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  • 1. Experimental Validation of a Multibody Model for a Vehicle Prototype and its Application to State Observers Roland Pastorino A thesis submitted for the degree of Doctor Ingeniero Industrial June 25, 2012, Ferrol, SpainMechanical Engineering Laboratory, University of La Coruña
  • 2. 0  Outline 1 Motivations 2 Vehicle eld testing 3 Vehicle modeling and simulation environment 4 Validation results 5 State observers 6 Conclusions Mechanical Engineering Laboratory, University of La Coruña 2/48
  • 3. 1  Outline 1 Motivations 2 Vehicle eld testing 3 Vehicle modeling and simulation environment 4 Validation results 5 State observers 6 Conclusions Mechanical Engineering Laboratory, University of La Coruña 3/48
  • 4. 1  Motivations Laboratorio de Ingeniería Mecánica (LIM). Specialized in realtime simulations of rigid and exible multibody systems Fig. 1  Realtime simulations of Fig. 2  Realtime simulations of vehicles excavators Fig. 3  Realtime simulations of Fig. 4  HumanInTheLoop container cranes simulators of excavators Mechanical Engineering Laboratory, University of La Coruña 4/48
  • 5. 1  Motivations Multibody dynamics analysis in the automotive eld. comfort ride accuracy analysis noise & vibration highly durability detailed analysis models crash worthiness crash ease ANALYSIS analysis of use MB MODELS TYPES nonlinear vehicle handling dynamics special analysis formu. design & realtime eciency tuning of reduced app required controllers models HIL & HITL Mechanical Engineering Laboratory, University of La Coruña 5/48
  • 6. 1  Motivations Multibody dynamics analysis in the automotive eld. comfort ride accuracy analysis noise & vibration highly durability detailed analysis models crash worthiness crash ease ANALYSIS analysis of use MB MODELS TYPES nonlinear vehicle handling dynamics special analysis formu. design & realtime eciency tuning of reduced app required controllers models HIL & HITL Mechanical Engineering Laboratory, University of La Coruña 5/48
  • 7. 1  Motivations Multibody dynamics analysis in the automotive eld. comfort ride accuracy analysis noise & vibration highly durability detailed analysis models crash worthiness crash ease ANALYSIS analysis of use MB MODELS TYPES nonlinear vehicle handling dynamics special analysis formu. design & realtime eciency tuning of reduced app required controllers models HIL & HITL Mechanical Engineering Laboratory, University of La Coruña 5/48
  • 8. 1  Motivations Multibody dynamics analysis in the automotive eld. comfort ride accuracy analysis noise & vibration highly durability detailed analysis models crash worthiness crash ease ANALYSIS analysis of use MB MODELS TYPES nonlinear vehicle handling dynamics special analysis formu. design & realtime eciency tuning of reduced app required controllers models HIL & HITL Mechanical Engineering Laboratory, University of La Coruña 5/48
  • 9. 1  Motivations Multibody dynamics analysis in the automotive eld. comfort ride accuracy analysis noise & vibration highly durability detailed analysis models crash worthiness crash ease ANALYSIS analysis of use MB MODELS TYPES nonlinear vehicle handling dynamics special analysis formu. design & realtime eciency tuning of reduced app required controllers models HIL & HITL Mechanical Engineering Laboratory, University of La Coruña 5/48
  • 10. 1  Motivations Multibody dynamics analysis in the automotive eld. comfort ride accuracy analysis noise & vibration highly durability detailed analysis models crash worthiness crash ease ANALYSIS analysis of use MB MODELS TYPES nonlinear vehicle handling dynamics special analysis formu. design & realtime eciency tuning of reduced app required controllers models HIL & HITL Mechanical Engineering Laboratory, University of La Coruña 5/48
