A Volumetric Contact Model for Space Robot and Planetary Rover Application

Transcription

1 Introduction Elastic Foundation Model Experimental Validation Hyperelastic Foundation Model Planetary Rover Simulation Platform Future Work A Volumetric Contact Model for Space Robot and Planetary Rover Application Willem Petersen Mike Boos John McPhee Yves Gonthier University of Waterloo Systems Design Engineering Agence Spatiale Canadienne Canadian Space Agency Y. Gonthier A Volumetric Contact Model for Space Application

2 Outline Introduction Elastic Foundation Model Experimental Validation Hyperelastic Foundation Model Planetary Rover Simulation Platform Future Work 1 Introduction 2 Elastic Foundation Model 3 Experimental Validation 4 Hyperelastic Foundation Model 5 Planetary Rover Simulation Platform 6 Future Work Y. Gonthier A Volumetric Contact Model for Space Application

3 Motivation Motivation Model Experiments Results Figure: Dextre at the tip of Canadarm2 (Gonthier, 27). Mike Boos and John McPhee Volumetric Contact Dynamics Models and Validation 4/ 32

4 Contact Models Motivation Model Experiments Results Electrical Connectors Alignment Sleeve 36" Micro Fixture 28" 12" Coarse Alignment Bumper Point contact models Small contact patches only Simple, convex geometries SPDM OTCM Alignment Pins No rolling resistance, spinning friction torque Battery Battery Worksite FEM Worksite Too complex for real-time ISS battery box (Gonthier, 27). Mike Boos and John McPhee Volumetric Contact Dynamics Models and Validation 5/ 32

5 Motivation Model Experiments Results Volumetric contact model Ball-table simulation: real-time (Gonthier, 27) Mike Boos and John McPhee Volumetric Contact Dynamics Models and Validation 6/ 32

6 Motivation Model Experiments Results Volumetric contact model Advantages Larger, more complex, and conforming contact patches possible Includes both translational (normal and friction forces) and rotational (rolling resistance and spinning friction torque) dynamics. Validation of the model still required for hard contact (metals) Mike Boos and John McPhee Volumetric Contact Dynamics Models and Validation 7/ 32

7 Goals Motivation Model Experiments Results 1 Experimentally validate the normal force components of the volumetric contact dynamics model for hard-on-hard (metal) contact 2 Demonstrate parameter identification for this model Mike Boos and John McPhee Volumetric Contact Dynamics Models and Validation 8/ 32

8 Volumetric model Motivation Model Experiments Results Volumetric model Normal forces fn S s δ(s) B i B j Figure: A volumetric contact model based on a Winkler foundation. p(s) = dfn ds = k vδ(s)(1 + av n ) V Mike Boos and John McPhee Volumetric Contact Dynamics Models and Validation 1/ 32

9 Volumetric properties Motivation Model Experiments Results Volumetric model Normal forces B i δ(s) j n S δ(s) s δ(s) i V B j Volumetric properties V - volume of interference n - contact normal J s - surface-inertia tensor J v - volume-inertia tensor Mike Boos and John McPhee Volumetric Contact Dynamics Models and Validation 11/ 32

10 Normal forces Motivation Model Experiments Results Volumetric model Normal forces V Normal force f n = k v V (1 + av cn )n n v cn S Mike Boos and John McPhee Volumetric Contact Dynamics Models and Validation 12/ 32

11 Rolling resistance Motivation Model Experiments Results Volumetric model Normal forces V Rolling resistance torque τ r = k v a J s ω t n ω t S Mike Boos and John McPhee Volumetric Contact Dynamics Models and Validation 13/ 32

12 Friction Motivation Model Experiments Results Volumetric model Normal forces The model can include tangential friction forces and spinning friction torque. (Gonthier et al., 27) f t = µ c f n v ct v avg τ s = µ cf n V v avg J s ω n Mike Boos and John McPhee Volumetric Contact Dynamics Models and Validation 14/ 32

13 Goals Normal contact force Apparatus in normal configuration Quasi-static experiments Dynamic experiments Cylindrical payload Force sensor Linear encoder Encoder reference Contact surface Mike Boos Volumetric Contact Dynamics Models and Validation 3/ 21

14 Goals Normal contact force Quasi-static experiments Dynamic experiments Quasi-static results with sphere on aluminum 1 8 Measured data Volumetric fit Hertzian fit Contact force (N) Displacement (µm) Volumetric stiffness k v = N/m 3 Mike Boos Volumetric Contact Dynamics Models and Validation 4/ 21

15 Goals Normal contact force Quasi-static experiments Dynamic experiments Quasi-static results with sphere on magnesium Contact force (N) Measured data Volumetric fit Hertzian fit Displacement (µm) Magnesium surface tarnished quickly after polishing Anisotropic material Volumetric stiffness k v = N/m 3 Mike Boos Volumetric Contact Dynamics Models and Validation 5/ 21

