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Robot
Locomotion
Henrik I
Christensen
Robot Locomotion
Introduction
Concepts Henrik I Christensen
Legged
Wheeled
Summary
Centre for Autonomous Systems
o
Kungl Tekniska H¨gskolan
hic@kth.se
March 22, 2006
Outline
Robot
Locomotion
Henrik I
Christensen
Introduction
Concepts
Legged
Concepts
Wheeled
Summary
Legged Locomotion
Wheel Locomotion
The overall system layout
Robot
Locomotion
Henrik I
Christensen
Introduction
Concepts
Legged
Wheeled
Summary
Locomotion Concepts: those found in nature
Robot
Locomotion
Henrik I
Christensen
Introduction
Concepts
Legged
Wheeled
Summary
Locomotion Concepts
Robot
Locomotion
Henrik I
Christensen
Introduction
Concepts Concepts found in nature
Legged Difficult to imitate technically
Wheeled
Technical systems often use wheels or caterpillars/tracks
Summary
Rolling is more efficient, but not found in nature
Nature never invented the wheel!
However the movement of walking biped is close to rolling
Biped Walking
Robot
Locomotion
Henrik I
Christensen
Introduction
Biped walking mechanism
Concepts
not to far from real rolling
Legged
rolling of a polygon with side
Wheeled
length equal to step length
Summary
the smaller the step the closer
approximation to a circle
However, full rolling not
developed in nature
Passive walking examples
Robot
Locomotion
Henrik I
Christensen
Introduction
Concepts
Legged
Video of passive walking example
Wheeled
Summary
Video of real passive walking system (Steve)
Video of passive walking system (Delft)
Walking or rolling?
Robot
Locomotion
Henrik I
Christensen
Introduction Number of actuators
Concepts
Structural complexity
Legged
Wheeled
Control Expense
Summary Energy sufficient
Terrain characteristics
Movement of the system
Movement of COG
Extra loss
RoboTrac – A Hybrid Vehicle
Robot
Locomotion
Henrik I
Christensen
Introduction
Concepts
Legged
Wheeled
Summary
Characterisation of locomotion concept
Robot
Locomotion
Henrik I
Christensen
Introduction Locomotion
Concepts Physical interaction between the vehicle and its
Legged environment
Wheeled Locomotion is concerned with the interaction forces and
Summary
the actuators that generate them
Most important issues include:
Stability
Contact characteristics
Type of environment
Mobile systems with legs – Walking machines
Robot
Locomotion
Henrik I
Christensen
Fewer legs ⇒ complicated locomotion
Introduction
Concepts
stability requires at least 3 legs
Legged During walking some legs are in the air
Wheeled Thus a reduction in stability
Summary
Static walking requires at least 4 legs (and simple gaits)
Number of joint for each leg (DOF: Degrees of
freedom)
Robot
Locomotion
Henrik I
Christensen
Introduction
Concepts
A minimum of 2 DOF is required to move a leg
Legged
A lift and a swing motion
Wheeled
Sliding free motion in more than 1 direction is not possible
Summary In many cases a leg has 3 DOF
With 4-DOF an ankle joint can be added
Increased walking stability
Increase in mechanical complexity and control
Control of a walking robot
Robot
Locomotion
Henrik I
Christensen
Introduction
Concepts
Motion control should provide leg movements that
Legged
generate the desired body motion.
Wheeled
Control must consider:
Summary
The control gait: the sequencing of leg movement
Control of foot placement
Control body movement for supporting legs
Leg control patterns
Robot
Locomotion
Henrik I
Christensen
Introduction
Concepts Legs have two major states:
Legged 1 Stance: One the ground
Wheeled
2 Fly: in the air moving to a new postion
Summary Fly phase has three main components
1 Lift phase: leaving the gound
2 Transfer: moving to a new position
3 Landing: smooth placement on the ground
Example 3 DOF Leg design
Robot
Locomotion
Henrik I
Christensen
Introduction
Concepts
Legged
Wheeled
Summary
Gaits
Robot
Locomotion
Henrik I
Christensen
Introduction
Concepts
Gaits determine the sequence of configurations of the legs
Legged
Gaits can be divided into two main classes
Wheeled
1 Periodic gaits, which repeat the same sequence of
Summary
movements
2 Non-periodic or free gaits, which have no periodicity in the
control, could be controlled by layout of environment
The number of possible gaits?
Robot
Locomotion
Henrik I
Christensen
The gait is characterised as the sequence of lift and release
Introduction events of individual legs
Concepts it depends on the number of legs
Legged the number of possible events N for a walking machine
Wheeled with k legs is:
Summary N = (2k − 1)!
