Contact Modeling for Climbing Environments

1. Contact Modeling for Climbing Environments Daniel Santos PhD Qualifying Exam Presentation Biomimetics Laboratory Stanford University Daniel Santos

2. Background • Biologically-inspired Climbing Robots in Unstructured Terrain • Must Understand: Adhesive Properties FOOT  SURFACE Biomimetics Laboratory Stanford University Daniel Santos

3. Introduction • Simple Adhesion Model • Static Analysis of Simple Adhesion • Modified Karnopp Friction Model • Simulation of Multi-Legged Robots using Simple Adhesion Biomimetics Laboratory Stanford University Daniel Santos

4. Contact Models • What are they? • Mathematical Descriptions of the Interaction between Two Objects in Physical Contact • Examples • Hertz Contact Model • Stress & Deformation • Classic Coulomb Friction • Forces Biomimetics Laboratory Stanford University Daniel Santos

5. Basic Coulomb Friction Friction FStatic FDynamic Velocity Biomimetics Laboratory Stanford University Daniel Santos

6. Static Friction Cone Simple Adhesion Model Region of Stability { Stability Requirement Adhesion Parameter Stability Requirement FNormal FTangential Biomimetics Laboratory Stanford University Daniel Santos

7. Static Analysis Analysis adapted from Kerr & Roth, 1987, Grasp Theory mg F1T F1N F2T F2N q Biomimetics Laboratory Stanford University Daniel Santos

8. Static Analysis Linear Programming Problem Region of Stability d d Maximize Distance from Violating Friction Cone λ1- Direction Optimal λ1 Inequality Constraints • 3 Equalities and 4 Unknowns • Infinite # of Solutions • Inequalities from Contact Models • Determine optimal solution Biomimetics Laboratory Stanford University Daniel Santos

9. Stability with Coulomb Friction FB FB Internal Body Force Front = Rear = Model Geometry COM Normal Forces Tangential Forces Stability Measure 45° MAX Optimal Internal Body Force Is Tensile Angle of Inclination Angle of Inclination Angle of Inclination Biomimetics Laboratory Stanford University Daniel Santos

10. Stability with Simple Adhesion FB FB Internal Body Force Front = Rear = Model Geometry COM Normal Forces Tangential Forces Stability Measure 65° MAX Optimal Force Changes Angle of Inclination Angle of Inclination Angle of Inclination Biomimetics Laboratory Stanford University Daniel Santos

11. Forces in Nature 0.03 Level Climbing 0.02 Fore Hind 0.01 0 -0.01 Fore Hind -0.02 Force (N) Left Right Left Right Fore Fore Hind Hind Fore Fore-Aft Aft Right Lateral Left Aft Normal Fore Angle of Inclination Biomimetics Laboratory Stanford University Daniel Santos

12. Implementation • Arachi DE • Add Simple Adhesion Model • Build on top: • Basic Coulomb Friction • Other Coulomb Friction Models Biomimetics Laboratory Stanford University Daniel Santos

13. Basic Coulomb Friction Problems Friction FS FD Velocity Reversals Friction Force Biomimetics Laboratory Stanford University Daniel Santos

14. Karnopp Friction Model DV STUCK SLIDING Karnopp, 1985 Friction FS FD Velocity Biomimetics Laboratory Stanford University Daniel Santos

15. Karnopp State Diagram STUCK SLIDING Biomimetics Laboratory Stanford University Daniel Santos

16. Limitations of Karnopp Model • Originally only for Pure Sliding • In general, Stuck means both: • Stationary contact points • Moving contact points due to Pure Rolling Transition to STUCK A B Biomimetics Laboratory Stanford University Daniel Santos

17. Limitations of Karnopp Model Transition to Stuck Δt Later g With Rolling, Contact Point Moves in Space Biomimetics Laboratory Stanford University Daniel Santos

18. Modified Karnopp Model ti-1 ti Biomimetics Laboratory Stanford University Daniel Santos

19. Final Implementation • Modified Karnopp Force: • Simple Adhesion by adding: Biomimetics Laboratory Stanford University Daniel Santos

20. Simulation • Evaluate Modified Karnopp Model • Jitter Reduction in Friction Force • Stability of Multi-Legged Robots with Optimal Contact Forces Biomimetics Laboratory Stanford University Daniel Santos

21. Simple Experiments Biomimetics Laboratory Stanford University Daniel Santos

22. Modified Karnopp ModelPure Sliding FFriction FApplied FFriction Velocity STUCK-to-SLIDING SLIDING-to-STUCK Biomimetics Laboratory Stanford University Daniel Santos

23. Modified Karnopp ModelSliding->Rolling Sliding & Rolling Pure Rolling Matches Theoretical Value Biomimetics Laboratory Stanford University Daniel Santos

24. TestTrack Simulation Biomimetics Laboratory Stanford University Daniel Santos

25. Modified Karnopp ModelJitter Reduction Basic Coulomb Modified Karnopp Biomimetics Laboratory Stanford University Daniel Santos

26. Multi-Legged Robotwith Optimal Contact Forces Instability Occurs With Optimal Control qMax= 65 degrees Without Optimal Control qMax= 52 degrees Model Geometry Tangential Forces Stability Measure Analysis 65° MAX COM Simulation Biomimetics Laboratory Stanford University Daniel Santos

27. Conclusions • Simple Adhesion Model captures stability on vertical surfaces • Static Analysis can generate desired internal force profiles • Modified Karnopp Model yields good results for general sliding AND rolling contacts Biomimetics Laboratory Stanford University Daniel Santos

28. Future Work • Compare Simple Adhesion Model to: • Biological creatures (geckos) • Sticky materials (PSA) • Quasi-Dynamic Analysis • Calculate Optimal Force Trajectory as robot moves through stance • Model Contact Interaction as series of impulses through time Biomimetics Laboratory Stanford University Daniel Santos

29. Thanks to • RiSE Project • BDML • Engineering Diversity Program • NIH Biotechnology Grant Questions? Biomimetics Laboratory Stanford University Daniel Santos