  • 11. 1  Motivations Objectives. Without validation of the vehicle dynamics there is only speculation that a given model accurately predicts a vehicle response A.H. Hoskins and M. El-Gindy, Technical report: Literature survey on driving simulator validation studies, International Journal of Heavy Vehicle Systems, vol. 13 (3), pp. 241252, (2006) reliability and validity of the modeling procedure and MB formulation to simulate new insigths into comprehensive vehicle models the automotive re- search line of the LIM state estimation using MB models applied to vehicle dynamics Mechanical Engineering Laboratory, University of La Coruña 6/48
  • 12. 2  Outline 1 Motivations 2 Vehicle eld testing 3 Vehicle modeling and simulation environment 4 Validation results 5 State observers 6 Conclusions Mechanical Engineering Laboratory, University of La Coruña 7/48
  • 13. 2  Vehicle eld testing Validation methodology. based on the validation methodology developed by the VRTC (Vehicle Research and Test Center) for the NADS (National Advanced Driving Simulator) composed of 3 main phases 1  experimental 2  vehicle parameter 3  simulation predictions data collection measurement vs experimental data vehicle eld testing parameter simulations using the same maneuvers → broad range of measurements for the control inputs that were vehicle operating conditions MB model and the measured at the 1st phase subsystem models comparisons between the repetitive maneuvers to determine the random simulation & experimental uncertainty results experimental postprocessing Fig. 5  NADS bay Mechanical Engineering Laboratory, University of La Coruña 8/48
  • 14. 2  Vehicle eld testing Diagram of the iterative validation methodology. vehicle reference maneuver brake model tire model maneuver MB formu. repetitions + integrator sensor outputs vehicle model Mechanical Engineering Laboratory, University of La Coruña 9/48
  • 15. 2  Vehicle eld testing Diagram of the iterative validation methodology. test track topo. survey virtual en- vironment vehicle reference maneuver brake model tire model maneuver benchmark MB formu. repetitions input data + integrator sensor outputs vehicle model vehicle parameter measurement Mechanical Engineering Laboratory, University of La Coruña 9/48
  • 16. 2  Vehicle eld testing Diagram of the iterative validation methodology. test track topo. survey virtual en- vironment vehicle reference maneuver brake model tire model maneuver benchmark MB formu. repetitions input data + integrator sensor outputs sensor outputs comparisons vehicle model vehicle parameter measurement Mechanical Engineering Laboratory, University of La Coruña 9/48
  • 17. 2  Vehicle eld testing Diagram of the iterative validation methodology. test track topo. survey virtual en- vironment vehicle reference maneuver brake model tire model maneuver benchmark MB formu. repetitions input data + integrator sensor outputs sensor outputs comparisons vehicle model vehicle parameter measurement Mechanical Engineering Laboratory, University of La Coruña 9/48
  • 18. 2  Vehicle eld testingThe XBW vehicle prototype. selfdeveloped from scratch onboard digital acquisition system longitudinal and lateral maneuver repetition capabilityMechanical characteristics. Fig. 6  Design and manufacturing tubular frame internal combustion engine (4 cylinders, 2barrel carburator) automatic gearbox transmission front suspension → double wishbone rear suspension → MacPherson tyres → Michelin E3B1 Energy 155/80 R13 Fig. 7  XBW vehicle prototype Mechanical Engineering Laboratory, University of La Coruña 10/48