For the biped walker (k=2) the possible events are 3! = 6
lift left leg, lift right leg, release left leg, release right leg,
light both legs, release both legs
For a robot with 6 legs the number of gaits are: 11! =
39.916.800
Most obvious 4 legged gaits
Robot
Locomotion
Henrik I
Christensen
Introduction
Concepts
Legged
Wheeled
Summary
Static gaits for 6 legged vehicle
Robot
Locomotion
Henrik I
Christensen
Introduction
Concepts
Legged
Wheeled
Summary
Walking vs Running
Robot
Locomotion
Henrik I
Christensen
Introduction
Concepts Motion of a legged system is called walking if in all
Legged instances at least one leg is supporting the body
Wheeled
If there are instances where no legs are on the ground it is
Summary
called running
Walking can be statically or dynamically stable
Running is always dynamically stable
Stability
Robot
Locomotion
Henrik I
Christensen
Stability means the capability to maintain the body
Introduction
posture given the control patterns
Concepts
Legged
Statically stable walking implies that the posture can be
Wheeled
achieved even if the legs are frozen / the motion is
Summary
stoppped at any time, without loss of stability
Dynamic stability implies that stability can only be
achieved through active control of the leg motion.
Statically stable systems can be controlled using kinematic
models. Dynamic walking or running requires use of
dynamical models.
Stability
Robot
Locomotion
Henrik I
Christensen
Define Centre of Mass as
Introduction PCM (t)
Concepts
The ASUP (t) is the area of
Legged
support
Wheeled
Summary
Stable walking: ⇒
PCM (t) ∈ ASUP (t)∀t
Dynamic walking: ⇒
PCM (t) ∈ ASUP (t)∃t
/
Stability margin:
min PCM − ASUB
Examples of walking machines
Robot
Locomotion
Henrik I
Christensen
Introduction
Concepts
So far limited industrial applications of walking
Legged
Wheeled
A popular research field
Summary An excellent overview from the clawar project
http://www.uwe.ac.uk/clawar
Video of 1 legged example
Honda P2-6 Humanoid
Robot
Locomotion
Henrik I
Christensen
Max speed: 2km/h
Introduction
Concepts Autonomy: 15 minutes
Legged Weight: 210 kg
Wheeled
Height: 1.82 m
Summary
Leg DOF: 2 * 6
Arm DOF: 2 * 7
Video 1
Video 2
Bipedal Robot
Robot
Locomotion
Henrik I
Christensen
Introduction
Concepts
Legged
MIT Leg Lab has developed a number of biped robots
Wheeled Spring flamingo (a large simple walker)
Summary
The M2 robot for walking humanoid (Video example)
The early two legged systems by Raibert (Video)
Humanoid Robots
Robot
Locomotion
Henrik I
Christensen
Introduction A highly popular topic in japan
Concepts More than 65 robots at present
Legged
on display
Wheeled
Wabian built at Waseda
Summary
University
Weight: 107 kg
Autonomy: none
Height: 1.66 m
DOF in total: 43
Walking robots with four legs - Quadrupeds
Robot
Locomotion
Henrik I
Christensen
A highly popular toy (300.000
Introduction
copies sold)
Concepts
Legged
Involves an advanced control
Wheeled
design
Summary has vision, ranging, sound,
orientation sensors
Has a separate league in the
RoboCup tournament
(Example video)
TITAN-VIII a Quadruped
Robot
Locomotion
Henrik I
Christensen
Introduction
Concepts Developed by Hirose at Univ of
Legged
Tokyo
Wheeled
Summary
Weight: 19 kg
Height: 0.25 m
DOF: 4 * 3
WARP – KTH Walking Machine
Robot
Locomotion
Henrik I
Christensen
Introduction
Concepts
Early test platform
Legged
Weight: 225 kg
Wheeled
Summary Height: 0.7 m
Length: 1.1 m
Autonomy: 15 min
DOF: 4 * 3
Hexapods – six legged robots
Robot
Locomotion
Henrik I
Christensen Most popular due
Introduction
to the statically
Concepts
stable walking
Legged Ex: Ohio walker
Wheeled
Speed: 2.3 m/s
Summary
Weight: 3.2 t
Height: 3 m
Length: 5.2 m
Legs: 6
DOF: 6 * 3
Lauron II – Hexapod
Robot
Locomotion
Henrik I
Christensen
Univ of Karlsruhe
Introduction
Concepts
Speed: 0.5 m/s
Legged Weight: 6 kg
Wheeled
Height: 0.3 m
Summary
Length: 0.7 m
Legs: 6
DOF: 6 * 3
Power: 10 W
Genghis – Subsumption Platforms
Robot
Locomotion
Henrik I
Christensen
Introduction
iRobot/MIT AI
Concepts
Legged
Weight: 4 kg
Wheeled Autonomy: 30 min
Summary
Length: 0.4 m
Height: 0.15 m
Speed: 0.1 m/s
Systems with wheels
Robot
Locomotion
Henrik I
Christensen
Introduction
Concepts
Wheels is often a good solution – in particular indoor
Legged
Wheeled
Three wheels enough to guarantee stability
Summary More than three wheels requires suspension
Wheel configuration and type depends upon the
application
Types of wheels
Robot
Locomotion
Henrik I
Christensen
Introduction There are four types of wheels
Concepts Standard wheel: two degrees of
Legged
freedom – rotation around
Wheeled
motorized axle and the contact
Summary
point
Castor wheel: three degrees of
freedom: wheel axle, contact
point and castor axle
Types of wheels – II
Robot
Locomotion
Henrik I
Christensen
Introduction
Concepts
Swedish wheel: three degrees of
Legged
freedom - motorized wheel
Wheeled
axles, rollers, and contact point
Summary (Video)
Ball or spherical wheel:
suspension not yet technically
solved
Characteristics of wheeled systems
Robot
Locomotion
Henrik I
Christensen
Introduction
Stability of vehicle is guaranteed with three wheels, i.e.
