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What Is Haptic Rendering?

Master-Slave Systems

Human-in-the-Loop

Robot

Force Feedback

Haptic

Device

Human

Simulation

Tactile Feedback

Virtual Reality

Pictures: http://haptic.mech.nwu.edu/intro/gallery/

M. C. Lin

Why Haptics?

- Natural 3D interaction with a simulated environment. Not constrained by a 2D projection.
- Additional sensorial input. Visual is dominant. Exploit extra dimensions, ‘cheat the user through the eyes’… In case of inconsistencies, visual wins.

M. C. Lin

Inter-disciplinary Research

Computer

Science

Electrical

Engineering

Mechanical

Engineering

Haptic Rendering

Control and actuators

Mechanical design

Computation of the forces output by the device

M. C. Lin

To be covered

Haptic rendering for pen-type devices:

Point-Object interaction

Object-Object interaction

- 3DOF Haptics(3D force output)
- 6DOF Haptics (3D force + torque output)

DOF = Degree of Freedom

M. C. Lin

Some History

- Argonne ’54, first master-slave systems. Master=slave.
- Salisbury ’80, independent master and slave. Cartesian control of robot arm. Later, interaction with computer simulated slave (VR).
- GROPE project UNC ’67-’90, molecular docking.
- Minsky ’90, the Sandpaper.
- Massie & Salisbury ’94, the Phantom.
- Early 90’s to ’97, 3DOF haptics.
- Late 90’s to today, 6DOF haptics.

M. C. Lin

Control of Haptic Devices

- Admittance devices

- Impedance devices

User

x, v

Simulation

User

F

Simulation

F

Actuators

F*

x

Actuators

x*

- Collision detection + contact response model
- More popular

- Collision detection + position constraints
- Bulkier and more expensive
- Very good for virtual walls

M. C. Lin

1KHz Performance Requirement

- The user becomes part of the simulation loop.
- 1KHz is necessary so that the whole system doesn’t suffer from disturbing oscillations.

Think of the analogy with numerical integration of a system with spring, mass and damper, where the frequency of the haptic loop sets the integration step.

- The Phantom haptic devices run their control loop at 1KHz.
- Consequence: we are very limited on the amount of computation that we can do.

M. C. Lin

Object-object

3DOF Haptics: Intro- Output: 3D force 3DOF haptics
- Limited to applications where point-object interaction is enough.
- Haptic visualization of data
- Painting and sculpting
- Some medical applications

M. C. Lin

3DOF Haptics: Basic approach

- Check if point penetrates an object.
- Find closest point on the surface.
- Penalty-based force.

x

F

M. C. Lin

3DOF Haptics: The problems

- Force discontinuities when crossing boundaries of internal Voronoi cells.

Unexpected force discontinuities (both in magnitude and direction) are very disturbing!

F2

F1

M. C. Lin

3DOF Haptics: The problems

- Pop-through thin objects.

After the mid line is crossed, the force helps popping through.

motion

M. C. Lin

3DOF Haptics: Point-to-plane

- Mark et al., 1996.
- For distributed applications. The simulator sends the equation of a plane to the haptic loop. The update of the plane is asynchronous.
- Forces are computed between the haptic point and the plane.
- Possible stiffness is limited, because too stiff would bring a jerky behavior at low update rates.

M. C. Lin

3DOF Haptics: God-object

- Zilles and Salisbury, 1995.
- Use the position of the haptic interface point (HIP) and a set of local constraint surfaces to compute the position of god-object (GO).
- Constraint surfaces defined using heuristics.
- Compute GO as the point that minimizes the distance from HIP to the constraint surfaces. Lagrange multipliers.

M. C. Lin

Concavity: 2/3 constraint planes in 3D

motion

motion

3DOF Haptics: God-object- Constraint surfaces:
- Surfaces impeding motion
- GO is outside (orientation test) and in the extension of the surface.
- The HIP is inside the surface.

M. C. Lin

3DOF Haptics: God-object

- Constraint plane equations:
- Energy function that will account for the distance.
- Define cost function using Lagrange multipliers.
- Minimize, solving for x, y, z, l1, l2 and l3.

3 planes at most

M. C. Lin

3DOF Haptics: God-object

- Partial derivatives on x, y, z, l1, l2 and l3 yield 6 linear equations:
- In case of less than 3 planes, the problem has a lower dimension.