  • 19. 2  Vehicle eld testing Steering wheel Encoder BThe bywire systems of the prototype. Precision gearbox Encoders A Coreless DC motor SBW → steerbywire Precision gearbox Torque sensor TBW → throttlebywire Rack and pinion gear system BBW → brakebywire Fig. 8  Steerbywire systemExtra sensors. Measured magnitudes Sensors vehicle accelerations (X,Y,Z) accelerometers (m/s2 ) vehicle angular rates (X,Y,Z) gyroscopes (rad/s) vehicle orientation angles inclinometers (rad) wheel rotation angles halleect sensor (rad) Fig. 9  Throttlebywire brake line pressure pressure sensor (kP a) system steering wheel and steer angles encoders (rad) engine speed halleect sensors (rad/s) steering torque inline torque sensor (N m) throttle pedal angle encoder (rad) rear wheel torque wheel torque sensor (N m) Fig. 10  Brakebywire system Mechanical Engineering Laboratory, University of La Coruña 11/48
  • 20. 2  Vehicle eld testingDrivers force feedback of the SBW. objective → accurate torque feedback to the driver problem → exibility, backlash & friction solution → highly accurate model of the assembly ampliermotorgearbox future work → model based torque controller Fig. 12  Steering wheel system 4 1 3 2 4 Quadrant Linear PMDC Motor Gearbox Steering Wheel Servoamplifier Fig. 11  Scheme of the modeling Fig. 13  CAD model of the steering wheel system Mechanical Engineering Laboratory, University of La Coruña 12/48
  • 21. 2  Vehicle eld testing 7 repetitions of a low speed straightline maneuver. total distance = 63.5 m max speed = 23 km/h Mechanical Engineering Laboratory, University of La Coruña 13/48
  • 22. 2  Vehicle eld testing 6 repetitions of a lowspeed Jturn maneuver. total distance = 59.6 m max speed = 18 km/h Mechanical Engineering Laboratory, University of La Coruña 14/48
  • 23. 3  Outline 1 Motivations 2 Vehicle eld testing 3 Vehicle modeling and simulation environment 4 Validation results 5 State observers 6 Conclusions Mechanical Engineering Laboratory, University of La Coruña 15/48
  • 24. 3  Vehicle modeling and simulation environment Vehicle modeling. Type of coordinates : natural + some relative coordinates (angles & distances) MB formulation : index3 augmented Lagrangian formulation with massdampingstinessorthogonal projections Bodies / Variables : 18 → all the vehicle bodies / 168 → points and vectors Steering : kinematically guided Forces : gravity forces, tire forces, engine torque, brake torques Degrees of freedom : 14 → suspension systems (4) chassis (6) wheels (4) Fig. 14  CAD model of the prototype Fig. 15  Points & vectors of the MB model Mechanical Engineering Laboratory, University of La Coruña 16/48
  • 25. 3  Vehicle modeling and simulation environment Ecient MB formulation developed and used at LIM. index3 augmented Lagrangian formulation with massdampingstinessorthogonal projections integration → the trapezoidal rule and the NewtonRaphson method eq. of motion→ 2 rst order trap. rule predictor → ∆t f = (Mq + ¨ approx. → & q, q, q ˙ ¨ 4 ΦT αΦ + ΦT λ − Q) fq ∆q = −f λ = λ + αΦ q q tangent matrix → eq. of motion→ tangent matrix → ∆t ∆t fq = M + C+ ∆t 2 fq = M + C+ 2 f = (Mq + ¨ 2 ∆t2 T 4 ∆t2 T (Φq αΦq + K) ΦT αΦ + ΦT λ − Q) q q (Φq αΦq + K) 4 4 no error < min → projections in velocities t = t + ∆t ∆t ∆t2∆t2 T fq q = ˙ M+ C+ K q − ˙ ∗ Φq αΦt yes 2 4 4 projections in accelerations → ∆t ∆t2 ∆t2 T fq q = M + ¨ C+ K q − ¨∗ Φq α(Φq q + Φt ) ˙ ˙ ˙ 2 4 4 Mechanical Engineering Laboratory, University of La Coruña 17/48
  • 26. 3  Vehicle modeling and simulation environmentTire model. part of the empirical and physical TMeasy model rstorder dynamics → longitudinal and lateral deections transition to standstill → stickslip behavior tire curves → linearized model Fig. 17  Longitudinal deformation of the tireFig. 16  Points & vectors for the tire modeling Fig. 18  Lateral deformation of the tire Mechanical Engineering Laboratory, University of La Coruña 18/48
