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Contact Modeling for Climbing Environments. Daniel Santos PhD Qualifying Exam Presentation. Background. Biologically-inspired Climbing Robots in Unstructured Terrain Must Understand:. Adhesive Properties. FOOT SURFACE. Introduction. Simple Adhesion Model
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Contact Modeling for Climbing Environments Daniel Santos PhD Qualifying Exam Presentation Biomimetics Laboratory Stanford University Daniel Santos
Background • Biologically-inspired Climbing Robots in Unstructured Terrain • Must Understand: Adhesive Properties FOOT SURFACE Biomimetics Laboratory Stanford University Daniel Santos
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
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
Basic Coulomb Friction Friction FStatic FDynamic Velocity Biomimetics Laboratory Stanford University Daniel Santos
Static Friction Cone Simple Adhesion Model Region of Stability { Stability Requirement Adhesion Parameter Stability Requirement FNormal FTangential Biomimetics Laboratory Stanford University Daniel Santos
Static Analysis Analysis adapted from Kerr & Roth, 1987, Grasp Theory mg F1T F1N F2T F2N q Biomimetics Laboratory Stanford University Daniel Santos
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
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
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
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
Implementation • Arachi DE • Add Simple Adhesion Model • Build on top: • Basic Coulomb Friction • Other Coulomb Friction Models Biomimetics Laboratory Stanford University Daniel Santos
Basic Coulomb Friction Problems Friction FS FD Velocity Reversals Friction Force Biomimetics Laboratory Stanford University Daniel Santos
Karnopp Friction Model DV STUCK SLIDING Karnopp, 1985 Friction FS FD Velocity Biomimetics Laboratory Stanford University Daniel Santos
Karnopp State Diagram STUCK SLIDING Biomimetics Laboratory Stanford University Daniel Santos
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
Limitations of Karnopp Model Transition to Stuck Δt Later g With Rolling, Contact Point Moves in Space Biomimetics Laboratory Stanford University Daniel Santos
Modified Karnopp Model ti-1 ti Biomimetics Laboratory Stanford University Daniel Santos
Final Implementation • Modified Karnopp Force: • Simple Adhesion by adding: Biomimetics Laboratory Stanford University Daniel Santos
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
Simple Experiments Biomimetics Laboratory Stanford University Daniel Santos
Modified Karnopp ModelPure Sliding FFriction FApplied FFriction Velocity STUCK-to-SLIDING SLIDING-to-STUCK Biomimetics Laboratory Stanford University Daniel Santos
Modified Karnopp ModelSliding->Rolling Sliding & Rolling Pure Rolling Matches Theoretical Value Biomimetics Laboratory Stanford University Daniel Santos
TestTrack Simulation Biomimetics Laboratory Stanford University Daniel Santos
Modified Karnopp ModelJitter Reduction Basic Coulomb Modified Karnopp Biomimetics Laboratory Stanford University Daniel Santos
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
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
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
Thanks to • RiSE Project • BDML • Engineering Diversity Program • NIH Biotechnology Grant Questions? Biomimetics Laboratory Stanford University Daniel Santos