Synthesis of spatial parallel mechanisms for a vertical and longitudinal all-terrain suspension Parallel Vertical & Longitudinal Suspension
[email protected] Clermont University French Institute for Advanced Mechanics (IFMA) EA3867, FR TIMS / CNRS 2856 Mechanical Engineering Research Group (LaMI)
Jean-Christophe FAUROUX BP 10448, F-63000, FRANCE IFMA, Clermont-Ferrand
The Joint International Conference of the XI International Conference on Mechanisms and Mechanical Transmissions (MTM) and the International Conference on Robotics (Robotics’12)
11th International Conference MTM-Robotics 2012, 6-8 June 2012, Clermont-Ferrand
1
Longitudinal suspension Wheeled locomotion on surfaces Parallel Vertical & Longitudinal Suspension
✔
Wheels are mostly suitable for motion on C1 continuous surfaces (tangency continuity)
✔
Obstacles in unstructured environment may provide only C0 continuity (contour continuity)
Positive obstacles & Bumps
Prev. Prev. works works
Considered obstacles have a C1 continuity and possibly only C0
Synthesis Synthesis
8
Purpose Purpose
h C1 but non C2
C0 but non C1
Non C0
h
8
Dimensioning Dimensioning
Negative obstacles & Holes
Conclusion Conclusion
Slope bike competition: C1 and C0
BMX race bike: C1 obstacles Jean-Christophe FAUROUX IFMA, Clermont-Ferrand
Trial bike: C0 obstacles
11th International Conference MTM-Robotics 2012, 6-8 June 2012, Clermont-Ferrand
2
Wheels for obstacle crossing Vehicle reference frame Parallel Vertical & Longitudinal Suspension Purpose Purpose Prev. Prev. works works
✔
X in the direction of longitudinal motion
✔
Z in the ascending direction
✔
Y oriented laterally so that (X,Y,Z) is direct
Obstacles ✔
Obstacles ≃ shapes with a roughly vertical front surface along Z
✔
Strong component of their normal vector along -X
✔
At high speed, the X reaction component becomes important
Synthesis Synthesis Dimensioning Dimensioning
Z Z
FV2
Conclusion Conclusion
G FH2 X X
Jean-Christophe FAUROUX IFMA, Clermont-Ferrand
FV1
FH1 N
Concept of a suspension allowing also the longitudinal X damping motion for better obstaclecrossing.
11th International Conference MTM-Robotics 2012, 6-8 June 2012, Clermont-Ferrand
3
2D dynamic modelling A suspension with 2 DOF ✔
Parallel Vertical & Longitudinal Suspension Purpose Purpose
Work published in [HUDEM 2010] J.C. Fauroux, J. Dakhlallah, B.C. Bouzgarrou, " A New Concept of FAST Mobile Rover with Improved Stability on Rough Terrain ", in Proc. of HUDEM'2010, 8th International Advanced Robotics Programme (IARP) Workshop on Robotics and Mechanical assistance in Humanitarian De-mining and Similar risky interventions, 10-12 May, 2010, National Engineering School of Sousse, Tunisia. Paper #26, 16 p.
✔ ✔
Multibody model (Adams) with 2DOF suspensions (vertical Z and longitudinal X) and a serial structure Simplified hypotheses: rigid bodies and wheels with contact and friction
Front suspension : V1 only Rear suspension : V2
Videos
Prev. Prev. works works ● ●
HUDEM HUDEM 10 10
● ●
CLAWAR CLAWAR 11 11
● ●
Vehicles Vehicles
● ●
Patents Patents
Synthesis Synthesis Dimensioning Dimensioning Conclusion Conclusion Jean-Christophe FAUROUX IFMA, Clermont-Ferrand
Front suspension : V1 + H1 Rear suspension : V2
Encouraging results ✔ ✔
With a longitudinal X supension on front wheel, a high obstacle can be dynamically crossed. Without the X suspension → tip-over A longitudinal DOF in the suspensions could benefit to longitudinal stability
11th International Conference MTM-Robotics 2012, 6-8 June 2012, Clermont-Ferrand
4
Experimental obstacle-crossing First, an experimental approach of obstacle-crossing Parallel Vertical & Longitudinal Suspension Purpose Purpose Prev. Prev. works works ● ●
HUDEM HUDEM 10 10
● ●
CLAWAR CLAWAR 11 11
● ●
Vehicles Vehicles
● ●
Patents Patents
Synthesis Synthesis Dimensioning Dimensioning Conclusion Conclusion Jean-Christophe FAUROUX IFMA, Clermont-Ferrand
✔
Complex phenomena : non-linear fast crash of deformable mechanisms with friction and sliding
✔
Published in [CLAWAR 2011] J.C. Fauroux and B.C. Bouzgarrou. " Dynamic Obstacle-Crossing of a Wheeled Rover with Double-Wishbone Suspension ", in "Field Robotics", Edited by Philippe BIDAUD, Mohammad O. TOKHI, Christophe GRAND and Gurvinder S. VIRK, World Scientific Publishing, ISBN-13 978-981-4374-27-9, Proc. 14th International Conference on Climbing and Walking Robots, CLAWAR'11, Septembre 06-08, 2011, Paris, France, pp. 642-649.