  • 27. 3  Vehicle modeling and simulation environment Road prole. topographical survey of the test track with a total station 300 points for a track of 80 meters long interpolation of the scattered points Delaunay triangulation → mesh of triangles for the collision detection 1 Height (m) 0.5 0 0 80 −10 60 40 −20 20 −30 Length (m) 0 Width (m) Fig. 19  Total station used for Fig. 20  3D scattered points Fig. 21  3D model of the test the topographical survey track Mechanical Engineering Laboratory, University of La Coruña 19/48
  • 28. 3  Vehicle modeling and simulation environmentCollision detection. tire normal force → function of the interpenetration of the stepped triangles of the ground mesh 4 spheres for the collision geometry of Fig. 22  3D model of the test track the tiresSimulation environment. realistic graphical environment of the campus selfdeveloped 3D environment opensource 3D graphics toolkit (C++) inclusion of the topographical survey of the test track Mechanical Engineering Laboratory, University of La Coruña 20/48
  • 29. 4  Outline 1 Motivations 2 Vehicle eld testing 3 Vehicle modeling and simulation environment 4 Validation results 5 State observers 6 Conclusions Mechanical Engineering Laboratory, University of La Coruña 21/48
  • 30. 4  Validation results MB model inputs. averaging of the experimental data 100 100 Torque (Nm) 0 Torque (Nm) 0 −100 −100 −200 −200 0 2 4 6 8 10 12 14 16 18 20 0 2 4 6 8 10 12 14 16 18 20 Time (s) Time (s) Fig. 23  Repetitions (wheel torque) Fig. 24  Mean and CI (wheel torque) Condence intervals. assumption → the uncertainty follows a normal distribution small number of samples → Students t distribution S C.I. bounds: x ± tn−1 ¯ (1−α/2) · √ n n n 1 1 sample mean → x = ¯ xi sample variance → S 2 = 2 (xi − x) ¯ n i=1 (n − 1) i=1 (1 − α/2) critical value for the t distribution with (n − 1) degrees of freedom Mechanical Engineering Laboratory, University of La Coruña 22/48
  • 31. 4  Validation results Simulation of the low speed straightline maneuver. MB model inputs → averaged experimental data road prole → topographical survey Mechanical Engineering Laboratory, University of La Coruña 23/48
  • 32. 4  Validation results Validation results for the low speed straightline maneuver. 25 3 Angular velocity ( °/s) 20 2 Speed (km/h) 15 1 10 0 5 −1 0 −2 −5 −3 0 2 4 6 8 10 12 14 16 18 20 0 2 4 6 8 10 12 14 16 18 20 Time (s) Time (s) Fig. 25  Left front wheel speed Fig. 26  Roll rate of the chassis 1 Acceleration (m/s2) 0 −1 −2 0 2 4 6 8 10 12 14 16 18 20 Time (s) Fig. 27  Longitudinal acceleration of the chassis Mechanical Engineering Laboratory, University of La Coruña 24/48
  • 33. 4  Validation results Simulation of the lowspeed Jturn maneuver. MB model inputs → averaged experimental data road prole → topographical survey Mechanical Engineering Laboratory, University of La Coruña 25/48
  • 34. 4  Validation results Validation results for the low speed Jturn maneuver. 5 3Angular velocity ( °/s) 0 Acceleration (m/s2) 2 −5 −10 1 −15 0 −20 −25 −1 0 2 4 6 8 10 12 14 16 18 20 22 0 2 4 6 8 10 12 14 16 18 20 22 Time (s) Time (s) Fig. 28  Yaw rate of the chassis Fig. 29  Lateral acceleration of the chassis 1 2 Angular velocity ( °/s) Acceleration (m/s2) 0 0 −1 −2 −2 −4 −3 0 2 4 6 8 10 12 14 16 18 20 22 0 2 4 6 8 10 12 14 16 18 20 22 Time (s) Time (s) Fig. 30  Roll rate of the chassis Fig. 31  Longitudinal acceleration of the chassis Mechanical Engineering Laboratory, University of La Coruña 26/48
