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1. Introduction 2. Leg Actuation System Design 3. Parallel Processing in Mobile Robot Controllers 4. Design Principles for Energy Efficient Legged Locomotion 5. What’s Next?
1. Introduction
http://www.youtube.com/watch?v=KYKg9-T2eNU 2012 BMW 3 Series Production - BMW Munich Plant - Body Shop
BMW 3 Series Production Boston Dynamics Atlas
Manufacturing Robot vs. Mobile Robot
1.1 Running
[1] P. WEYAND et al., “Faster top running speeds are achieved with greater ground forces not more rapid leg movements”, J. Appl. Physiol. 89: 1991–1999, 2000
𝐹 𝑧 (
N) 𝑇
𝑡𝑠 𝑡𝑠 𝑡𝑎 𝑡𝑎
M=70 kg V=4.5 m/s
700N
𝐹𝑧(𝑡) ⅆ𝑡 = 𝑚𝑔𝑇
𝑇
0
Vertical Momentum Conservation
1.2 In the Blink of an Eye
Airbag: 30ms
Playback speed: 0.06x MIT Cheetah running at 6m/s • Swing time: 250ms • Stance time: 57ms
Blink: 400ms
1.3 Requirements • Ground reaction force at 6m/s:
– Maximum: 450N
– Stance time: 57ms
• Leg actuation system’s force bandwidth:
– 120Hz (MIT Cheetah’s real spec)
• Main controller’s control sampling frequency:
– 20~30x of the closed loop bandwidth [64]
– 2.4-3.6kHz
– At 4 kHz, sampling period is 250𝜇𝑠
Fy
57ms
Touchdown angle
2. Leg Actuation System Design
Seok, Sangok, et al. "Actuator design for high force proprioceptive control in fast legged locomotion." Intelligent Robots and Systems (IROS), 2012 IEEE/RSJ International Conference on. IEEE, 2012.
2.1EM Motors
Recommended operation range
Short-term operation range
Torque
Angular speed
Maximum Continuous
Torque/Current
Demagnetization Torque/Current
10X of max. cont. Torque/Current
V= Vrecommended
𝑟 𝑡
𝑙
𝑟 : gap radius 𝑡 : rotor thickness 𝑙 : rotor length
Stator
Rotor
Torque Density ∝ 𝑟
2.2 Force Control
Geared Motor with Torque(Force) Sensor
Leg
Motor
High Gear Ratio Transmission
Stiff Sensor
Series Elastic Actuator
Leg
Spring, Encoder
Motor
High Gear Ratio Transmission
2.3 High Force Proprioceptive Actuation
High Torque Density Motor
Low Gear Ratio Transmission
Low Inertia Leg
No Force (Torque) Sensor No Series Elastic
Proprioceptive Actuation: Collocated force control through (1) maximizing torque density (2) minimizing mechanical impedance
2.4 Impedance Control
0
50
100
150
200
250
Time(ms)
400 0 50 100 150 200 250 300 350
Fo
rce(N
)
k=5,000N/m, d=100Ns/m Commanded Force Sensor
5cm
Force
Sensor
Sorbothane
Foot
3. Parallel Processing in Mobile Robot Controllers
A Highly Parallelized Control System Platform Architecture using Multicore CPU and FPGA for Multi-DoF Robots Sangok Seok, Dong Jin Hyun, SangIn Park, David Otten, and Sangbae Kim Submitted: 2014 IEEE International Conference on Robotics and Automation (ICRA)
3.1 Importance of Fast Processing MIT Cheetah: 12 DoF
Asimo: 34 DoF
More Functions (More Actuators and Sensors) More Agile (Higher System Bandwidth)
3.2 Solutions Faster system: - Faster Bus - Faster CPU [66],[67]
Main Controller Fast CPU
Distributed Controller 1
⋮ Distributed Controller 2
Distributed Controller N
Main Controller Multicore CPU, FPGA
Distributed Controller 1
⋮ Distributed Controller 2
Distributed Controller N
Fast BUS Parallel connection
Parallel Processing: - Parallel connection - Multicore CPU, FPGA
3.3 Parallel Processing
Single Worker:
1. Task Parallelism
Wash Iron Dry
4h 5h 6h
Dish Vacuum Cook
1h 2h 3h
Wash Iron Dry
1h 2h 3h
Worker 1:
Worker 2:
Worker 3:
Vacuum
Cook
Dish
4h 1h 2h 3h
Vacuum
Cook
Dish
4h
Wash
Iron
Dry
Vacuum
Cook
Dish
Wash
Iron
Dry
Wash
Dry
Iron
Vacuum
Cook
Dish
5h 6h
= 6 Tasks, 6 Hour
= 6 Tasks, 4 Hour = 6 Tasks, 1 Hour
Worker 1:
Worker 2:
Worker 3:
Worker 4:
Worker 5:
Worker 6:
2. Pipelining
Independent Dependent
3.4 Processing Sequence in MIT Cheetah
Forward Kinematics
Running Algorithm
PD Control Jacobian Current
Commands Receive
Sensor Data
Distributed Controller 1
Distributed Controller 2
Distributed Controller N
Main Controller ⋮
Ind
epen
den
t P
roce
ss
Dependent Process
3.5 Overall Process
Current 1 Current 2
: Current n
Current
Current
Current
Communication Output Emulator
Motor Driver 1
Motor Driver 2
.
.
.
Motor Driver n
.
.
.
Angle Current
Angle Current
Angle Current
Communication Input Emulator
Angle 1 Angle 2
: Angle n
Current 1 Current 2
: Current n
Front Left Leg Front Right Leg Rear Left Leg Rear Right Leg
Kinematics
.
.
.
