Haptics and Virtual Reality

1. Haptics and Virtual Reality Lecture 8: Haptic Rendering-Virtual Proxy M. Zareinejad

2. Introduction • What’s Virtual Proxy? • A substitute for the probe in the VE • An extension of the ‘God-Object’ • A finite sized massless sphere that runs after the probe

3. Introduction • Why sphere? • To solve the ‘fall-through’ problem of the God-Object method • For easy collision-detection

4. Introduction • ‘Fall-through’ of the God-Object

5. Introduction • Virtual Proxy’s behavior in the same situation

6. Collision Detection • Example

7. Collision Detection • Check whether a line-segment, specified by the proxy and the probe, falls within one radius of any obstacle in the environment • This line-segment checking method can successfully render thin objects

8. Collision Detection • Configuration space obstacle • A mapped obstacle to the configuration space • In our problem, it consists of all points within one proxy radius of the original obstacle • Constraint plane • Where the line-segment intersects the configuration space obstacle

9. Updating Proxy Position • The proxy moves to the probe until it makes a contact with a C-obstacle • If the proxy makes a contact, it moves to the closest position to the probe on the constraint plane

10. Updating Proxy Position • A sub-goal can be represented byminimize ∥x-p∥subject to nix ≥ 0, 0 ≤ i ≤ m • p is the vector from the current proxy to the probe • x is the sub-goal • ni, 0 ≤ i ≤ m, are the unit normals of the constraint planes • The problem can be solved using a standard quadratic programming package, or a similar method that the God-Object method uses

11. Static Friction • the force exerted on the proxy by the user can be estimated byf = kp(p-v) • kp is the proportional gain of the haptic controller • p is the position of the proxy • v is the position of the probe

12. Static Friction • If ∥ft∥≤μs∥fn∥, proxy is not moved • f is the estimated force exerted on the proxy • fn is the vertical element of f on the constraint plane • ft is the horizontal element of f on the constraint plane • μs is static friction parameter of constraint surface

13. Viscous and Dynamic Friction • The motion of one dimensional object is • μd is the dynamic friction parameter of the surface • m is the mass of the object • x’’ is the acceleration of the object • x’ is the velocity of the object • b is the viscous damping parameter

14. Viscous and Dynamic Friction • Because the mass of the proxy is 0, the previous equation can be rewritten as • This equation can be used to bound the amount that the proxy can move in one clock cycle

15. Stiffness - Motivation • Stiffness of a surface can be modeled by reducing the position gain of the haptic controller • But changing the position gain is not desirable • Solve this problem by repositioning the proxy

16. Stiffness - Method • p is the position of the proxy • p’ is the new position of the proxy • v is the position of the probe • s is the stiffness parameter of the surface, 0≤s≤1 • p’ is used for the haptic control loop • p is retained for surface following

17. Reference • D. Ruspini, K. Kolarov, and O. Khatib, "The Haptic Display of Complex Graphical Environments," in Computer Graphics Proceedings (ACM SIGGRAPH 97), 1997, pp. 345-352.