  • 35. 5  Outline 1 Motivations 2 Vehicle eld testing 3 Vehicle modeling and simulation environment 4 Validation results 5 State observers 6 Conclusions Mechanical Engineering Laboratory, University of La Coruña 27/48
  • 36. 5  State observersModel running in realtime with the same inputs DISTURBANCES unknown forces, etc OUTPUTS sensors set of sensors INPUTS forces, Real Mechanism torques, etc CONTROLLERS MODEL OUTPUTS variables of model variables = the model numerous avail- Realtime model able magnitudes Mechanical Engineering Laboratory, University of La Coruña 28/48
  • 37. 5  State observersModel running in realtime with the same inputs DISTURBANCES unknown forces, etc OUTPUTS sensors set of sensors INPUTS forces, Real Mechanism torques, etc CONTROLLERS DRIFT OF THE MODEL disturbances,unmodeled dynamics, param- eters of the model MODEL OUTPUTS variables of model variables = the model numerous avail- Realtime model able magnitudes Mechanical Engineering Laboratory, University of La Coruña 28/48
  • 38. 5  State observersState observers for mechanical systems based on Kalman lters DISTURBANCES unknown forces, etc OUTPUTS sensors set of sensors INPUTS forces, Real Mechanism torques, etc CONTROLLERS + Kalman corrections - sensors of the model MODEL OUTPUTS variables of model variables the model = virtual sensors Realtime model State observer based on Kalman lters Mechanical Engineering Laboratory, University of La Coruña 28/48
  • 39. 5  State observersState observers for mechanical systems based on Kalman lters DISTURBANCES unknown forces, etc OUTPUTS sensors minimum set of sensors INPUTS forces, Real Mechanism torques, etc CONTROLLERS + Kalman the model follows the corrections - motion of the mechanism with sensors of delay minimum the model MODEL OUTPUTS variables of model variables the model = virtual sensors Realtime model State observer based on Kalman lters Mechanical Engineering Laboratory, University of La Coruña 28/48
  • 40. 5  State observers State estimation in mechanical systems. Advantages minimum set new sensors virtual sensors of sensors ubiquitous reduced reduced costs magnitude failure rate The more detailed the model is, the more it provides information about the motion of the mechanism Past researches  Kalman lter + linear mechanical systems  lack of generality linearized Kalman lter + nonlinear mechanical  linear models systems simple nonlinear models Mechanical Engineering Laboratory, University of La Coruña 29/48
  • 41. 5  State observers First implementations using a 4bar linkage and a VW Passat. Recent researches at the LIM extended Kalman lter + realtime MB general approach models complex nonlinear models A D B C s Fig. 32  4bar linkage Fig. 33  VW passat & model & state observer w/ MB model Mechanical Engineering Laboratory, University of La Coruña 30/48
  • 42. 5  State observersDescription. simple mechanism: 5bar linkage → 2 DOFs mechanism parameters → experimental measurements parameters of the sensors → characteristics from otheshelf sensorsMB Modeling. Fig. 34  5bar linkage image natural coordinates (8 variables, 6 constraints, 2 DOFs) MB formulations independent coordinates → projection matrixR method dependent coordinates → penalty formulation simulation of the real mechanism for Fig. 35  5bar linkage modeling scheme comprehensive comparisons known errors between the real mechanism and its MB model → lengths, masses, inertias. . . Mechanical Engineering Laboratory, University of La Coruña 31/48
  • 43. 5  State observers Free motion simulation. Drift of the model due to errors in the parameters of the model real mechanism (matrixR, trap. rule) model (matrixR, trap. rule) Mechanical Engineering Laboratory, University of La Coruña 32/48