𝑇1 = 17.24𝜇𝑠 𝑇2 = 22𝜇𝑠 𝑇3 = 50𝜇𝑠 𝑇4 = 44𝜇𝑠 𝑇5 = 36.85𝜇𝑠
3.6 Overall Process
𝜏1
𝜏2
𝜏3
𝜏4
𝜏5
𝜏1
𝜏2
𝜏3
𝜏4
𝜏5
𝜏1
𝜏2
𝜏3
𝜏4
𝜏5
𝜏1
𝜏2
𝜏3
𝜏4
𝜏5
Worker 1:
Worker 2:
Worker 3:
Worker 4:
𝜏1
𝜏2
𝜏3
𝜏4
𝜏5 Worker 5:
System throughput is governed by the slowest worker: 50us (Worker 3)
3.7 Process in Dualcore
Forward Kinematics
Running Algorithm
PD Control Jacobian Current
Commands Receive
Sensor Data
Main Controller
Think (Process)
Act (Transmit)
Sense (Receive)
Main Controller
Dualcore CPU
3.7 Process in Dual-core
𝑇𝑘 𝑅𝑘 𝑃𝑘 𝑇𝑘+1 𝑅𝑘+1 𝑃𝑘+1
Time
· · · · · ·
∆𝑇𝑅 ∆𝑇𝑃 ∆𝑇𝑇
∆𝑇
CPU
𝑇𝑘 𝑅𝑘
𝑃𝑘
𝑇𝑘+1 𝑅𝑘+1
𝑃𝑘+1
Time
· · · · · · CPU 2
CPU 1
∆𝑇
𝑘𝑡ℎ iteration 𝑘 + 1𝑡ℎ iteration
Single CPU
Dual-core CPU
3.7 Process in Dual-core
idle
idle
𝑇𝑘 𝑅𝑘
𝑃𝑘
Time
· · · · · · CPU 2
CPU 1
∆𝑇
𝑘𝑡ℎ iteration
𝑇𝑘+1 𝑅𝑘+1
𝑃𝑘+1
𝑘 + 1𝑡ℎ iteration
idle
idle 𝑇𝑘+2 𝑅𝑘+2
𝑃𝑘+2
𝑇𝑘+3 𝑅𝑘+3
𝑃𝑘+3
𝑇𝑘−1 𝑅𝑘+3 𝑇𝑘 𝑅𝑘
𝑃𝑘
𝑇𝑘+2 𝑅𝑘+2
𝑃𝑘+2
Time
· · · · · · CPU 2
CPU 1
∆𝑇 2
𝑘𝑡ℎ iteration
𝑇𝑘+1 𝑅𝑘+1
𝑃𝑘+1
𝑘 + 1𝑡ℎ iteration
Make ∆𝑇𝑃𝑟𝑜𝑐𝑒𝑠𝑠 = ∆𝑇𝑅𝑒𝑐𝑒𝑖𝑣𝑒 + ∆𝑇𝑇𝑟𝑎𝑛𝑠𝑚𝑖𝑡
Removing the idle states
3.8 Final Magic: SIMD Scalar Operation a=[1 3 5 7]; b=[2 4 6 8]; for i=1:4 c(i)=a(i)+b(i); end
SIMD Operation a=[1 3 5 7]; b=[2 4 6 8]; c=a+b;
a0 b0 c0
a1 b1 c1
a2 b2 c2
a3 b3 c3
+ =
+ =
+ =
+ =
a0 b0 c0
a1 b1 c1
a2 b2 c2
a3 b3 c3
+ =
3.8 Final Magic: SIMD
Benchmark test results with many legs: 1. PD Control 50000
0
10000
20000
30000
40000
1000 0 200 400 600 800
Number of Legs
Exe
cuti
on
Tim
e (n
s)
20
0
5
10
15
1000 0 200 400 600 800
Number of Legs
Scalar Operation
SIMD Operation
2500 times faster for 1000 legs
4. Design Principles for Energy Efficient Legged Locomotion
Design Principles for Highly Efficient Quadrupeds and Implementation on the MIT Cheetah Sangok Seok, Albert Wang, Meng Yee (Michael) Chuah, David Otten, Jeffrey Lang and Sangbae Kim 2013 IEEE International Conference on Robotics and Automation (ICRA)
Design Principles for Energy Efficient Legged Locomotion and Implementation on the MIT Cheetah Sangok Seok, Albert Wang, Meng Yee (Michael) Chuah, Dong Jin Hyun, Jongwoo Lee, David Otten, Jeffrey Lang, and Sangbae Kim 2014 IEEE/ASME Transactions on Mechatronics
4.1 Energy Flow Diagram
Energy Source (Battery)
Actuator (EM Motor)
Positive work
(Wposi)
Mechanical Transmission
Ej
Negative work
(Wneg)
Mechanical Energy (Ek + Ep)
Ef
Ei
Principles Implementation System Energy Flow
High Torque Density Motor
Energy Regeneration
Low Impedance Transmission
(Back Drivability)
Low Inertia Leg
Large Gap Radius Motor
Efficient Driver Design
Single-stage Low Gear Transmission
Dual Coaxial Motor
Differential Actuated Spine
Composite Leg/ Biotensegrity
Joule Heating
Friction
Interaction
4.2 Energy Regeneration
Deceleration Acceleration
Touch Down Lift Off
m
Stance Phase Flight Phase
Ground
4.3 Energy Efficiency for Animals and Robots
MIT Cheetah (0.5)
ASIMO (2) Bigdog (15)
Human Running
Cheetah
Log
Min
imu
m c
ost
of T
ran
spo
rt, P
/(W
V)
Eff
icie
ncy
Hig
her
(lo
g s
cale
)
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