LaMI Mechanical Engineering Research Group

TIMS

UBP

IFMA

Research Federation

Blaise Pascal University Clermont-Ferrand II

French Institute for Advanced Mechanics

Improving Obstacle Climbing with the Hybrid Mobile Robot OpenWHEEL i3R [email protected] [email protected] Frédé[email protected] IFMA Campus de Clermont-Ferrand / Les Cézeaux, B.P. 265 63175 AUBIERE Cedex FRANCE

Fauroux / Bouzgarrou / Chapelle LaMI, Clermont-Ferrand, France CLAWAR ' 09, Istanbul, Turkey

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Hybrid Locomotion Locomotion systems can be defined as poly-articulated mechanical systems that interact with environment via a set of unilateral adherent or slipping contacts to the ground. These contacts may change in nature and number according to time and space [Ben Amar, Bidaud 2007]

Introduction Introduction Hybrid Hybrid locom. locom. Hybrid Hybrid robots robots Objectives Objectives

OpenWHEEL OpenWHEELi3R i3R Non-symmetry Non-symmetry Dim. Dim.analysis analysis

Terrestrial vehicles & robots

• • •

Hybrid locomotion

• •

● ● ●

Fauroux / Bouzgarrou / Chapelle LaMI, Clermont-Ferrand, France CLAWAR ' 09, Istanbul, Turkey

Combining the advantages of wheel and leg Other solution: deformable frame

Our objective: Improving locomotion ●

Conclusion Conclusion

Wheeled robots prevail (excellent energetic efficiency) Lack of agility / blocked on obstacles Legs / Tracks interesting for all terrain / climbing

Wheeled robots That climb step obstacles With only four wheels And a stable behaviour 2

Existing Hybrid Mobile Robots Categories of Hybrid robots

Introduction Introduction Hybrid Hybrid locom. locom. Hybrid Hybrid robots robots

• • •

Wheels on legs vs. deformable frame Active / passive Difficulties: stiffness, power, control

RobuROC 6 (150 kg, 1.5m long) Active deformable frame 3 tiltable axles with passive warping Able to turn on itself, climb obstacles www.robosoft.fr

WorkPartner (230 kg, 1.4m long, 7km/h) 4 wheels on legs (3 DOF per leg) Steering via central joint Many locomotion modes automation.tkk.fi

Objectives Objectives

OpenWHEEL OpenWHEELi3R i3R Non-symmetry Non-symmetry

Shrimp Passive deformable frame 6 wheels on 2 // bogies and 1 front linkage Excellent climbing abilities but requires 6 wheels www.asl.ethz.ch

Dim. Dim.analysis analysis Conclusion Conclusion

Fauroux / Bouzgarrou / Chapelle LaMI, Clermont-Ferrand, France CLAWAR ' 09, Istanbul, Turkey

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Objectives of the Work Within the OpenWHEEL project

Introduction Introduction

• • •

End of the car central-engine paradigm New articulated frames OpenWHEEL project, an open architecture for hybrid wheeled robots Wireless connection

Hybrid Hybrid locom. locom.

S 32

A3

Hybrid Hybrid robots robots

Rear

Control

A2

W22

Wheel W31

S 21

W21

W12

Camera

S22

S 12

A1

Control

I2

S 31

Objectives Objectives

CAN Bus

W 32

Control

I1

S 11

W11

nt Fro Z X Y

OpenWHEEL OpenWHEELi3R i3R Suspension mechanism Saw

Non-symmetry Non-symmetry

Swing arm

Double wishbone

Innovative suspension

Inter-axle mechanism Ia Serial Parallel Innovative mechanism mechanism mechanism

Dim. Dim.analysis analysis Conclusion Conclusion

Fauroux / Bouzgarrou / Chapelle LaMI, Clermont-Ferrand, France CLAWAR ' 09, Istanbul, Turkey

Objectives of this work

• • •

Study the OpenWHEEL i3R specific robot Analyse its behaviour during obstacle climbing Dimensional analysis for better climbing

4

OpenWHEEL i3R Architecture Exploring wheel (W12) Wheel (W12) joint R12

OpenWHEEL OpenWHEELi3R i3R Architecture Architecture

y12

Central warping joint R0 Rear frame (F2) Rear steering joint R2

Climbing Climbing proc. proc.

