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RobotLocomotion
Henrik IChristensen
Introduction
Concepts
Legged
Wheeled
Summary
Robot Locomotion
Henrik I Christensen
Centre for Autonomous Systems
Kungl Tekniska Hogskolanhic@kth.se
March 22, 2006
RobotLocomotion
Henrik IChristensen
Introduction
Concepts
Legged
Wheeled
Summary
Outline
Concepts
Legged Locomotion
Wheel Locomotion
RobotLocomotion
Henrik IChristensen
Introduction
Concepts
Legged
Wheeled
Summary
The overall system layout
RobotLocomotion
Henrik IChristensen
Introduction
Concepts
Legged
Wheeled
Summary
Locomotion Concepts: those found in nature
RobotLocomotion
Henrik IChristensen
Introduction
Concepts
Legged
Wheeled
Summary
Locomotion Concepts
Concepts found in nature
Difficult to imitate technically
Technical systems often use wheels or caterpillars/tracks
Rolling is more efficient, but not found in nature
Nature never invented the wheel!
However the movement of walking biped is close to rolling
RobotLocomotion
Henrik IChristensen
Introduction
Concepts
Legged
Wheeled
Summary
Biped Walking
Biped walking mechanism
not to far from real rollingrolling of a polygon with sidelength equal to step lengththe smaller the step the closerapproximation to a circle
However, full rolling notdeveloped in nature
RobotLocomotion
Henrik IChristensen
Introduction
Concepts
Legged
Wheeled
Summary
Passive walking examples
Video of passive walking example
Video of real passive walking system (Steve)
Video of passive walking system (Delft)
RobotLocomotion
Henrik IChristensen
Introduction
Concepts
Legged
Wheeled
Summary
Walking or rolling?
Number of actuators
Structural complexity
Control Expense
Energy sufficient
Terrain characteristics
Movement of the system
Movement of COGExtra loss
RobotLocomotion
Henrik IChristensen
Introduction
Concepts
Legged
Wheeled
Summary
RoboTrac – A Hybrid Vehicle
RobotLocomotion
Henrik IChristensen
Introduction
Concepts
Legged
Wheeled
Summary
Characterisation of locomotion concept
Locomotion
Physical interaction between the vehicle and itsenvironment
Locomotion is concerned with the interaction forces andthe actuators that generate them
Most important issues include:
StabilityContact characteristicsType of environment
RobotLocomotion
Henrik IChristensen
Introduction
Concepts
Legged
Wheeled
Summary
Mobile systems with legs – Walking machines
Fewer legs ⇒ complicated locomotion
stability requires at least 3 legs
During walking some legs are in the air
Thus a reduction in stability
Static walking requires at least 4 legs (and simple gaits)
RobotLocomotion
Henrik IChristensen
Introduction
Concepts
Legged
Wheeled
Summary
Number of joint for each leg (DOF: Degrees offreedom)
A minimum of 2 DOF is required to move a leg
A lift and a swing motionSliding free motion in more than 1 direction is not possible
In many cases a leg has 3 DOF
With 4-DOF an ankle joint can be added
Increased walking stabilityIncrease in mechanical complexity and control
RobotLocomotion
Henrik IChristensen
Introduction
Concepts
Legged
Wheeled
Summary
Control of a walking robot
Motion control should provide leg movements thatgenerate the desired body motion.
Control must consider:
The control gait: the sequencing of leg movementControl of foot placementControl body movement for supporting legs
RobotLocomotion
Henrik IChristensen
Introduction
Concepts
Legged
Wheeled
Summary
Leg control patterns
Legs have two major states:1 Stance: One the ground2 Fly: in the air moving to a new postion
Fly phase has three main components1 Lift phase: leaving the gound2 Transfer: moving to a new position3 Landing: smooth placement on the ground
RobotLocomotion
Henrik IChristensen
Introduction
Concepts
Legged
Wheeled
Summary
Example 3 DOF Leg design
RobotLocomotion
Henrik IChristensen
Introduction
Concepts
Legged
Wheeled
Summary
Gaits
Gaits determine the sequence of configurations of the legs
Gaits can be divided into two main classes1 Periodic gaits, which repeat the same sequence of
movements2 Non-periodic or free gaits, which have no periodicity in the
control, could be controlled by layout of environment
RobotLocomotion
Henrik IChristensen
Introduction
Concepts
Legged
Wheeled
Summary
The number of possible gaits?