Concepts
Legged
PCM (t) ∈ ASUP (t) ∀t
Wheeled Four wheels improves stability if suspended
Summary Bigger wheels ⇒ Handling of larger obstacles
Imposes extra torque and higher reduction in gear ratio
Most arrangements are non-holonomic (see Lecture 3)
Control is more complex (Video commercial)
Wheel arrangements
Robot
Locomotion
Henrik I
Christensen
Two wheels
Introduction
Concepts
Legged
Wheeled
Summary Three wheels
Wheel arrangements – II
Robot
Locomotion
Henrik I
Christensen
Introduction Four wheels
Concepts
Legged
Wheeled
Summary
Synchro Drive
Robot
Locomotion
Henrik I
Christensen
Introduction All wheels are driven
Concepts synchronously by one motor
Legged Defines speed
Wheeled
All wheels are steered
Summary synchronously by second motor
Define direction of motion
orientation of inertial frame
remains the same
Differential drive setup
Robot
Locomotion
Henrik I
Christensen
Introduction
Two wheeled or possible two wheels and a castor
Concepts Control of each wheel independently
Legged
Control discussed in lecture 3
Wheeled
Summary
Bicycle drive
Robot
Locomotion
Henrik I
Christensen
Introduction Two wheeled with one wheel control of direction
Concepts
Only dynamically stable
Legged
Wheeled
Summary
Catarpillar / Tracked vehicles
Robot
Locomotion
Henrik I
Christensen
Introduction
Concepts Frequently used in rough terrain
Legged
Requires skid steering
Wheeled
Summary Poor control of motion.
Requires external sensors for
accurate control
Hybrid Locomotion
Robot
Locomotion
Henrik I
Christensen
Introduction
Concepts
Mix of contact configurations
Legged (small / large configuration)
Wheeled Developed for Mars Exploration
Summary (ESA) by Mecanex and EPFL
Named the SpaceCat
Walking with wheels
(Video)
SHRIMP – wheeled climbing
Robot
Locomotion
Henrik I
Christensen
Introduction
Concepts
Passive handling of rough
Legged
terrain
Wheeled 6 wheels for stability
Summary
Size 60 x 20 cm
Overcomes obstacles upto
double wheel diameter
SHRIMP Motion
Robot
Locomotion
Henrik I
Christensen
Introduction
Concepts
Legged
Wheeled
Summary
Summary/Discussion
Robot
Locomotion
Henrik I
Christensen
Different types of locomotion
Introduction Legged
Concepts Well suited for unstructured terrain
Legged Power efficiency still an issue
Wheeled
Wheeled
Summary
Suited for planar surfaces
Different configurations – control varies (see Lecture 3)
Tracked
Suited for rough terrain
Skid steering poses a challenge to control
Intelligent design is key to design of an efficient system
Lecture Schedule
Robot
Locomotion
Henrik I
Christensen
Introduction
Concepts Mon. March 27 @ 10–12 / Q2 (Kinematic modelling)
Legged
Thu. March 30 @ 10–12 / E3 (Lab session 2)
Wheeled
Summary Mon. April 3 @ 10–12 / E2 (Sensors/Features)
Thu. April 6 @ 15-17 / Q2 (Mapping/Estimation)
Thu April 20 @ 10-12 / Q33 (Planning and Integration)
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