institute for software technology
TRANSCRIPT
![Page 1: Institute for Software Technology](https://reader031.vdocuments.site/reader031/viewer/2022012915/61c4fd0fb95fa5299960ca21/html5/thumbnails/1.jpg)
Gerald Steinbauer
Institute for Software Technology
1
Mobile Robots - Locomotion
Mobile RobotsLocomotion
Gerald SteinbauerInstitute for Software Technology
![Page 2: Institute for Software Technology](https://reader031.vdocuments.site/reader031/viewer/2022012915/61c4fd0fb95fa5299960ca21/html5/thumbnails/2.jpg)
Gerald Steinbauer
Institute for Software Technology
2
Mobile Robots - Locomotion
Course Outline
1. Introduction to Mobile Robots2. Locomotion3. Sensors4. Localization5. Environment Modelling6. Reactive Navigation
![Page 3: Institute for Software Technology](https://reader031.vdocuments.site/reader031/viewer/2022012915/61c4fd0fb95fa5299960ca21/html5/thumbnails/3.jpg)
Gerald Steinbauer
Institute for Software Technology
3
Mobile Robots - Locomotion
Today’s Agenda
• Motivation for Locomotion• Basic Definitions• Legged Locomotion• Wheeled Locomotion• Properties of Locomotion and their Application• Feedback Control
![Page 4: Institute for Software Technology](https://reader031.vdocuments.site/reader031/viewer/2022012915/61c4fd0fb95fa5299960ca21/html5/thumbnails/4.jpg)
Gerald Steinbauer
Institute for Software Technology
4
Mobile Robots - Locomotion
Literature
Introduction to Autonomous Mobile Robots. 2nd Edition. Roland Siegwart, Illah Reza Nourbakhsh, DavideScaramuzza. MIT Press. 2011.
Springer Handbook of Robotics. Bruno Siciliano and Oussama Khatib.
Springer. 2008.
![Page 5: Institute for Software Technology](https://reader031.vdocuments.site/reader031/viewer/2022012915/61c4fd0fb95fa5299960ca21/html5/thumbnails/5.jpg)
Gerald Steinbauer
Institute for Software Technology
5
Mobile Robots - Locomotion
Again, Robotics is Easy …
environment/worldsensing
informationextraction
raw data
acting
pathexecution
actuatorcommands
domainmodel
environmentmodel
pathplanning
navigation
perc
eptio
nm
odel
ling
beha
vior
cont
rol
planning reasoning
cognition
task
![Page 6: Institute for Software Technology](https://reader031.vdocuments.site/reader031/viewer/2022012915/61c4fd0fb95fa5299960ca21/html5/thumbnails/6.jpg)
Gerald Steinbauer
Institute for Software Technology
6
Mobile Robots - Locomotion
Locomotion
• Oxford Dictionary: movement or the ability to movefrom one place to another
![Page 7: Institute for Software Technology](https://reader031.vdocuments.site/reader031/viewer/2022012915/61c4fd0fb95fa5299960ca21/html5/thumbnails/7.jpg)
Gerald Steinbauer
Institute for Software Technology
7
Mobile Robots - Locomotion
Locomotion
• a mobile robot needs locomotion
• has a long history in nature
• different optimizations for• speed• stability• efficiency
http://www.youtube.com/watch?v=TIFoWAZ0EEg
![Page 8: Institute for Software Technology](https://reader031.vdocuments.site/reader031/viewer/2022012915/61c4fd0fb95fa5299960ca21/html5/thumbnails/8.jpg)
Gerald Steinbauer
Institute for Software Technology
8
Mobile Robots - Locomotion
Locomotion in Biological Systems[S
iegwart, N
ourbakhsh, Scaram
uzza, 2011, MIT P
ress]
![Page 9: Institute for Software Technology](https://reader031.vdocuments.site/reader031/viewer/2022012915/61c4fd0fb95fa5299960ca21/html5/thumbnails/9.jpg)
Gerald Steinbauer
Institute for Software Technology
9
Mobile Robots - Locomotion
Inspiration by Nature
• biological locomotion is hard to replicate• mechanical complexity• duplication• miniaturization• actuation• energy storage
[Siegwart, Nourbakhsh, Scaramuzza, 2011, MIT Press]
![Page 10: Institute for Software Technology](https://reader031.vdocuments.site/reader031/viewer/2022012915/61c4fd0fb95fa5299960ca21/html5/thumbnails/10.jpg)
Gerald Steinbauer
Institute for Software Technology
10
Mobile Robots - Locomotion
Efficiency I