The gait is characterised as the sequence of lift and releaseevents of individual legs
it depends on the number of legsthe number of possible events N for a walking machinewith k legs is:
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
RobotLocomotion
Henrik IChristensen
Introduction
Concepts
Legged
Wheeled
Summary
Most obvious 4 legged gaits
RobotLocomotion
Henrik IChristensen
Introduction
Concepts
Legged
Wheeled
Summary
Static gaits for 6 legged vehicle
RobotLocomotion
Henrik IChristensen
Introduction
Concepts
Legged
Wheeled
Summary
Walking vs Running
Motion of a legged system is called walking if in allinstances at least one leg is supporting the body
If there are instances where no legs are on the ground it iscalled running
Walking can be statically or dynamically stable
Running is always dynamically stable
RobotLocomotion
Henrik IChristensen
Introduction
Concepts
Legged
Wheeled
Summary
Stability
Stability means the capability to maintain the bodyposture given the control patterns
Statically stable walking implies that the posture can beachieved even if the legs are frozen / the motion isstoppped at any time, without loss of stability
Dynamic stability implies that stability can only beachieved through active control of the leg motion.
Statically stable systems can be controlled using kinematicmodels. Dynamic walking or running requires use ofdynamical models.
RobotLocomotion
Henrik IChristensen
Introduction
Concepts
Legged
Wheeled
Summary
Stability
Define Centre of Mass asPCM(t)
The ASUP(t) is the area ofsupport
Stable walking: ⇒PCM(t) ∈ ASUP(t)∀tDynamic walking: ⇒PCM(t) /∈ ASUP(t)∃tStability margin:min ‖PCM − ASUB‖
RobotLocomotion
Henrik IChristensen
Introduction
Concepts
Legged
Wheeled
Summary
Examples of walking machines
So far limited industrial applications of walking
A popular research field
An excellent overview from the clawar projecthttp://www.uwe.ac.uk/clawar
Video of 1 legged example
RobotLocomotion
Henrik IChristensen
Introduction
Concepts
Legged
Wheeled
Summary
Honda P2-6 Humanoid
Max speed: 2km/h
Autonomy: 15 minutes
Weight: 210 kg
Height: 1.82 m
Leg DOF: 2 * 6
Arm DOF: 2 * 7
Video 1
Video 2
RobotLocomotion
Henrik IChristensen
Introduction
Concepts
Legged
Wheeled
Summary
Bipedal Robot
MIT Leg Lab has developed a number of biped robots
Spring flamingo (a large simple walker)
The M2 robot for walking humanoid (Video example)
The early two legged systems by Raibert (Video)
RobotLocomotion
Henrik IChristensen
Introduction
Concepts
Legged
Wheeled
Summary
Humanoid Robots
A highly popular topic in japan
More than 65 robots at presenton display
Wabian built at WasedaUniversity
Weight: 107 kgAutonomy: noneHeight: 1.66 mDOF in total: 43
RobotLocomotion
Henrik IChristensen
Introduction
Concepts
Legged
Wheeled
Summary
Walking robots with four legs - Quadrupeds
A highly popular toy (300.000copies sold)
Involves an advanced controldesign
has vision, ranging, sound,orientation sensors
Has a separate league in theRoboCup tournament
(Example video)
RobotLocomotion
Henrik IChristensen
Introduction
Concepts
Legged
Wheeled
Summary
TITAN-VIII a Quadruped
Developed by Hirose at Univ ofTokyo
Weight: 19 kg
Height: 0.25 m
DOF: 4 * 3
RobotLocomotion
Henrik IChristensen
Introduction
Concepts
Legged
Wheeled
Summary
WARP – KTH Walking Machine
Early test platform
Weight: 225 kg
Height: 0.7 m
Length: 1.1 m
Autonomy: 15 min
DOF: 4 * 3
RobotLocomotion
Henrik IChristensen
Introduction
Concepts
Legged
Wheeled
Summary
Hexapods – six legged robots
Most popular dueto the staticallystable walking
Ex: Ohio walker
Speed: 2.3 m/s
Weight: 3.2 t
Height: 3 m
Length: 5.2 m
Legs: 6
DOF: 6 * 3
RobotLocomotion
Henrik IChristensen
Introduction
Concepts
Legged
Wheeled
Summary
Lauron II – Hexapod
Univ of Karlsruhe
Speed: 0.5 m/s
Weight: 6 kg
Height: 0.3 m
Length: 0.7 m
Legs: 6