  • 44. 5  State observers Comparison of NL Kalman lters. SPKF EKF ,UKF ,SSUKFWhat is it? de facto NL Kalman lter recent NL Kalman ltersWhy to use it ? eciency accuracy and easy implementationWhich form ? continuous discreteHow does it state estimates → propaga- state estimates → propagationwork ? tion through NL system. through NL system. mean and state estimation mean and state estimation uncer- uncertainty → propagation tainty → propagation of sigma through linearization points through the NL systemAssumptions additive white Gaussian noises rst order dierential equations x(t) = f(x(t)) + w (t) ˙ with independent states System dynamics nonlinear dierence equations xk+1 = φk (xk ) + w k with independent states Mechanical Engineering Laboratory, University of La Coruña 33/48
  • 45. 5  State observers The extended Kalman lter  EKF. rst order ODEs rst order DAEs Mq + ΦT λ = Q ¨ q x(t) = f(x(t)) ˙ = Φ=0 Mechanical Engineering Laboratory, University of La Coruña 34/48
  • 46. 5  State observers The extended Kalman lter  EKF. rst order ODEs rst order DAEs Mq + ΦT λ = Q ¨ q x(t) = f(x(t)) ˙ = Φ=0 independent coordinates duplication of variables state space reduction (positions & velocities) method matrix R z(t) x= ¨ = (RT MR)−1 [RT (Q − MRz)] z ˙˙ w(t) z(t) ˙ w = = w(t) ˙ (RT MR)−1 [RT (Q − MRz)] ˙˙ integration implicit integrator trapezoidal rule Mechanical Engineering Laboratory, University of La Coruña 34/48
  • 47. 5  State observers The extended Kalman lter  EKF. state estimates ˆ(t) = f(ˆ(t), t) + K[y(t) − ˆ(t)] x ˙ x ¯ y Kalman gain K(t) = P(t)H[1]T (t)R(t) ¯ Riccati equation P(t) = F[1] P(t) + P(T)F[1]T + GQ(t)GT − KR(t)K ˙ ¯ ¯ ∂ f(x, t) ∂ h(x, t) linear approximations F[1] (t) H[1] (t) ∂x ∂x 0 I   0 I F[1] (t) =  ∂(M−1 Q) ¯ ¯ ¯ −1 ¯ ∂(M Q)  −1 −1 −M ¯ RT (KR + 2MRq Rw) ˙ −M ¯ RT (CR + MR) ˙ ∂z ∂w Mechanical Engineering Laboratory, University of La Coruña 35/48
  • 48. 5  State observers The unscented Kalman lter  UKF.nonlinear recurrences rst order DAEswith independent states Mq + Φ T λ = Q ¨ q xk+1 = φk (xk ) = Φ=0 Mechanical Engineering Laboratory, University of La Coruña 36/48
  • 49. 5  State observers The unscented Kalman lter  UKF.nonlinear recurrences rst order DAEswith independent states Mq + Φ T λ = Q ¨ q xk+1 = φk (xk ) = Φ=0 independent coordinates state space reduction method matrix R ¨ = (RT MR)−1 [RT (Q − MRz)] z ˙˙ = integration Mechanical Engineering Laboratory, University of La Coruña 36/48
  • 50. 5  State observers The unscented Kalman lter  UKF.nonlinear recurrences rst order DAEswith independent states Mq + Φ T λ = Q ¨ q xk+1 = φk (xk ) = Φ=0 independent coordinates dependent coordinates state space reduction penalty formulation method matrix R q = (M + ΦT αΦ)−1 [Q − ΦT α(Φq q + 2ζω Φ + ω 2 Φ)] ¨ q q ˙ ˙ ˙ ¨ = (RT MR)−1 [RT (Q − MRz)] z ˙˙ = integration = integration Mechanical Engineering Laboratory, University of La Coruña 36/48
  • 51. 5  State observers The unscented Kalman lter  UKF.measurementupdate equations (executed iftimeupdate equations (always executed) information from the sensors is available) 2L x xk ˆk = ˆ− + Kk (yk − ˆ− ) ¯ yk xk ˆ− = wim χi,k|k−1 i=0 χk|k−1 = φk−1 (χk−1 ) Kk = Pxk yk P˜k ¯ −1 y 2L  x   ˆk−1 yk ˆ− = ωim Y i,k|k−1 x Pk−1 χi,k−1 = ˆk−1 + γ i=0 i x Pk−1   ˆk−1 − γ  i Y k|k−1 = hk (χk|k−1 ) 2L Pxk = − ωic (χk|k−1 − xk ˆ− )(χk|k−1 − xk ˆ− )T T i=0 Pxk = P− − Kk P˜k Kk xk ¯ y ¯ Mechanical Engineering Laboratory, University of La Coruña 37/48
  • 52. 5  State observers The unscented Kalman lter  UKF.timeupdate equations (always executed) zk+1 , zk+1 ˙ 2L xk ˆ− = wim χi,k|k−1 integ. i=0 χk|k−1 = φk−1 (χk−1 ) z ¨k+1  x   ˆk−1 zk+1 ¨1 zk+1 ¨2 zk+1 ¨3 zk+1 ¨4 zk+1 ¨5 x Pk−1 χi,k−1 = ˆk−1 + γ i x Pk−1   ˆk−1 − γ  φk φk φk φk φk i z ¨k z ¨k z ¨k z ¨k z ¨k zk ˙ zk ˙ zk ˙ zk ˙ zk ˙ z1 k z2 k z3 k z4 k z5 kFig. 36  Set of sigmapoints (2 dim. GR variable) ¨k , zk , zk z ˙ Mechanical Engineering Laboratory, University of La Coruña 37/48