16 Goals Normal contact force Problems with cylinders Quasi-static experiments Dynamic experiments Non-linear force-displacement relationship Either misalignment or surface asperities γ Used a cylindrical wedge to estimate possible misalignment for the volumetric model Mike Boos Volumetric Contact Dynamics Models and Validation 6/ 21

17 Goals Normal contact force Quasi-static experiments Dynamic experiments Quasi-static results with cylinder on aluminum Measured data Perpendicular fit Off angle fit Theoretical volumetric stiffness k v = N/m 3 Contact force (N) Estimated misalignment γ = Displacement (µm) Mike Boos Volumetric Contact Dynamics Models and Validation 7/ 21

18 Goals Normal contact force Quasi-static experiments Dynamic experiments Quasi-static results with cylinder on magnesium Contact force (N) Measured data Perpendicular fit Off angle fit Theoretical volumetric stiffness k v = N/m 3 Estimated misalignment γ = Displacement (µm) Mike Boos Volumetric Contact Dynamics Models and Validation 8/ 21

19 Goals Normal contact force Quasi-static experiments Dynamic experiments Dynamic experiment with magnesium at.58 mm/s Displacement (mm) 4 2 x Measured 5 Model with damping Model no damping 4 Force (N) Damping factor a = s/m Time (s) Mike Boos Volumetric Contact Dynamics Models and Validation 9/ 21

20 Goals Normal contact force Measured damping factors Quasi-static experiments Dynamic experiments Damping factor (s/m) 1 x Estimated factors for Al Fit of a 1/v i for Al Estimated factors for Mg Fit of a 1/v i for Mg Impact velocity (mm/s) Model in free collision a 1 e2 eff e eff v i n e eff = 1 αv i n Measurements (driven) a Al 18.7 v i n a Mg 8.68 v i n Mike Boos Volumetric Contact Dynamics Models and Validation 1/ 21

21 Goals Normal contact force Apparatus in friction configuration Translation experiments Rotation experiments Contensou effect experiments Linear motor Rotational motor Contact surface Cylindrical payload Linear encoder Encoder reference 3DOF force sensors Mike Boos Volumetric Contact Dynamics Models and Validation 11/ 21

22 Static friction Goals Normal contact force Translation experiments Rotation experiments Contensou effect experiments.25 Force measurements Force measurements adjusted by rotation.3.25 Measured coefficients Model bristle stiffness only Model bristle stiffness and damping Friction over normal force magnitudes Coefficient of friction Displacement (mm) Time (s) Coefficient of static friction µ s.2 Bristle stiffness and damping σ = 45m 1 σ 1 = 3s/m Mike Boos Volumetric Contact Dynamics Models and Validation 12/ 21

23 Kinetic friction Goals Normal contact force Translation experiments Rotation experiments Contensou effect experiments Coefficient of friction.2.15 Coefficient of friction Measured coefficients of friction Linear regression Time (s) Velocity (mm/s) Coefficient of kinetic friction µ d.2 Mike Boos Volumetric Contact Dynamics Models and Validation 13/ 21

24 Goals Normal contact force Dwell-time dependency experiment Translation experiments Rotation experiments Contensou effect experiments.6.5 Coefficient of friction Could not detect dwell-time dependency Adhesion effect observed where friction force increased with time Time (s) Mike Boos Volumetric Contact Dynamics Models and Validation 14/ 21

25 Rotation experiments Goals Normal contact force Translation experiments Rotation experiments Contensou effect experiments Coefficient of friction.1.5 Coefficient of friction Rotation (degrees) Measured coefficients of friction Linear regression Angular velocity (radians/s) Coefficient of static friction µ s.2 Coefficient of kinetic friction µ d.2 Mike Boos Volumetric Contact Dynamics Models and Validation 15/ 21

26 Goals Normal contact force Conensou effect experiment Translation experiments Rotation experiments Contensou effect experiments Tangential force measurements Spinning torque measurements.45.4 Measured coefficients Model coefficients.5.45 Measured coefficients Model coefficients.35.4 Coefficient of Friction Coefficient of Friction Time (s) Time (s) Mike Boos Volumetric Contact Dynamics Models and Validation 16/ 21

27 Goals Normal contact force Normal contact Experiments compare well against Hertzian models Applicability to unusual geometries demonstrated Inverse relationship between impact velocity and damping Friction contact Similar results for translation and rotation Adhesion effect observed Contensou effect demonstrated Mike Boos Volumetric Contact Dynamics Models and Validation 17/ 21

28 Goals Normal contact force Recommendations Incremental improvements to apparatus: Alignment Force and speed ranges Increased surface area/reduced contact pressure in friction contact Investigate other aspects of contact: Rolling resistance torque Understanding of adhesion effect Mike Boos Volumetric Contact Dynamics Models and Validation 18/ 21