M. C. Lin

3DOF Haptics: Virtual proxy

- Ruspini et al., 1997.
- Based on god-object.
- Virtual proxy is a small sphere, instead of a point. Use configuration-space obstacles (C-obstacles), from robotics.
- More formal definition of constraint planes.
- Implementation of additional features, based on relocation of the virtual proxy.

M. C. Lin

3DOF Haptics: Virtual proxy

- C-obstacles: for a spherical object, is reduced to computing offset surfaces at a distance equal to the radius of the sphere.
- Check the HIP against the offset surface.
- This is done to avoid problems with small gaps in the mesh.

M. C. Lin

3DOF Haptics: Virtual proxy

- Finding the virtual proxy is based on an iterative search.
- Basically, find subgoals based on the same distance minimization as for the god-object.
- At each subgoal, all the planes that go through that point are potential constraints. The minimum set of active constraints is selected.
- If the subgoal is in free space, set as new subgoal the HIP. The path might intersect the C-obstacles. Add the first plane intersected as a constraint and the intersection point as the current subgoal.
- The process ends when the virtual proxy becomes stable.

M. C. Lin

3DOF Haptics: Virtual proxy

HIP(t)

Perform collision detection between the path of the HIP and the C-obstacles

HIP(t+Dt)

M. C. Lin

3DOF Haptics: Virtual proxy

HIP(t)

Find a new subgoal using the active planes and the minimization based on Lagrange multipliers

HIP(t+Dt)

M. C. Lin

3DOF Haptics: Virtual proxy

HIP(t)

Since the subgoal is in free space, drop the constraints, set the HIP as the new subgoal and perform collision detection between the path and the C-obstacles

HIP(t+Dt)

M. C. Lin

3DOF Haptics: Virtual proxy

HIP(t)

The path to the new subgoal intersects another plane, so this is added to the set of constraints

HIP(t+Dt)

M. C. Lin

3DOF Haptics: Virtual proxy

HIP(t)

Compute active constraints (in 2D there are only 2) and find subgoal

For this example, this is the final position of the virtual proxy

HIP(t+Dt)

M. C. Lin

3DOF Haptics: Virtual proxy

- Quadratic programming approach:
- The constraint planes define an open convex region (bounded by the plane at infinity).
- The function to minimize is the distance from the haptic device (HIP) to the new subgoal (VPi+1):
- The translation from the current location to the new subgoal cannot intersect the constraint planes. Define linear constraints based on the normals of the planes.

Quadratic function

Linear constraints

M. C. Lin

Plane at

Plane at

Plane at

Face (all surrounded by the plane at )

Edge

Vertex

3DOF Haptics: Virtual proxy- Special case: simplified approach.
- Let’s look at the convex region defined by the constraint planes

M. C. Lin

3DOF Haptics: Virtual proxy

- Normals (n) become points (-n) in a dual space (Gauss map).
- The plane at infinity is the origin (o).
- Points (-n) are joint together if the associated planes intersect.
- The position of the virtual proxy also has a dual:
- The vertices of the closest feature to P are the duals of the active constraint planes that are used for the minimization with Lagrange multipliers.

M. C. Lin

3DOF Haptics: Virtual proxy

M. C. Lin

3DOF Haptics: Virtual proxy

- Force output: PD (proportional- derivative) control. Produces a force that will try to keep the VP and the HIP at the same position.

VP

F*

F

Simulation

PD control

Actuators

HIP

User

It’s like a spring+damper, but the authors look at it from a control engineering approach

M. C. Lin

A1

A2

A3

v2

v1

3DOF Haptics: Additional features- Force shading by Basdogan et al., 1997.
- Interpolate per-vertex normals using baricentric coordinates (same as Gouraud shading)
- Effect: edges and vertices seem ‘rounded’

M. C. Lin

VP

Original plane

HIP’

HIP

3DOF Haptics: Additional features- Force shading by Ruspini et al., 1997.
- Modify the position of the VP.
- A subgoal (HIP’) is computed changing the normal of the plane.
- This subgoal replaces the HIP, and the final VP is computed.

M. C. Lin

3DOF Haptics: Additional features

- Other effects by Ruspini et al., 1997.
- Friction.
- Textures.
- Deformation.
- All of them are achieved performing operations that modify the position of the VP.