A22 O22

Non-symmetry Non-symmetry W22

Dim. Dim.analysis analysis

P22 Rear axle steering angle 2

Fauroux / Bouzgarrou / Chapelle LaMI, Clermont-Ferrand, France CLAWAR ' 09, Istanbul, Turkey

B12 zF1

yF2 O

yA2

B22

x

P11

A21

G'

O21 P21 rW x0

Step Obstacle

Advantages

W21

O0

hS

Lifting polygon Stability on three wheels

B21

y0

O11 W11

xA2

z0

A11

G1 B11

H

Reconfigured rear axle (A2)

OA1

Front steering joint R1 Exploring front axle (A1)

2 =O F

G

G2

= xF

F1

Front axle steering angle 1

xA1

2

F1

T2 zA2

zA1 T1 yA1

zF2

OA2

Conclusion Conclusion

x12 A12

O12 W12

Warping angle 0

Introduction Introduction

Front frame (F1)

z12

Only four wheels like most vehicles Active frame with only one actuator Stable when climbing obstacle 5 Precise steering via double Ackermann

OpenWHEEL i3R Climbing Process Properties for stability ● ●

OpenWHEEL OpenWHEELi3R i3R Architecture Architecture

Checking stability on three wheels ● ●

Climbing Climbing proc. proc.

Non-symmetry Non-symmetry Dim. Dim.analysis analysis

Fauroux / Bouzgarrou / Chapelle LaMI, Clermont-Ferrand, France CLAWAR ' 09, Istanbul, Turkey

Wheel W11 (front-right)

Wheel W12 (front-left)

Wheel W21 (rear-right)

1)

2)

3)

W12

Wheel W22 (rear-left) 4)

W11 G

G

G

W22

G

W21 5)

Rear axle steering

Conclusion Conclusion

●

2D model Stable if the lifted wheel is inside the turn Climbing process in 19 stages and 6 phases

Front axle steering

Introduction Introduction

Can be stable on three wheels Axle steering - does not change the position of the centre of mass - changes the position of the contact points

W11

G

6)

W12

7)

G

8)

G

G W21

Stable

Unstable

Stable

W22

Unstable

6

OpenWHEEL i3R Climbing Process A - Prepairing

Low

W22

Introduction Introduction

W11

W21

2

W12

B - W11 climbing

3

4

5

7

8

9

12

13

14

17

18

19

High

1

Wheel center motion

6

C - W12 climbing

Wheel lifting

OpenWHEEL OpenWHEELi3R i3R Architecture Architecture

Wheel landing Support polygon For a very stable configuration (Four contact points)

For a stable configuration (Three contact points)

Climbing Climbingproc. proc.

Non-symmetry Non-symmetry

10

D – Going forward

11

E - W21 climbing

Dim. Dim.analysis analysis Conclusion Conclusion 15

Fauroux / Bouzgarrou / Chapelle LaMI, Clermont-Ferrand, France CLAWAR ' 09, Istanbul, Turkey

F - W22 climbing

16

G - Conclusion

7

OpenWHEEL i3R Climbing Process Modeling and testing ● ●

Introduction Introduction OpenWHEEL OpenWHEELi3R i3R

●

●

Architecture Architecture Climbing Climbingproc. proc.

Non-symmetry Non-symmetry

●

2D model very helpful to build the complete climbing process Not acceptable for high pitch angles or strong warping Validation in 3D required 3D Multibody model with Adams

02

03

Reduced size demonstrator built in Lego Mindstorms 04

Dim. Dim.analysis analysis Conclusion Conclusion

eo d Vi

1

2 o05 e d Vi 06

Fauroux / Bouzgarrou / Chapelle LaMI, Clermont-Ferrand, France CLAWAR ' 09, Istanbul, Turkey

8

Front-Rear Non-Symmetry Real testing revealed a non-symmetric behaviour ●

Axle A1 climbs easily whereas axle A2 has difficulties

Introduction Introduction OpenWHEEL OpenWHEELi3R i3R

G1 170 mm

Non-symmetry Non-symmetry

G G2

CW 150 g

Dim. Dim.analysis analysis W12 b  =  17 5 

m

m

  90  1 t =

h l = 72 mm

Conclusion Conclusion

m

m

Mass: 1.5 kg W22

● ●

Fauroux / Bouzgarrou / Chapelle LaMI, Clermont-Ferrand, France CLAWAR ' 09, Istanbul, Turkey

Solved by adding a counter-weight CW of 150 g Best obstacle height : 55 mm, 67% of the height of the centre of mass