Choosing a mobile platform ✔
A fast & robust vehicle
✔
Small scale decreases the repair cost
✔
Easy to tip-over
Vehicle Mass Lxlxh Wheelbase Track width Centre of mass Wheel diameter Transmission Max speed
E-Maxx electric model #3903 (Traxxas) www.traxxas.com
E-Maxx 5.16 kg 518 x 419 x 242 mm 335 mm 330 mm Centred 150 mm 4x4 14 m/s
11th International Conference MTM-Robotics 2012, 6-8 June 2012, Clermont-Ferrand
5
Parallel Vertical & Longitudinal Suspension
Jean-Christophe FAUROUX IFMA, Clermont-Ferrand
11th International Conference MTM-Robotics 2012, 6-8 June 2012, Clermont-Ferrand
6
Parallel Vertical & Longitudinal Suspension
Jean-Christophe FAUROUX IFMA, Clermont-Ferrand
Double wishbone suspension, very close to real cars
11th International Conference MTM-Robotics 2012, 6-8 June 2012, Clermont-Ferrand
7
Experimental obstacle h
Adjustable C0 obstacle Parallel Vertical & Longitudinal Suspension Purpose Purpose
✔
Steel bar adjustable in height h
✔
Includes force measurement devices (Kistler 9257B)
C0 obstacle
Vertical rail for obstacle height adjustment
Prev. Prev. works works ● ●
HUDEM HUDEM 10 10
● ●
CLAWAR CLAWAR 11 11
● ●
Vehicles Vehicles
● ●
Patents Patents
Steel bracket
Synthesis Synthesis Dimensioning Dimensioning Conclusion Conclusion Jean-Christophe FAUROUX IFMA, Clermont-Ferrand
Kistler 3 component force sensor
Steel obstacle square section 25mm x 25mm
Steel mass of 5kg Adhesive
11th International Conference MTM-Robotics 2012, 6-8 June 2012, Clermont-Ferrand
8
Speed measurement 300 mm Distance ran in 1/30th of second (30Hz camera)
Parallel Vertical & Longitudinal Suspension Purpose Purpose Prev. Prev. works works ● ●
HUDEM HUDEM 10 10
● ●
CLAWAR CLAWAR 11 11
● ●
Vehicles Vehicles
● ●
Patents Patents
Synthesis Synthesis
Speed measured by vision Video
✔
30 Hz camera located on top of the impact zone
✔
Tiled floor with periodic pattern of 300mm
✔
Instantaneous speed comes from the 2 last images before impact
Dimensioning Dimensioning Conclusion Conclusion Jean-Christophe FAUROUX IFMA, Clermont-Ferrand
11th International Conference MTM-Robotics 2012, 6-8 June 2012, Clermont-Ferrand
9
Force measurement Fz
3 DOF force-plate Parallel Vertical & Longitudinal Suspension
Parameter Dimensions (mm) Force range (kN) Stiffness (kN/µm) Natural frequency (Hz) Mass (kg)
✔
X 170 -5 +5 1 2300 7,3
Acquisition 1kHz
Purpose Purpose Prev. Prev. works works
Impact force increases with obstacle height
Vehicles Vehicles
✔
Peaks of 400N
Patents Patents
✔
Fx ≈ Fz for v=8m/s and h=65mm
Synthesis Synthesis
✔
Need for a horizontal component of suspension
HUDEM HUDEM 10 10
● ●
CLAWAR CLAWAR 11 11
● ●
● ●
Dimensioning Dimensioning
Y 140 -5 +5 1 2300
Z 60 -5 +10 2 3500
Fy
Forces Fx and Fz for variable height h and speed v=8m/s h=25mm h=35mm h=45mm h=55mm h=65mm
Results ✔
● ●
Fx
Conclusion Conclusion Time [ms]
Jean-Christophe FAUROUX IFMA, Clermont-Ferrand
11th International Conference MTM-Robotics 2012, 6-8 June 2012, Clermont-Ferrand
10
Design of experiment (DoE) Summary of 77 experiments Parallel Vertical & Longitudinal Suspension
(h:25→75mm,v:3→8m/s)
✔
High obstacles → crash by tip-over (red dots)
✔
A stability front (red line) separates experiment with / without tip-over
✔
The front has a decreasing non-linear shape
✔