  • 53. 5  State observersThe spherical simplex UKF. same equations as for the UKF reduced set of sigmapoints UKF → (2L+1) sigmapoints SSUKF → (L+2) sigmapoints equations of the reduced set of sigmapoints χj−1   0 for i = 0   0    χj−1       i   1 for i = 1, . . . , jχj = −  i   j(j + 1)w1 0j−1     Fig. 37  Reduced set of sigmapoints (2     1 for i = j + 1 dim. GR variable     j(j + 1)w1 Mechanical Engineering Laboratory, University of La Coruña 38/48
  • 54. 5  State observers Free motion simulation. Drift of the model due to errors in the parameters of the model The observers estimate correctly the motion of the real mechanism real mechanism (matrixR, trap. rule) model (matrixR, trap. rule) EKF (matrixR, trap. rule) UKF (matrixR, trap. rule) SSUKF (matrixR, trap. rule) SSUKF (matrixR, RK2) SSUKF (penal, RK2) Mechanical Engineering Laboratory, University of La Coruña 39/48
  • 55. 5  State observers Performance comparisons of the lters → eciency vs RMSE. non multirate 10 ∆tinteg = 2ms 9 ∆tsensors = 2ms multirate 8 ∆tinteg = 2ms 7 ∆tsensors = 6ms multirate case 6 EKF (matrixR, trap. rule) RMSE 5 UKF (matrixR, trap. 4 rule) 3 SSUKF (matrixR, trap. rule) non multi 2 SSUKF (matrixR, RK2) rate case 1 Simulation SSUKF (penal, RK2) 100 125 150 175 200 225 250 time (%) Mechanical Engineering Laboratory, University of La Coruña 40/48
  • 56. 5  State observers Data acquisition EKF system param- eters UKF NL mechanism Kalman SPKF SSUKF STATE OB- lters SERVERS sensors NL Kalman lters with MB models indepen- dent coord. MB matrix implicit integrators R formulation method depen- TR dent coord. explicit penalty- formu. RK2 Mechanical Engineering Laboratory, University of La Coruña 41/48
  • 57. 5  State observers Pros & Cons. EKF Pros → most ecient lter with independent coordinates Cons → involved and errorprone calculation of the Jacobian, not suitable to employ with dependent coordinates, not multirate SPKFs Pros → easiest implementation, possible use of dependent coordinates, highest accuracy Cons → high computational cost due to the sigmapoints Mechanical Engineering Laboratory, University of La Coruña 42/48
  • 58. 6  Outline 1 Motivations 2 Vehicle eld testing 3 Vehicle modeling and simulation environment 4 Validation results 5 State observers 6 Conclusions Mechanical Engineering Laboratory, University of La Coruña 43/48
  • 59. 6  Conclusions Vehicle eld testing. 1 X-by-wire vehicle prototype from scratch 2 highly detailed model of the drivers force feedback system 3 repetitions of 2 reference manoeuvres in the campus Vehicle modeling and simulation environment. 1 real-time 14 DOFs MB model 2 modelling of subsystems → tire, brake 3 topographical survey of the test track 4 realistic 3D simulation environment Mechanical Engineering Laboratory, University of La Coruña 44/48
  • 60. 6  Conclusions Validation results. 1 condence intervals for the experimental data 2 simulation of the test manoeuvres using the experimental data 3 evaluation of the accuracy of the MB model State observers. 1 use of MB models with the extended Kalman lter 2 application to a 4bar linkage and a VW Passat 3 use of MB models with SPKFs lters 4 implementation using a 5bar linkage Mechanical Engineering Laboratory, University of La Coruña 45/48