M. C. Lin

3DOF Haptics: Additional features

- Friction by Hayward and Armstrong, 2000.
- Model friction as an elasticity between the actual contact point (x) and a fictitious point, called adhesion point (w).
- The adhesion point remains static or follows the actual contact depending on the ‘state’ (sliding, static…)

w

x

M. C. Lin

3DOF Haptics: H-Collide

- What about the collision detection?
- Spatial uniform decomposition of space. Locate the path traversed by the probe in that grid, using a hash table.
- Test the path against an OBBTree. Optimized test.
- Use frame-to-frame coherence, caching the previous contact, and perform incremental computation.
- When the leaf intersects, compute the surface contact point (SCP). Pass this to GHOST (haptic rendering library used by the Phantoms).

M. C. Lin

3DOF Haptics: H-Collide

Ray Vs. OBBTree test

Spatial partitioning with hash table

SCP computation

SCP

M. C. Lin

6DOF Haptics: Intro

- Output: 3D force + 3D torque
- For applications related to manipulation.
- Assembly and maintenance oriented design. Removal of parts from complex structures.
- Typical problem: peg-in-the-hole.

There is a net torque

M. C. Lin

6DOF Haptics: Intro

- Formulate the problem as a rigid body simulation problem and output to the user the forces exerted on the object. Why not?
- Too expensive
- Constantly facing a situation of resting contacts.
- Too much time performing collision detection to find non-penetrating situations.
- Solve the linear complementarity problem.
- Theoretically, it seems like the natural extension of the virtual proxy, though.

M. C. Lin

com

com

com

Haptic device (xh, qh)

6DOF Haptics: IntroThe position of the center of mass (com) and the orientation cannot be governed directly by the haptic device.

Interpenetrations would be unavoidable.

M. C. Lin

Contact area

Contact points (e.g. local minima of distance function)

6DOF Haptics: Contacts- We cannot afford to compute ‘exact’ contacts.
- Allow tolerances. Consider as valid contact whatever is inside a distance tolerance.
- Outward offset surfaces are better. Distance is cheaper to compute than penetration.

M. C. Lin

6DOF Haptics: Major approaches

- All the approaches suffer from the fact that it’s an output-dependant problem.
- Point cloud Vs. voxelized model. It can be linear on the number of points. The number of points grows quadratically with the resolution.
- Polygonal models. At least linear on the number of convex pairs inside the tolerance.
- NURBS. Very complex exact distance computation between NURBS surfaces.

M. C. Lin

6DOF Haptics: Voxel sampling

- McNeely et al., 1999.
- Voxelize all the models in the scene.
- For the haptic object, represent each voxel by a point Point Shell.
- Test points against voxels of the scene.
- Compute force at each point that penetrates an object.
- Add up all the force and torque, and apply them to the user through virtual coupling.

M. C. Lin

6DOF Haptics: Voxel sampling

- All the objects are voxelized.
- For the haptic object, store points at the center of the voxels, with inward normals determined by the polygonal model.
- For the objects in the scene, create the voxmap, a 512-tree with 3 levels (the 512-tree is an extension of the octree, with 512 children per node, cube of 8*8*8). The 512-tree optimizes memory.
- The initial implementation is only for static objects.

M. C. Lin

surface

proximity

free space

6DOF Haptics: Voxel sampling- All the voxels in the voxmap store info about their position in the object: interior, surface, proximity or free space.

M. C. Lin

6DOF Haptics: Voxel sampling

- To start the collision query, all the pointshell has to be transformed to the local coordinates of the voxelized objects.
- Points that are in the surface or proximity voxels are considered as contacts.

M. C. Lin

Take the plane with normal N that goes through the center of the voxel. Compute d as the distance from the point to that plane.

d

6DOF Haptics: Voxel sampling- Forces at each contact are computed according to the tangent-plane force model.
- Contacts are valid if d<0 (penetration).
- If penetration to the interior happens, the contact is missed. One might think of computing a distance field in the interior, but the distance depends on the normal N.

M. C. Lin

d1

d1d2

The contact might even show up or disappear suddenly

d2

motion

6DOF Haptics: Voxel sampling- The force is continuous in direction, but discontinuous in magnitude.
- The virtual coupling (see later) is supposed to filter these discontinuities.

M. C. Lin

6DOF Haptics: Voxel sampling

- Force per contact:
- Add all the forces together.
- Several contacts act as a single contact with higher stiffness.
- Limit the total stiffness:
- There can still be problems of irregular distribution of stiffness.

If n<10

If n>10

M. C. Lin

F2=k*d2

1 contact

5 contacts

6DOF Haptics: Voxel sampling- Irregular distribution of stiffness.
- Geometry-driven instabilities

F2=F1 d2=5*d1

Risk of penetration!