Traxxas E-Maxx standard Future suspension with 2 DOF will enhance stability zone (green line) Liste des essais
9
Purpose Purpose 8
Prev. Prev. works works ● ●
61 1
7 42
7
34 35 4 33 32
HUDEM HUDEM 10 10
● ●
Vehicles Vehicles Patents Patents
Synthesis Synthesis Dimensioning Dimensioning
Speed before Vitesse avantimpact impact (m/s) (m/s)
● ●
CLAWAR CLAWAR 11 11
Crossing without tip-over
60 19
47
24 68
12
56
11
6 ● ●
Crossing with tip-over
49
16
5
3
15 51 9 50 48
41 5
4
69 23
59
6
67
58 14
76 77
13 57
2 31 8
30
Stability front of the future FAST rover
22 70
21 66
75 26
40
3
20
Stability front of a classical rover
25
2
Videos
1
Conclusion Conclusion 0 20
Jean-Christophe FAUROUX IFMA, Clermont-Ferrand
25
30
35
40
45
50
55
60
65
70
75
80
Hauteur obstacle (mm)
Obstacle height (mm)
11th International Conference MTM-Robotics 2012, 6-8 June 2012, Clermont-Ferrand
11
Existing all-terrain vehicles Designed to be efficient for obstacle-crossing Parallel Vertical & Longitudinal Suspension Purpose Purpose
✔
Wheels of great diameter with respect to the obstacles to cross
✔
Robust rigid axle (a) or double wishbone suspensions (b-d)
✔
Deformable frame with parallel linkage for trial low speed crossing (e)
✔
Some mobile robots have joints between axles but no suspension (f)
✔
No commercial vehicle has a long-travel X-suspension of its wheels
(a) Car GMC 2500 HD
(b) Military truck Nexter Aravis
(c) ATV Polaris Sportsman XP850
Prev. Prev. works works ● ●
HUDEM HUDEM 10 10
● ●
CLAWAR CLAWAR 11 11
● ●
Vehicles Vehicles
● ●
Patents Patents
(d) Buggy BooXT
(e) RC car HPI Maverick Scout Crawler
(f) Robot Robosoft RobuROC 6
Synthesis Synthesis Dimensioning Dimensioning Conclusion Conclusion Jean-Christophe FAUROUX IFMA, Clermont-Ferrand
11th International Conference MTM-Robotics 2012, 6-8 June 2012, Clermont-Ferrand
12
Suspension patent analysis Longitudinal X motion is uncommon in suspension patents Parallel Vertical & Longitudinal Suspension
✔
Trailing and leading (a) arms allow coupled X-longi motion of the wheel
✔
Front-rear coupled trailing arms (b) or crash-deformable (c)
✔
6 DOF coupled motions with a Gough-Stewart parallel suspension (d)
✔
OCP (e) or SACLI suspensions couple vertical and lateral motions (a) US4179135
(b) EP1655159
(d) US6293561
Purpose Purpose Prev. Prev. works works ● ●
HUDEM HUDEM 10 10
● ●
CLAWAR CLAWAR 11 11
● ●
Vehicles Vehicles
● ●
Patents Patents
(c) US3869016
Synthesis Synthesis Dimensioning Dimensioning (f) WO2009/126787
Conclusion Conclusion Jean-Christophe FAUROUX IFMA, Clermont-Ferrand
(e) WO2004/009383
11th International Conference MTM-Robotics 2012, 6-8 June 2012, Clermont-Ferrand
13
Synthesis of new suspensions
Parallel Vertical & Longitudinal Suspension
New suspensions must be designed ✔
To absorb both vertical (Z) and longitudinal (X) reaction forces against obstacles (cf. models [HUDEM 10])
✔
The X and Z motions should be of the same order of magnitude (cf. experiments [CLAWAR 11])
✔
Usable on front and rear axles → the wheel needs 4 DOF
Purpose Purpose Prev. Prev. works works Synthesis Synthesis Dimensioning Dimensioning ✔
Conclusion Conclusion
✔
Z and X suspension translations
✔
Z rotation for steering
✔
Y rotation for transmission