DOF: 6 * 3
Power: 10 W
RobotLocomotion
Henrik IChristensen
Introduction
Concepts
Legged
Wheeled
Summary
Genghis – Subsumption Platforms
iRobot/MIT AI
Weight: 4 kg
Autonomy: 30 min
Length: 0.4 m
Height: 0.15 m
Speed: 0.1 m/s
RobotLocomotion
Henrik IChristensen
Introduction
Concepts
Legged
Wheeled
Summary
Systems with wheels
Wheels is often a good solution – in particular indoor
Three wheels enough to guarantee stability
More than three wheels requires suspension
Wheel configuration and type depends upon theapplication
RobotLocomotion
Henrik IChristensen
Introduction
Concepts
Legged
Wheeled
Summary
Types of wheels
There are four types of wheels
Standard wheel: two degrees offreedom – rotation aroundmotorized axle and the contactpoint
Castor wheel: three degrees offreedom: wheel axle, contactpoint and castor axle
RobotLocomotion
Henrik IChristensen
Introduction
Concepts
Legged
Wheeled
Summary
Types of wheels – II
Swedish wheel: three degrees offreedom - motorized wheelaxles, rollers, and contact point(Video)
Ball or spherical wheel:suspension not yet technicallysolved
RobotLocomotion
Henrik IChristensen
Introduction
Concepts
Legged
Wheeled
Summary
Characteristics of wheeled systems
Stability of vehicle is guaranteed with three wheels, i.e.PCM(t) ∈ ASUP(t) ∀tFour wheels improves stability if suspended
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)
RobotLocomotion
Henrik IChristensen
Introduction
Concepts
Legged
Wheeled
Summary
Wheel arrangements
Two wheels
Three wheels
RobotLocomotion
Henrik IChristensen
Introduction
Concepts
Legged
Wheeled
Summary
Wheel arrangements – II
Four wheels
RobotLocomotion
Henrik IChristensen
Introduction
Concepts
Legged
Wheeled
Summary
Synchro Drive
All wheels are drivensynchronously by one motor
Defines speed
All wheels are steeredsynchronously by second motor
Define direction of motion
orientation of inertial frameremains the same
RobotLocomotion
Henrik IChristensen
Introduction
Concepts
Legged
Wheeled
Summary
Differential drive setup
Two wheeled or possible two wheels and a castor
Control of each wheel independently
Control discussed in lecture 3
RobotLocomotion
Henrik IChristensen
Introduction
Concepts
Legged
Wheeled
Summary
Bicycle drive
Two wheeled with one wheel control of direction
Only dynamically stable
RobotLocomotion
Henrik IChristensen
Introduction
Concepts
Legged
Wheeled
Summary
Catarpillar / Tracked vehicles
Frequently used in rough terrain
Requires skid steering
Poor control of motion.
Requires external sensors foraccurate control
RobotLocomotion
Henrik IChristensen
Introduction
Concepts
Legged
Wheeled
Summary
Hybrid Locomotion
Mix of contact configurations(small / large configuration)
Developed for Mars Exploration(ESA) by Mecanex and EPFL
Named the SpaceCat
Walking with wheels(Video)
RobotLocomotion
Henrik IChristensen
Introduction
Concepts
Legged
Wheeled
Summary
SHRIMP – wheeled climbing
Passive handling of roughterrain
6 wheels for stability
Size 60 x 20 cm
Overcomes obstacles uptodouble wheel diameter
RobotLocomotion
Henrik IChristensen
Introduction
Concepts
Legged
Wheeled
Summary
SHRIMP Motion
RobotLocomotion
Henrik IChristensen
Introduction
Concepts
Legged
Wheeled
Summary
Summary/Discussion
Different types of locomotion
Legged
Well suited for unstructured terrainPower efficiency still an issue
Wheeled
Suited for planar surfacesDifferent configurations – control varies (see Lecture 3)
Tracked
Suited for rough terrainSkid steering poses a challenge to control
Intelligent design is key to design of an efficient system
RobotLocomotion
Henrik IChristensen
Introduction
Concepts
Legged
Wheeled
Summary
Lecture Schedule
Mon. March 27 @ 10–12 / Q2 (Kinematic modelling)
Thu. March 30 @ 10–12 / E3 (Lab session 2)
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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