  • 61. 6  Conclusions Future research. 1 eld testing manoeuvres at higher speeds → new test track GPS RTK for realtime positioning of the vehicle 2 vehicle modelling and simulation environment better characterization of the tire curves HumanInTheLoop simulation using experimental inputs 3 state observers EKF in discrete form research on the observability of MB models tests of the UKF/SSUKF with more complex mechanisms implementation using the MB model of the XBW prototype Mechanical Engineering Laboratory, University of La Coruña 46/48
  • 62. 6  Conclusions Congress papers.[1] J. Cuadrado, D. Dopico, J. A. Pérez, and R. Pastorino. Inuence of the sensored magnitude in the performance of observers based on multibody models and the extended Kalman lter. In Proceedings of the Multibody Dynamics ECCOMAS Thematic Conference, Warsaw, Poland, June 2009.[2] R. Pastorino, M. A. Naya, J. A. Pérez, and J. Cuadrado. Xbywire vehicle prototype: a steerbywire system with geared PM coreless motors. In Proceedings of the 7th EUROMECH Solid Mechanics Conference, Lisbon, Portugal, September 2009.[3] J. Cuadrado, D. Dopico, M. A. Naya, and R. Pastorino. Automotive observers based on multibody models and the extended Kalman lter. In The 1st Joint International Conference on Multibody System Dynamics, Lappeenranta, Finland, May 2010.[4] R. Pastorino, M. A. Naya, A. Luaces, and J. Cuadrado. Xbywire vehicle prototype: automatic driving maneuver implementation for realtime MBS model validation. In Proceedings of the 515th EUROMECH Colloquium, Blagoevgrad, Bulgaria, 2010.[5] R. Pastorino. La simulation des systèmes multicorps dans lautomobile. Interface, revue des ingénieurs des INSA de Lyon, Rennes, Rouen, Toulouse, (111):22, 3ème et 4ème trimestre 2011.[6] R. Pastorino, D. Dopico, E. Sanjurjo, and M. A. Naya. Validation of a multibody model for an xbywire vehicle prototype through eld testing. In Proceedings of the ECCOMAS Thematic Conference Multibody Dynamics 2011, Brussels, Belgium, 2011.[7] R. Pastorino, M. A. Naya, A. Luaces, and J. Cuadrado. Xbywire vehicle prototype : a tool for research on realtime vehicle multibody models. In Proceedings of the 13th EAEC European Automotive Congress, Valencia, Spain, June 2011.[8] R. Pastorino, D. Richiedei, J. Cuadrado, and A. Trevisani. State estimation using multibody models and nonlinear Kalman lters. In The 2nd Joint International Conference on Multibody Systems Dynamics, Stuttgart, Germany, May 2012.[9] R. Pastorino, D. Richiedei, J. Cuadrado, and A. Trevisani. State estimation using multibody models and unscented Kalman lters. In Proceedings of the 524th EUROMECH Colloquium, Enschede, Netherlands, 2012.[10] E. Sanjurjo, R. Pastorino, D. Dopico, and M. A. Naya. Validación experimental de un modelo multicuerpo de un prototipo de vehículo automatizado. In XIX Congreso Nacional de Ingeniería Mecánica (to be presented), Castellón, Spain, Nov. 2012. Mechanical Engineering Laboratory, University of La Coruña 47/48
  • 63. 6  Conclusions Journal papers.[1] J. Cuadrado, D. Dopico, J. A. Pérez, and R. Pastorino. Automotive observers based on multibody models and the Extended Kalman Filter. Multibody System Dynamics, 27(1):319, 2011.[2] R. Pastorino, M. A. Naya, J. A . Pérez, and J. Cuadrado. Geared PM coreless motor modelling for drivers force feedback in steerbywire systems. Mechatronics, 21(6):10431054, 2011. Journal papers in preparation.[1] R. Pastorino, M.A. Naya, and J. Cuadrado. Experimental validation of a multibody model for a vehicle prototype. Vehicle System Dynamics, 2012.[2] R. Pastorino, D. Richiedei, J. Cuadrado, and A. Trevisani. State estimation using multibody models and nonlinear kalman lters. Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multibody Dynamics, 2012. Acknowledgments. Spanish Ministry of Science and Innovation  Grant TRA200909314 (ERDF funds) Mechanical Engineering Laboratory, University of La Coruña 48/48