caterpillar
New module design
28
Live modular Robots!
Dr. Houxiang Zhang Faculty of Mathematics, Informatics and Natural Sciences University of Hamburg
Dr. Juan González-Gómez School of Engineering Universidad Autonoma de Madrid
DFKI Bremen – Robotics Innovation Center. Jun, 16th, 2009
29
Dr. Houxiang Zhang Faculty of Mathematics, Informatics and Natural Sciences University of Hamburg
Dr. Juan González-Gómez School of Engineering Universidad Autonoma de Madrid
DFKI Bremen – Robotics Innovation Center. Jun, 16th, 2009
Outline
Outline 1.
Introduction
2. Locomotion in 1D 3. Locomotion in 2D 4. Minimal configurations 5. Cube-M modules 6. Conclusions and current work
Live modular Robots!
DFKI Bremen – Robotics Innovation Center. Jun, 16th, 2009
2
The Locomotion Problem Classic approach
Bio-inspired approach
CMU Ambler
Aramies
Dante II
Big Dog
Modular approach
Polybot 3
Modular Robotics
●
Two important aspects: ●
Robot morphology
●
Controller 4
Morphology Modular Robot classification 1D Topology
2D Topology
3D Topology
1D topology sub-classification Pitch-Pitch
Yaw-yaw
Pitch-yaw
5
Controller ●
Coordination problem: Calculation of the joint's angles to realize a gait: i t
●
Classic approach: Mathematical modeling ● Calculation by inverse kinematics ● Disadvantages: The equations are only valid for an specific morphology
CPG ●
CPG
CPG
Bio-inspired controllers: CPGs ● Central Pattern Generators ● CPGs control the rhythmic activities ● Ej. The locomotion of the lamprey
6
Hypothesis: Sinusoidal oscillators
●
CPGs are replaced by a Simplified model CPG
●
CPG
CPG
Sinusoidal oscillators:
2 i t=A i sin i O i T
●
Advantages: ● Few resources required
7
Outline
Outline 1.
Introduction
2. Locomotion in 1D 3. Locomotion in 2D 4. Minimal configurations 5. Cube-M modules 6. Conclusions and current work
Live modular Robots!
DFKI Bremen – Robotics Innovation Center. Jun, 16th, 2009
8
Y1 Modules
●
One degree of freedom
●
Easy to build
●
Cheap
●
Open and “Free”
9
Electronics & control
10
Cube Revolutions (I)
●
Videos
Morphology: 8 modules with pitch-pitch connection
●
Controller: ● ●
8 equal oscillators Parameters:
A , ,T
11
Locomotion mechanism
Locomotion performed by the body wave propagation ●
●
Step: x
V=
●
Mean Speed:
●
Serpenoid curve
●
Step calculation:
x T
l
l 2 k x= −∫0k cos cos sds k l
12
Outline
Outline 1.
Introduction
2. Locomotion in 1D 3. Locomotion in 2D 4. Minimal configurations 5. Cube-M modules 6. Conclusions and current work
Live modular Robots!
DFKI Bremen – Robotics Innovation Center. Jun, 16th, 2009
13
Hypercube (I)
●
Demo
Morphology 8 modules with pitch-yaw connection
●
Controller: ● ● ●
4 vertical oscillators 4 horizontal oscillators Parameters:
A h , A v , h , v , vh ,T 14
Locomotion gaits
●
Searching: Genetic algorithms
●
5 categories of gaits
●
Characterized by the 3D body wave
15
Locomotion mechanism ●
3D Body wave propagation
●
Linear Step: r
●
Angular Step:
●
Dimensions: width (w) x length (lx) x heigth (h)
16
Outline
Outline 1.
Introduction
2. Locomotion in 1D 3. Locomotion in 2D 4. Minimal configurations 5. Cube-M modules 6. Conclusions and future work
Live modular Robots!
DFKI Bremen – Robotics Innovation Center. Jun, 16th, 2009
17
Minimal configurations ●
Configurations with the minimal number of modules that are able to move
●
Searching the control space using genetic algorithms
●
Straight line
●
5 gaits
18
Minicube-I
●
Demo
Morphology 2 modules with a Pitchpitch connection
●
Controller: ●
Two generators
●
Parameters:
A , , T
19
Minicube-II
Demo
Morphology:
●
3 modules with Pitch-yawpitch connection
●
Controller: ●
3 oscillators
●
Parameters:
A v ,A h , v , vh , T 20
Locomotion gaits Forward
Av =40, Ah=0 v =120
Lateral shifting
Av = Ah40 vh =90, v=0 Av = Ah60
Turning Rotating
Av =40, Ah=0 Oh =30, v =120
Rolling
Av =10, Ah=40 vh =90, v=180
vh =90, v=0
21
Outline
Outline 1.
Introduction
2. Locomotion in 1D 3. Locomotion in 2D 4. Minimal configurations 5. Cube-M modules 6. Conclusions and current work
Live modular Robots!
DFKI Bremen – Robotics Innovation Center. Jun, 16th, 2009
22
Cube-M module(I) ●
●
●
Low cost mechanical design Simple robust modules assembling manually and int a quick-to-build, easy-tohandle design Onboard electronics and sensors
23
Cube-M module (II)
Demo
24
Software ● ● ●
Demo
1D topology simulator (Based on Open Dynamics Engine [ODE]) Generics algorithms: PGAPack Mathematical models in Octave/Matlab
25
Outline
Outline 1.
Introduction
2. Locomotion in 1D 3. Locomotion in 2D 4. Minimal configurations 5. Cube-M modules 6. Conclusions and current work
Live modular Robots!
DFKI Bremen – Robotics Innovation Center. Jun, 16th, 2009
26
Conclusions
The controller based on sinusoidal oscillators is valid for the locomotion of the 1D-topology modular robots
● ● ●
Very few resources are required for its implementation The locomotion gaits are very smooth and natural At least 5 different gaits can be achieved
i t =Ai sin
2 i Oi T 27
Current work Locomotion of 2D Topology modular robots
Modular grasping
Climbing caterpillar
New module design
28
Live modular Robots!
Dr. Houxiang Zhang Faculty of Mathematics, Informatics and Natural Sciences University of Hamburg
Dr. Juan González-Gómez School of Engineering Universidad Autonoma de Madrid
DFKI Bremen – Robotics Innovation Center. Jun, 16th, 2009
29
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