X and Z translations should be as decoupled as possible (for active suspension control). Also decoupled from steering & power transmission
This work describes nine 2D and 3D kinematics
Jean-Christophe FAUROUX IFMA, Clermont-Ferrand
11th International Conference MTM-Robotics 2012, 6-8 June 2012, Clermont-Ferrand
14
V1 - 2D Serial suspension 2DOF with a serial mechanism Parallel Vertical & Longitudinal Suspension Purpose Purpose
✔
[HUDEM 10]
✔
Vertical joint: Wheel leg 120⟷ Glider 130
✔
Horizontal joint: Glider 130 ⟷ Frame 100
✔
Vertical joint is closer to the wheel → avoids collision of lower parts / ground
Prev. Prev. works works Synthesis Synthesis ● ●
2D 2D
● ●
3D 3D
✗
✗
101
130 150 100 140 110
Longitudinal crash generates bending of leg 120
111
No steering
Dimensioning Dimensioning Conclusion Conclusion
Jean-Christophe FAUROUX IFMA, Clermont-Ferrand
120
Y
Z X
Ground
11th International Conference MTM-Robotics 2012, 6-8 June 2012, Clermont-Ferrand
15
V2 - 2D Max. regular parallel 2DOF with a parallel decoupled mechanism
Prev. Prev. works works Synthesis Synthesis ● ●
2D 2D
● ●
3D 3D
✔
Cylinders can be active / adjustable / passive
✔
Same mobility, stiffness is improved in case of shocks
✗
Horizontal limb too low
✔
In (a), X shocks absorbed by Cylinder 2, no flexion of rod 243
✗
No steering
✗
✔
In (b), Cylinders 1-2 are attached to the frame to decrease the non- suspended mass
Prismatic joints: expensive & may lock (butting)
✔
The suspension is maximally regular: Jacobian ≡ Unit matrix
( ) [ ]( ) X˙ = 1 0 q˙1 0 1 q˙2 Z˙
255 252
Cylinder 2
251
242
Dimensioning Dimensioning
X
Conclusion Conclusion
254 241 243 242
200
Z
245 255
245
Cylinder 1
Purpose Purpose
2 PCR limbs copying the serial structure of V1
Cylinder 1
Parallel Vertical & Longitudinal Suspension
✔
200
Z
254
X
243 244
241
Cylinder 2
(a) Jean-Christophe FAUROUX IFMA, Clermont-Ferrand
244 251 253 252 220
210
(b)
244
253
220
210
11th International Conference MTM-Robotics 2012, 6-8 June 2012, Clermont-Ferrand
16
V3 - 2D Coupled Parallel 2DOF with a parallel coupled mechanism
Parallel Vertical & Longitudinal Suspension
✔
2 RCR limbs
✗
Coupled control
✔
No flexion, only compression → part downsizing
✗
Still no steering
✗
Lack of lateral Y stiffness
✔
R joints instead of P: cheaper, no butting
Purpose Purpose Prev. Prev. works works
2D 2D
● ●
3D 3D
Dimensioning Dimensioning
C yl in de r
351 353
2
352
Conclusion Conclusion
341 343 342
320
Z X Jean-Christophe FAUROUX IFMA, Clermont-Ferrand
344
355 345 1
● ●
354
C yl in de r
Synthesis Synthesis
300
310
11th International Conference MTM-Robotics 2012, 6-8 June 2012, Clermont-Ferrand
17
V4 - 3D Hybrid mechanism 4 DOF with a parallel-serial partially coupled mechanism
Parallel Vertical & Longitudinal Suspension Purpose Purpose
✔
Good lateral stiffness thanks to U-U bars 431-434
✔
Spherical translation of the wheel (N // bars, N>2)
✔
Steering the hub-carrier via a R joint put in series with the parallel structure (hybrid)
✔
Maximally regular behaviour ONLY in the neutral position of the spherical workspace No more 400 variations of 440 the pitch Z2 angle of the hub-carrier 420 410 (as 320 had)
Prev. Prev. works works Synthesis Synthesis ● ●
2D 2D
● ●
3D 3D
Dimensioning Dimensioning Conclusion Conclusion
✔
✔
Deep recessed tyre-rims prevent direct attachment of dampers 440-450 to 421