29 Introduction Elastic Foundation Model Experimental Validation Hyperelastic Foundation Model Planetary Rover Simulation Platform Future Work Motivation for Hyperelastic Foundation Model Highly nonlinear soil properties Large deformation of the soft soil Y. Gonthier A Volumetric Contact Model for Space Application

30 Introduction Elastic Foundation Model Experimental Validation Hyperelastic Foundation Model Planetary Rover Simulation Platform Future Work Volume vs. Hypervolume z y x Penetration Volume k f h f F n Elastic Foundation: F n,l = k v f S (S) ds n }{{} Volume V Hyperelastic Foundation: F n,nl = k v fs n (S) ds n }{{} Hypervolume V h Y. Gonthier A Volumetric Contact Model for Space Application

31 Introduction Elastic Foundation Model Experimental Validation Hyperelastic Foundation Model Planetary Rover Simulation Platform Future Work Cylinder on Flat Ground Exact Solution: Find m for a variation of n f n S (S) ds V m = Hypervolumen Exponent Field 3 Hypervolume Exponent Variation Hypervolume exponent m Bekker Exponent n Bekker Exponent n Penetration depth parameter a Hypervolume exponent m Y. Gonthier A Volumetric Contact Model for Space Application

32 Introduction Elastic Foundation Model Experimental Validation Hyperelastic Foundation Model Planetary Rover Simulation Platform Future Work Cylinder on Flat Ground Series Solution: Find α i for a certain n and dz =..R For n > 1: f n S (S) ds Normal force F n [N] numerically integrated series solution 4 α i V i = i=1 Contact Force Comparison For n < 1: f n S (S) ds Normal force F n [N] α i V 1/i = i=1 Contact Force Comparison Absolute error [N] Penetration depth dz [m] Absolute error [N] Penetration depth dz [m] Error: 1.38%.129% Y. Gonthier A Volumetric Contact Model for Space Application

33 Introduction Elastic Foundation Model Experimental Validation Hyperelastic Foundation Model Planetary Rover Simulation Platform Future Work Cylinder on Flat Ground Mean Value Solution: Find c v (V ) for a variation of n F n,nl = k v b = k v b Apply Mean Value Theorem F n,nl = k v bc v (V ) a a a a a a g (x) n dx g (x) (n 1) g (x) dx g (x) dx = k v bc v (V ) V with c v (V ) = a a g (x)n dx a a g (x) dx Y. Gonthier A Volumetric Contact Model for Space Application

34 Introduction Elastic Foundation Model Experimental Validation Hyperelastic Foundation Model Planetary Rover Simulation Platform Future Work Cylinder on Flat Ground Results of c v (V ) for wheel with R = ln c v n = n = 1 n = 2 n = Possible Solution : ln V c v (V ) = e a +a 1 ln V Y. Gonthier A Volumetric Contact Model for Space Application

35 Introduction Elastic Foundation Model Experimental Validation Hyperelastic Foundation Model Planetary Rover Simulation Platform Future Work Tire/Soil Contact Model z max z ω F T C D θ θ dz dx R c F soil x Vertical Force: Hyperelasic foundation model Bekker soil parameters Longitudinal Force: Traction force (Janosi-Hanamoto, grousers) Resistance force (soil compaction) Willem Petersen ME 62 Project Presentation 14 Y. Gonthier A Volumetric Contact Model for Space Application

36 Introduction Elastic Foundation Model Experimental Validation Hyperelastic Foundation Model Planetary Rover Simulation Platform Future Work Planetary Rover Model Developed MapleSim 4.5 Model Exported symbolic equations to S-function block Developed Simulink model and with LLG contact models Y. Gonthier A Volumetric Contact Model for Space Application

37 Introduction Elastic Foundation Model Experimental Validation Hyperelastic Foundation Model Planetary Rover Simulation Platform Future Work Planetary Rover Simulation Platform Rover Simulation Platform Combine tire model with rover dynamics MuT (Multibody Toolbox) Contact Model Libraries in Numeric Simulation Environment LLG CSA/MDA Project Final Review Y. Gonthier A Volumetric Contact Model for Space Application

38 Introduction Elastic Foundation Model Experimental Validation Hyperelastic Foundation Model Planetary Rover Simulation Platform Future Work Planetary Rover Simulation Simulation and animation of rover with Parallel Geometry Inc. (LLG) software Y. Gonthier A Volumetric Contact Model for Space Application

39 Introduction Elastic Foundation Model Experimental Validation Hyperelastic Foundation Model Planetary Rover Simulation Platform Future Work Future work 1. Experimental validation of hyperelastic contact models 2. Use more sophisticated tire and terrain geometries 3. Develop models to run on a high performance computer Y. Gonthier A Volumetric Contact Model for Space Application