Haptic Rendering

Stanford ME327: Design and Control of Haptic Systems — © Sonny Chan, 2014

Haptic Rendering

• “The process of computing and generating forces in response to user interaction with virtual objects”

- Kenneth Salisbury, 1995

Haptic Rendeing

Rendering DOF

1-DOF 3-DOF 6-DOF

How rendering works ?

Stiffness ?

Kinesthetic Impedance Type

1-DOF Virtual Wall Rendering

• Unilateral linear spring• Useful for mechanism design, control, stability

Potential Field Rendering

Virtual Box

Virtual Box

Virtual Box

Virtual Box

Virtual Box

Virtual Box

Virtual Box

Potential Field Problems

• Pop-out• Pop-through

• How do we deal with these ??

God-Object Algorithm

• Avata, virtual proxy, god-object, etc.

Geometric Representation

Polygonal Meshes

Other Representations

God-Object Main Idea

• Constrain a virtual proxy of the haptic interface to remain on the surfaces

Contact with a Surface

Contact with a Surface

Contact with a Surface

Contact with a Surface

Collision Detection

Simulation/Optimization

Force Feedback

Two Constraints

Two Constraints

Two Constraints

God-Object Location Computing

Partial derivative w.r.t. x,y,z, l1, l2, l3

Force Feedback

Tool-mediated Interaction

Needs higher than 3-DOF interaction

Proxy-Based Rendering

6-DOF virtual Coupling

• Translational and rotational spring/damper coupling– Force proportional

to displacement– Torque proportional

to orientation difference

Proxy Simulation in 3-DOF

Proxy Simulation in 6-DOF

How to Simulate Proxy ?

Soft Constraints

Proxy Motion Simulation

• Numerically integrate the ODE over time to obtain x, the position of the avatar:

• Do the same with moments to obtain orientation

Simulation may goes unstable

High Stiffness environments

Quasi-Static Equilibrium

Quasi-Static Equilibrium

Quasi-Static Equilibrium

Quasi-Static Proxy Motion

• Solve directly for the position x for which the net force acting on the proxy is zero

• Do the same with orientation to obtain net moment of zero

What if Hard Environments ?

Hard Constraints

How to Simulate Proxy ?

Gauss’ Principle

• The Proxy’s constrained motion is that which minimize the acceleration energy

• Subject to the contact constraints:

which is the augmented form of non-penentraion constraint

• Solution can be obtained via quadratic programming

Hard Constraints

• Can integrate acceleration to obtain position as in previous method– Constrained dynamics

• Can move proxy directly to position that does not violate constraints, and minimum distance– Quasi-static formulation

Taxonomy

Three Constraints