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Front-Rear Non-Symmetry Explanation ● ● ●

Introduction Introduction ●

OpenWHEEL OpenWHEELi3R i3R

●

Non-symmetry Non-symmetry

a)

Non-symmetry was not predicted because of 2D approximation On flat ground, the 2D model is exact With some pitch - In 2D, stability margin P 2 G ' =b cos / 2 P 2 G ' =b cos / 2−hl h s / b - In 3D Stability is favoured at stages 3 and 7 and penalized at stages 12 and 16 Adding CW equilibrates the climbing capacities of front and rear axles 2D model: On flat ground

Dim. Dim.analysis analysis

b)

2D model: On a step

3D model: stability margin nullifies

b G

G'

G

Conclusion Conclusion

hl z0 O0

rW

G' x0

P2

P1

 P1

z0 x0 P2

O0

3D model with counterweight CW: stability is back

hs

G'

3D model: On a step

c)

f)

e)

G'



Fauroux / Bouzgarrou / Chapelle LaMI, Clermont-Ferrand, France CLAWAR ' 09, Istanbul, Turkey

O0

CW

 P1

rW x0

G'

 G

hl z0

Example: Stage 12

2D model: supposed stable

d)

P2

G'

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Dimensional Analysis Which are the key parameters to maximize climbing performance ? Introduction Introduction

Dimensional analysis of several parameters

OpenWHEEL OpenWHEELi3R i3R

●

Non-symmetry Non-symmetry

● ●

Dim. Dim.analysis analysis Conclusion Conclusion

● ● ●

Track width t Wheelbase b Wheel radius rw Leg height hl Mass Mass repartition

hl

t

ar e R

W21 Fauroux / Bouzgarrou / Chapelle LaMI, Clermont-Ferrand, France CLAWAR ' 09, Istanbul, Turkey

W22

nt o r F

W12

W11 b

rw

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Dimensional Analysis: Track Width t Influence of t on the climbing capacity ● ●

Introduction Introduction

●

The bigger the track width, the higher the obstacle θ0Max is around 45° to avoid tire roll-off

h Max =t sin  0 Max 

Bound for the minimal value of t

t Min =h S / sin  0 Max 

OpenWHEEL OpenWHEELi3R i3R Non-symmetry Non-symmetry Dim. Dim.analysis analysis Track Track width width Wheelbase Wheelbase Wheel Wheel radius radius

hMax



hMax hs

Leg Leg height height Mass Mass

Conclusion Conclusion

t Fauroux / Bouzgarrou / Chapelle LaMI, Clermont-Ferrand, France CLAWAR ' 09, Istanbul, Turkey

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Dimensional Analysis: Wheelbase b Influence of b during steering ● ●

Introduction Introduction OpenWHEEL OpenWHEELi3R i3R

Minimum wheelbase bMin to avoid axle-collision when double steering b t Closure condition when wheels are in contact: = cos  1 Max r W sin  1 Max  2 2

●

Gives bMin

●

… or tMax

Non-symmetry Non-symmetry Dim. Dim.analysis analysis

b

Track Track width width

1 Max45°

Wheelbase Wheelbase Wheel Wheel radius radius

t/2

Leg Leg height height Mass Mass

rW

Conclusion Conclusion ● ● Fauroux / Bouzgarrou / Chapelle LaMI, Clermont-Ferrand, France CLAWAR ' 09, Istanbul, Turkey

Increasing b attenuates the front-rear non-symmetry b cannot be too long ! bMax = 2.t

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Dimensional Analysis: Wheel Radius rW Influence of wheel radius rw on the obstacle ●

Introduction Introduction OpenWHEEL OpenWHEELi3R i3R

● ●

Vehicles without articulated frame only cross small obstacles

rW

Min

= 4.ho

With the articulated frame, wheel radius is independent of obstacle height Suggested index of performance : % of the height of centre of mass

Non-symmetry Non-symmetry Dim. Dim.analysis analysis Track Track width width Wheelbase Wheelbase Wheel Wheel radius radius Leg Leg height height

Small obstacle

Mass Mass

Conclusion Conclusion

Fauroux / Bouzgarrou / Chapelle LaMI, Clermont-Ferrand, France CLAWAR ' 09, Istanbul, Turkey

ho

hs

Big Step

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Dimensional Analysis: Wheel Radius rW Maximum wheel radius rw Introduction Introduction