Object bounces from one side to the other.

More common due to torque on long objects.

M. C. Lin

6DOF Haptics: Voxel sampling

- Penetration has to be avoided.
- Pre-contact braking forces. Strong viscous force applied in the proximity layer.
- The viscosity is adjusted so that all the kinetic energy is dissipated in a distance equal to the width of the layer.

M. C. Lin

6DOF Haptics: Voxel sampling

- Virtual coupling, see Adams and Hannaford, 1998.
- Spring-damper between the position and orientation of the haptic device and the position and orientation of the object.
- Filters discontinuities, to enhance stability. We can run into numerical integration problems, though.

M. C. Lin

6DOF Haptics: Polygonal models

- Gregory et al., 2000; Kim et al., 2002.
- Convex decomposition of polygonal models.
- Collision detection (modified SWIFT++), returning all pairs of convex pieces within a tolerance. Handle shallow penetrations.
- Cluster contacts.
- Combination of penalty-based restoring forces and impulsive response.

M. C. Lin

6DOF Haptics: Polygonal models

- SWIFT++, by Ehmann and Lin, 2001.
- Hierarchy of convex pieces.
- Voronoi marching between pairs of pieces. Travel down if the distance is less than the tolerance.

M. C. Lin

6DOF Haptics: Polygonal models

- Modifications to SWIFT++:
- Return all pairs of pieces inside the tolerance (group that contains the set of local minima of the distance function).
- Handle shallow penetrations, computing penetration depth between convex pieces. Check for pairs of features with overlapping normals.

M. C. Lin

Surface decomposition

6DOF Haptics: Polygonal models- Convex decomposition:
- Hard problem. The decomposition might not be efficient. Explosion of pairs O(n4).
- Surface decomposition Convex patches, completed with virtual faces. Linear size.

M. C. Lin

6DOF Haptics: Polygonal models

- Surface decomposition good for finding global minimum in disjoint situation. Unique pair of features, both original.
- Problems for local minima and penetration. The features might be virtual.
- If a single face is a convex piece itself, penetrating contacts might be missed.

M. C. Lin

6DOF Haptics: Polygonal models

- Cluster contacts.
- Find unique contact (distance, normal and point), averaging contacts in a neighborhood.
- Weighted average, using distance as the weight.
- This solves the problem of the irregular distribution of stiffness.
- Pretty smooth varying forces in practice, without need of virtual coupling.
- Additional features (texture, friction…) can be rendered in a per-contact basis.

M. C. Lin

6DOF Haptics: Unsolved problems

- Generalization of Virtual Proxy to 6-DOF haptics
- Haptic Texture Synthesis
- Applications
- Endoscopic sinus surgery
- 3D Painting with deformable brushes
- 3D deformable objects

M. C. Lin

References

R. J. Adams and B. Hannaford. A Two-port Framework for the Design of Unconditionally Stable Haptic Interfaces. In Proc. of IEEE/RSJ Int. Conference on Intelligent Robots and Systems, 1998.

C. Basdogan, C. H. Ho and M. Srinivasan. A Ray-based Haptic Rendering Technique for Displaying Shape and Texture of 3D Objects in Virtual Environments. In the Proc. of ASME Dynamic Systems and Control Division, 1997.

G. Burdea. Force and Touch Feedback for Virtual Reality. John Wiley and Sons, 1996.

S. A. Ehmann and M. C. Lin. Accurate and Fast Proximity Queries between Polyhedra Using Surface Decomposition. In Proc. of Eurographics, 2001.

A. Gregory, M. C. Lin, S. Gottschalk and R. M. Taylor II. H-Collide: A Framework for Fast and Accurate Collision Detection for Haptic Interaction. In Proc. of IEEE Virtual Reality Conference, 1999.

A. Gregory, A. Mascarenhas, S. Ehmann, M. C. Lin and D. Manocha. Six Degree-of-Freedom Haptic Display of Polygonal Models. In Proc. of IEEE Visualization, 2000.

M. C. Lin

References

V. Hayward and B. Armstrong. A New Computational Method of Friction Applied to Haptic Rendering. In Lecture Notes in Control and Information Sciences, Vol. 250, Springer-Verlag, 2000.

Y. J. Kim, M. A. Otaduy, M. C. Lin and D. Manocha. Six-Degree-of-Freedom Haptic Display Using Localized Contact Computations. To appear in Proc. of Haptic Symposium, 2002.

W. R. Mark, S. C. