M. Zareinejad

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

Why sphere?
◦ To solve the ‘fall-through’ problem of the GodObject method
◦ For easy collision-detection

‘Fall-through’ of the God-Object

Virtual Proxy’s behavior in the same
situation

Example


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

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


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

A sub-goal can be represented by
minimize ∥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

the force exerted on the proxy by the user
can be estimated by
f = 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

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

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
f t  d f n  mx  bx

Because the mass of the proxy is 0, the
previous equation can be rewritten as
f t   d f n  bx ,
x 

( ft  d f n )
b
This equation can be used to bound the
amount that the proxy can move in one
clock cycle



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
p  v  s ( p  v )

◦
◦
◦
◦


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

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.