●

If rW grows too much → wheel-wheel collision

●

Exploring wheel has longer way along x0 to go above the obstacle:

OpenWHEEL OpenWHEELi3R i3R

Wall-Wheel contact

rW

Max

= t/2

Non-symmetry Non-symmetry Dim. Dim.analysis analysis Track Track width width Wheelbase Wheelbase

t/2

Wheel Wheel radius radius Leg Leg height height Mass Mass

Conclusion Conclusion

x0 Fauroux / Bouzgarrou / Chapelle LaMI, Clermont-Ferrand, France CLAWAR ' 09, Istanbul, Turkey

rW

15

Dimensional Analysis: Leg Height hl Which leg height hl ? Introduction Introduction

●

A minimum value of hl to avoid collision with obstacle edge

r W h l≥h s

●

Legs too high increase the front-rear non-symmetry

r W h l≤2 h s

OpenWHEEL OpenWHEELi3R i3R Non-symmetry Non-symmetry Dim. Dim.analysis analysis Track Track width width

Lower bound on hl hl Min=hs −r W

Wheelbase Wheelbase

Upper bound on hl

Wheel Wheel radius radius

hl Max=2 hs −r W

Leg Leg height height Mass Mass

Conclusion Conclusion

Fauroux / Bouzgarrou / Chapelle LaMI, Clermont-Ferrand, France CLAWAR ' 09, Istanbul, Turkey

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Dimensional Analysis: Mass Which mass ? ● ●

Introduction Introduction

●

Need for a minimal tangential force to climb When mass ↑, tangential force ↑ so mass is not a significant parameter On granular terrains, a heavy robot may dig ruts on the track

OpenWHEEL OpenWHEELi3R i3R

Which mass repartition ?

Non-symmetry Non-symmetry

●

Dim. Dim.analysis analysis Track Track width width Wheelbase Wheelbase

●

Which maximal obstacle height hs Max? ● ●

Wheel Wheel radius radius

Lateral symmetry must be respected Longitudinal symmetry must be broken for A2 to climb as well as A1

4

Critical stages = the third stages of each phase = stages 4, 8, 13 and 17 Direct geometric model + Static analysis must be solved for each stage 8

13

17

Leg Leg height height Mass Mass

Conclusion Conclusion ● Fauroux / Bouzgarrou / Chapelle LaMI, Clermont-Ferrand, France CLAWAR ' 09, Istanbul, Turkey

Approximation of hs Max

h s Max =t sin  0 Max 

17

Towards a Full Scale Experiment List of main parameters ●

Each parameter can be bounded (the bound values of

●

Parameters sorted by order of selection

Introduction Introduction OpenWHEEL OpenWHEELi3R i3R Non-symmetry Non-symmetry Dim. Dim.analysis analysis

●

Conclusion Conclusion Full Full scale scale Conclusion Conclusion

●

Parameter

Name

Lower bound

Track width

t

t Min =h S  2

t Max=b 2−2rW

Wheel radius

rW

r W Min=4 h O

r W Max =t / 2

Wheelbase

b

b Min =  2t / 2r W 

b Max =2 . t

Leg height

hl

h l Min =h s−r W

h l Max =2 h s−r W

θ0 , θ1 , θ2 are set to 45°)

Upper bound

CAD model of OpenWHEEL i3R fullscale

From these rules are deduced the dimensions of OpenWHEEL i3R in its fullscale implementation Main dimensions : - t = 1.2m - rw = 0.2m - Mass 150 kg - Five DC actuators of 330W 30Nm - Central warping joint with clutch

Fauroux / Bouzgarrou / Chapelle LaMI, Clermont-Ferrand, France CLAWAR ' 09, Istanbul, Turkey

18

Conclusion Main results ● ● ●

Introduction Introduction OpenWHEEL OpenWHEELi3R i3R

● ●

OpenWHEEL i3R: a hybrid mobile robot with deformable frame Front-Rear non-symmetry Dimensional analysis of its main parameters Design rules to build a robot according to the obstacles to be climbed Fullscale implementation of the robot is in progress

Non-symmetry Non-symmetry Dim. Dim.analysis analysis Conclusion Conclusion Full Full scale scale Conclusion Conclusion

Fauroux / Bouzgarrou / Chapelle LaMI, Clermont-Ferrand, France CLAWAR ' 09, Istanbul, Turkey

IFMA students working on the project Laurent GENEVAY et al.

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