✗
Collision 410-450 when steering
450
Transmission is easy to integrate CAD by Anthony Riesemann (IFMA project 2009)
Jean-Christophe FAUROUX IFMA, Clermont-Ferrand
✗
O X
Z Y
433 434 420 421 431 432 470
11th International Conference MTM-Robotics 2012, 6-8 June 2012, Clermont-Ferrand
18
V5 - 3D Hybrid mechanism 4DOF with a variant of V4
Parallel Vertical & Longitudinal Suspension
✔
Bars 531-534 located in a rhomboid layout
✔
Tob-bar 533 provides easy connection to Z damper 540
Purpose Purpose ✔
Prev. Prev. works works Synthesis Synthesis ● ●
2D 2D
● ●
3D 3D
Dimensioning Dimensioning
✔
Rear bar 534 provides easy connection to X damper 550
✗
500 X
Collision 510-550 when steering
540
510
Z
Y
Damping attachment at mid-bars (no more inside the rim)
Conclusion Conclusion
550 CAD by Richard Cousturier (IFMA project 2010) Jean-Christophe FAUROUX IFMA, Clermont-Ferrand
531 532 533 534 570 11th International Conference MTM-Robotics 2012, 6-8 June 2012, Clermont-Ferrand
19
V6 - 3D parallel mechanism 4DOF with only 3 bars ✔
Parallel Vertical & Longitudinal Suspension ✔
Purpose Purpose Prev. Prev. works works Synthesis Synthesis ● ●
2D 2D
● ●
3D 3D
Dimensioning Dimensioning Conclusion Conclusion
✗
Rotating rudder-bar 661 around Z1 → differential traction in 631 and 632 → rotation around Z2 of hubcarrier 720 Improved integration: Steering linkage re-uses bars 631632 from the lateral guidance linkage Deep recessed tyre-rims prevent direct attachment of dampers 640-650 to 620
640 Z1 Z2
Z 633 631
X
Y
620
661 600 632 610 650
Jean-Christophe FAUROUX IFMA, Clermont-Ferrand
11th International Conference MTM-Robotics 2012, 6-8 June 2012, Clermont-Ferrand
20
V7 - 3D parallel mechanism 4DOF with only 3 bars ✔
Parallel Vertical & Longitudinal Suspension
✔
Purpose Purpose Prev. Prev. works works Synthesis Synthesis ✔ ● ●
2D 2D
● ●
3D 3D
Dimensioning Dimensioning Conclusion Conclusion
Jean-Christophe FAUROUX IFMA, Clermont-Ferrand
✗
Dampers 740 and 750 attached around the middle of bars 733 and 732 → no collision with wheel 710 Steering axis Z2 passes through the centre of the wheel contact patch → Minimal steering friction Transmission line 770 with shafts connected by U joints
X
Z 740
Y
Z2
Z1
710 720 733
700 731
E E731 733
E770
Coupling between steering and horizontal damping
E732
761
770
732 750
11th International Conference MTM-Robotics 2012, 6-8 June 2012, Clermont-Ferrand
21
V8 - 3D parallel mechanism 4DOF with only 3 bars ✔
Parallel Vertical & Longitudinal Suspension ✔
Purpose Purpose
Dampers 840 and 850 attached around the middle of top-bar 833 → No more coupling steering/X motion
Z
833 820 810 840 Z1
X Z2
Y
850
No bottom bar → no interference with obstacles
Prev. Prev. works works Synthesis Synthesis ● ●
2D 2D
● ●
3D 3D
831 870 832
861
800
Dimensioning Dimensioning Conclusion Conclusion
Jean-Christophe FAUROUX IFMA, Clermont-Ferrand
11th International Conference MTM-Robotics 2012, 6-8 June 2012, Clermont-Ferrand
22
V9 - 3D parallel mechanism A variant of V8 ✔
Parallel Vertical & Longitudinal Suspension Purpose Purpose
✔
✔
Bars 932-933 (bottomtop) → lateral guidance Front bar 931 for steering
Z 940
900
X
Y 910
920
961 933 931
Compatible with existing vehicles with double-wishbone suspension.