[Siegwart, Nourbakhsh, Scaramuzza, 2011, MIT Press]
![Page 11: Institute for Software Technology](https://reader031.vdocuments.site/reader031/viewer/2022012915/61c4fd0fb95fa5299960ca21/html5/thumbnails/11.jpg)
Gerald Steinbauer
Institute for Software Technology
11
Mobile Robots - Locomotion
Efficiency II[S
icillano, Khatib, 2008, S
pringer]
![Page 12: Institute for Software Technology](https://reader031.vdocuments.site/reader031/viewer/2022012915/61c4fd0fb95fa5299960ca21/html5/thumbnails/12.jpg)
Gerald Steinbauer
Institute for Software Technology
12
Mobile Robots - Locomotion
Key Issues of Locomotion
• stability• number and geometry of contact points• center of gravity• static/dynamic stability• inclination of the terrain
• characteristics of contact• contact points/path size and shape• angle of contact• friction
• type of environment• structure• medium, e.g. water, air, soft or hard ground
![Page 13: Institute for Software Technology](https://reader031.vdocuments.site/reader031/viewer/2022012915/61c4fd0fb95fa5299960ca21/html5/thumbnails/13.jpg)
Gerald Steinbauer
Institute for Software Technology
13
Mobile Robots - Locomotion
Dimensionality
• the degree of freedom (DOF) of a workspace is its overall dimensionality• on (flat) ground DOF=3• in the air or below water DOF=6
![Page 14: Institute for Software Technology](https://reader031.vdocuments.site/reader031/viewer/2022012915/61c4fd0fb95fa5299960ca21/html5/thumbnails/14.jpg)
Gerald Steinbauer
Institute for Software Technology
14
Mobile Robots - Locomotion
Legs versus Wheels[S
iegwart, N
ourbakhsh, Scaram
uzza, 2011, MIT P
ress]
![Page 15: Institute for Software Technology](https://reader031.vdocuments.site/reader031/viewer/2022012915/61c4fd0fb95fa5299960ca21/html5/thumbnails/15.jpg)
Gerald Steinbauer
Institute for Software Technology
15
Mobile Robots - Locomotion
Zero Moment Point Movement (ZMP)
• commonly used method for stable walking• ZMP is defined as that point on the ground at which
the net moment of the inertial forces and the gravity has no component along the horizontal axes (Vukobratović and Branislav)
[Sicillano, Khatib, 2008, Springer]
![Page 16: Institute for Software Technology](https://reader031.vdocuments.site/reader031/viewer/2022012915/61c4fd0fb95fa5299960ca21/html5/thumbnails/16.jpg)
Gerald Steinbauer
Institute for Software Technology
16
Mobile Robots - Locomotion
Zero Moment Point Movement
• suppose a legged robot comprising several bodies
• … force vector acing on body (gravity plus external)
• … angular velocity of body • … inertia tensor (∈ ) of
body • … relative position
of body to ZMP [Sicillano, Khatib, 2008, Springer]
≡ 0,0,∗
![Page 17: Institute for Software Technology](https://reader031.vdocuments.site/reader031/viewer/2022012915/61c4fd0fb95fa5299960ca21/html5/thumbnails/17.jpg)
Gerald Steinbauer
Institute for Software Technology
17
Mobile Robots - Locomotion
Requirements for ZMP
• a robot able to use ZMP needs:• there are at least six
fully actuated joints for each leg
• the joints are positioncontrolled
• the feet are equipped with force sensors, which are used to measure the ZMP
http://www.youtube.com/watch?v=3aOuQ1_e--k
![Page 18: Institute for Software Technology](https://reader031.vdocuments.site/reader031/viewer/2022012915/61c4fd0fb95fa5299960ca21/html5/thumbnails/18.jpg)
Gerald Steinbauer
Institute for Software Technology
18
Mobile Robots - Locomotion
Wheel Types
Side View
Front View
Top View
standard castor Swedish spherical
[Siegwart, Nourbakhsh, Scaramuzza, 2011, MIT Press]
![Page 19: Institute for Software Technology](https://reader031.vdocuments.site/reader031/viewer/2022012915/61c4fd0fb95fa5299960ca21/html5/thumbnails/19.jpg)
Gerald Steinbauer
Institute for Software Technology
19
Mobile Robots - Locomotion
Typical Arrangements (2 and 3 Wheels)2 Wheels
3 Wheels
[Siegw
art, Nourbakhsh, S
caramuzza, 2011, M
