Robot Locomotion Robot Locomotion

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Robot Locomotion Henrik I Christensen Introduction Concepts Legged Wheeled Summary Robot Locomotion Henrik I Christensen Centre for Autonomous Systems Kungl Tekniska H¨ ogskolan [email protected] March 22, 2006

Transcript of Robot Locomotion Robot Locomotion

Page 1: Robot Locomotion Robot Locomotion

RobotLocomotion

Henrik IChristensen

Introduction

Concepts

Legged

Wheeled

Summary

Robot Locomotion

Henrik I Christensen

Centre for Autonomous Systems

Kungl Tekniska [email protected]

March 22, 2006

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Introduction

Concepts

Legged

Wheeled

Summary

Outline

Concepts

Legged Locomotion

Wheel Locomotion

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Concepts

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The overall system layout

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Concepts

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Locomotion Concepts: those found in nature

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Concepts

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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

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Concepts

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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

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Introduction

Concepts

Legged

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Summary

Passive walking examples

Video of passive walking example

Video of real passive walking system (Steve)

Video of passive walking system (Delft)

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Introduction

Concepts

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Walking or rolling?

Number of actuators

Structural complexity

Control Expense

Energy sufficient

Terrain characteristics

Movement of the system

Movement of COGExtra loss

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Concepts

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RoboTrac – A Hybrid Vehicle

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Introduction

Concepts

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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

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Concepts

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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)

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Introduction

Concepts

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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

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Concepts

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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

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Concepts

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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

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Example 3 DOF Leg design

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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

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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

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Concepts

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Most obvious 4 legged gaits

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Static gaits for 6 legged vehicle

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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

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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.

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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‖

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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

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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

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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)

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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

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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)

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TITAN-VIII a Quadruped

Developed by Hirose at Univ ofTokyo

Weight: 19 kg

Height: 0.25 m

DOF: 4 * 3

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WARP – KTH Walking Machine

Early test platform

Weight: 225 kg

Height: 0.7 m

Length: 1.1 m

Autonomy: 15 min

DOF: 4 * 3

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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

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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

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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

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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

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Introduction

Concepts

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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

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Types of wheels – II

Swedish wheel: three degrees offreedom - motorized wheelaxles, rollers, and contact point(Video)

Ball or spherical wheel:suspension not yet technicallysolved

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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)

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Wheel arrangements

Two wheels

Three wheels

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Wheel arrangements – II

Four wheels

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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

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Differential drive setup

Two wheeled or possible two wheels and a castor

Control of each wheel independently

Control discussed in lecture 3

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Bicycle drive

Two wheeled with one wheel control of direction

Only dynamically stable

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Catarpillar / Tracked vehicles

Frequently used in rough terrain

Requires skid steering

Poor control of motion.

Requires external sensors foraccurate control

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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)

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SHRIMP – wheeled climbing

Passive handling of roughterrain

6 wheels for stability

Size 60 x 20 cm

Overcomes obstacles uptodouble wheel diameter

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SHRIMP Motion

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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

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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)