Prev. Prev. works works Synthesis Synthesis ● ●
2D 2D
● ●
3D 3D
950 932 970
Dimensioning Dimensioning ✗ Conclusion Conclusion
Jean-Christophe FAUROUX IFMA, Clermont-Ferrand
Bottom bar → risk of interference with obstacles
11th International Conference MTM-Robotics 2012, 6-8 June 2012, Clermont-Ferrand
23
Dimensional synthesis of V8 CAD model and technological implementation Parallel Vertical & Longitudinal Suspension Purpose Purpose Prev. Prev. works works Synthesis Synthesis Dimensioning Dimensioning Conclusion Conclusion
✔
U-U limbs with double damper
✔
Limbs 840 and 850 connect to 832 on disjoint S joints
✔
840
800
854 Shifted U joint on 853 transmission line 852 852' 850
Z1
Z2
861 833 832 870 831 Z Y 810 820
Jean-Christophe FAUROUX IFMA, Clermont-Ferrand
11th International Conference MTM-Robotics 2012, 6-8 June 2012, Clermont-Ferrand
X 24
Dimensional synthesis of V8 CAD model and technological implementation
Parallel Vertical & Longitudinal Suspension
✔
Inter-bar distance B should be as large as possible: – Better steering stiffness – Limited by the non-interference between the bars and the tyre-rim – Avoid collision with transmission line, whatever the position
✔
Bar length L as long as possible → larger spherical translation radius –
XZ planar motion approximation
Purpose Purpose Prev. Prev. works works Synthesis Synthesis
Z X
Dimensioning Dimensioning Conclusion Conclusion
L B Y X
Jean-Christophe FAUROUX IFMA, Clermont-Ferrand
11th International Conference MTM-Robotics 2012, 6-8 June 2012, Clermont-Ferrand
25
Real implementation of V8 w1 > w2 New steering linkage and stronger servomotor Parallel Vertical & Longitudinal Suspension Purpose Purpose Prev. Prev. works works Synthesis Synthesis
Video
Dimensioning Dimensioning Conclusion Conclusion
Jean-Christophe FAUROUX IFMA, Clermont-Ferrand
w1
w2
11th International Conference MTM-Robotics 2012, 6-8 June 2012, Clermont-Ferrand
26
Conclusion
Z Z
FV2 G
X X
Parallel Vertical & Longitudinal Suspension Purpose Purpose Prev. Prev. works works Synthesis Synthesis Dimensioning Dimensioning
N
Innovating with a longitudinal suspension ✔
A suspension designed for FAST obstacle-crossing should have 4 DOF - Z vertical damping translation - Z steering rotation - X longitudinal damping translation - Y transmission rotation
✔
Confirmed by multibody 2D model Confirmed by 77 experiments Pushing-up the tip-over stability limit f(h,v)=cte
✔ ✔
Structural synthesis of nine suspensions ✔ ✔ ✔ ✔
Conclusion Conclusion
FV1
FH1
FH2
✔
3-2D and 6-3D kinematics 8 parallel and 6 spatial kinematics Most of them are patented [Fauroux-Cousturier 2012] Campaign of obstacle-crossing experiments → comparing 4DOF vs. 3DOF Associated control strategies.
Acknowledgements ✔ ✔
Jean-Christophe FAUROUX IFMA, Clermont-Ferrand
French National Research Agency (ANR) for funding this work through the FAST project (FAST Autonomous Rover) IFMA students for their contribution to the FAST project : Frédéric KREIT, Anthony RIESEMANN, Aurélien AUTHIER, Solange OVAZZA, Richard COUSTURIER, Thibaud DEJEANTE and Romain VENDRÔME 11th International Conference MTM-Robotics 2012, 6-8 June 2012, Clermont-Ferrand
27