IT Press]
![Page 20: Institute for Software Technology](https://reader031.vdocuments.site/reader031/viewer/2022012915/61c4fd0fb95fa5299960ca21/html5/thumbnails/20.jpg)
Gerald Steinbauer
Institute for Software Technology
20
Mobile Robots - Locomotion
Typical Arrangements ( 4 Wheels)
http://www.youtube.com/watch?v=XzkC4Ez8GYE
[Siegw
art, Nourbakhsh, S
caramuzza, 2011, M
IT Press]
http://www.youtube.com/watch?v=8sH1a511_q4
![Page 21: Institute for Software Technology](https://reader031.vdocuments.site/reader031/viewer/2022012915/61c4fd0fb95fa5299960ca21/html5/thumbnails/21.jpg)
Gerald Steinbauer
Institute for Software Technology
21
Mobile Robots - Locomotion
Advanced Mechanisms
• NASA Mars Rover - Rocker-Bogie
• hybrid between walking and driving
• allows to climb obstacles
• reduce movement of body
http://www.youtube.com/watch?v=BC441bV1wFc
[Nasa/JPL]
![Page 22: Institute for Software Technology](https://reader031.vdocuments.site/reader031/viewer/2022012915/61c4fd0fb95fa5299960ca21/html5/thumbnails/22.jpg)
Gerald Steinbauer
Institute for Software Technology
22
Mobile Robots - Locomotion
Other Forms of Locomotion
• in the air • below water
http://www.youtube.com/watch?v=9Vm-gQ9_H9Ihttp://www.youtube.com/watch?v=4ErEBkj_3PY
![Page 23: Institute for Software Technology](https://reader031.vdocuments.site/reader031/viewer/2022012915/61c4fd0fb95fa5299960ca21/html5/thumbnails/23.jpg)
Gerald Steinbauer
Institute for Software Technology
23
Mobile Robots - Locomotion
Homogeneous Transformation
• we need a transformationbetween the motion in the reference frame and the robot frame
• the transformation depend on the global angle
, ,
, ,
cos sin 0sin cos 00 0 1
![Page 24: Institute for Software Technology](https://reader031.vdocuments.site/reader031/viewer/2022012915/61c4fd0fb95fa5299960ca21/html5/thumbnails/24.jpg)
Gerald Steinbauer
Institute for Software Technology
24
Mobile Robots - Locomotion
Kinematic Constraints
• an arrangement comprises wheels of differenttypes
• each wheel provides an individual velocity and individual parameters, e.g. steering anlge
• to determine the maneuverability of an attunement we use 2 sorts of constraints• rolling constraints: all motions in the wheel plane have to be
accompanied with the appropriate wheel spin• sliding constraints: the motion orthogonal to the wheel has to be
zero
![Page 25: Institute for Software Technology](https://reader031.vdocuments.site/reader031/viewer/2022012915/61c4fd0fb95fa5299960ca21/html5/thumbnails/25.jpg)
Gerald Steinbauer
Institute for Software Technology
25
Mobile Robots - Locomotion
Fixed Standard Wheel
sin cos cos 0 RKC
cos sin 0 SKC
, ,
[Siegw
art, Nourbakhsh, S
caramuzza, 2011, M
IT Press]
![Page 26: Institute for Software Technology](https://reader031.vdocuments.site/reader031/viewer/2022012915/61c4fd0fb95fa5299960ca21/html5/thumbnails/26.jpg)
Gerald Steinbauer
Institute for Software Technology
26
Mobile Robots - Locomotion
Steered Standard Wheel
sin cos cos 0 RKC
cos sin 0 SKC
, ,
same as fixed standard wheel expect steering is now a function of time
[Siegw
art, Nourbakhsh,
Scaram
uzza, 2011, MIT P
ress]
![Page 27: Institute for Software Technology](https://reader031.vdocuments.site/reader031/viewer/2022012915/61c4fd0fb95fa5299960ca21/html5/thumbnails/27.jpg)
Gerald Steinbauer
Institute for Software Technology
27
Mobile Robots - Locomotion
Swedish Wheel
sin cos cos cos 0 RKC
cos sin sin 0 SKC
[Siegw
art, Nourbakhsh,
Scaram
uzza, 2011, MIT P
ress]
![Page 28: Institute for Software Technology](https://reader031.vdocuments.site/reader031/viewer/2022012915/61c4fd0fb95fa5299960ca21/html5/thumbnails/28.jpg)
Gerald Steinbauer
Institute for Software Technology
28
Mobile Robots - Locomotion
Spherical Wheel
sin cos cos 0 RKC
cos sin 0 SKC
same as fixed standard wheel expect steering is now a free variable
[Siegw
art, Nourbakhsh,
Scaram
uzza, 2011, MIT P
ress]
![Page 29: Institute for Software Technology](https://reader031.vdocuments.site/reader031/viewer/2022012915/61c4fd0fb95fa5299960ca21/html5/thumbnails/29.jpg)
Gerald Steinbauer
Institute for Software Technology
29
Mobile Robots - Locomotion
Combining the Constraints I
• the wheel arrangement comprises fixed and steerable wheels,
• denotes the steering angles while denotes all fixed angles
• denotes wheel speed of the fixed wheels while denotes wheel speed of the steered wheels,
denotes the combination
![Page 30: Institute for Software Technology](https://reader031.vdocuments.site/reader031/viewer/2022012915/61c4fd0fb95fa5299960ca21/html5/thumbnails/30.jpg)
Gerald Steinbauer
Institute for Software Technology
30
Mobile Robots - Locomotion
Combining the Constraints II
0 with and
0 00 ⋱ 00 0
Rolling Constraints
0 with
Sliding Constraints
0
All Together
![Page 31: Institute for Software Technology](https://reader031.vdocuments.site/reader031/viewer/2022012915/61c4fd0fb95fa5299960ca21/html5/thumbnails/31.jpg)
Gerald Steinbauer
Institute for Software Technology
31
Mobile Robots - Locomotion
Maneuverability
• we can use the constraints to investigate the mobilitypotential of a robot
• the degree of mobility• is defined as: 3• represents the number of DOF that can immediately manipulated
by changes in the wheel velocities• related to the location of the instantaneous center of rotation (ICR)
• the degree of steerability• is defined as: • 0 2 … depends on the number of steerable wheels
• robot maneuverability•• related to the DOF a robot is able to manipulate
![Page 32: Institute for Software Technology](https://reader031.vdocuments.site/reader031/viewer/2022012915/61c4fd0fb95fa5299960ca21/html5/thumbnails/32.jpg)
Gerald Steinbauer
Institute for Software Technology
32
Mobile Robots - Locomotion
Application of Constraints
![Page 33: Institute for Software Technology](https://reader031.vdocuments.site/reader031/viewer/2022012915/61c4fd0fb95fa5299960ca21/html5/thumbnails/33.jpg)
Gerald Steinbauer
Institute for Software Technology
33
Mobile Robots - Locomotion
Automatic Reconfigurable Omni-Drive
[Brandstötter, Hofbauer, Steinbauer, Wotawa – IROS 2007]
![Page 34: Institute for Software Technology](https://reader031.vdocuments.site/reader031/viewer/2022012915/61c4fd0fb95fa5299960ca21/html5/thumbnails/34.jpg)
Gerald Steinbauer
Institute for Software Technology
34
Mobile Robots - Locomotion
Automatic Reconfigurable Omni-Drive
motor 1 fails motor 2 fails motor 3 fails
![Page 35: Institute for Software Technology](https://reader031.vdocuments.site/reader031/viewer/2022012915/61c4fd0fb95fa5299960ca21/html5/thumbnails/35.jpg)
Gerald Steinbauer
Institute for Software Technology
35
Mobile Robots - Locomotion
(Non)-Holomorphic[S
iegwart, N
ourbakhsh,S
caramuzza, 2011, M
IT Press]
![Page 36: Institute for Software Technology](https://reader031.vdocuments.site/reader031/viewer/2022012915/61c4fd0fb95fa5299960ca21/html5/thumbnails/36.jpg)
Gerald Steinbauer
Institute for Software Technology
36
Mobile Robots - Locomotion
Feedback Control
• move a differential drive to a goal• non-holonomic constraints – we
need differential inverse kinematics
[Siegw
art, Nourbakhsh,
Scaram
uzza, 2011, MIT P
ress]
⋅
lim→
0
![Page 37: Institute for Software Technology](https://reader031.vdocuments.site/reader031/viewer/2022012915/61c4fd0fb95fa5299960ca21/html5/thumbnails/37.jpg)
Gerald Steinbauer
Institute for Software Technology
37
Mobile Robots - Locomotion
Control Law
[Siegwart, Nourbakhsh,Scaramuzza, 2011, MIT Press]3, 8, 1.5
⋅+
![Page 38: Institute for Software Technology](https://reader031.vdocuments.site/reader031/viewer/2022012915/61c4fd0fb95fa5299960ca21/html5/thumbnails/38.jpg)
Gerald Steinbauer
Institute for Software Technology
38
Mobile Robots - Locomotion
Questions?Thank you!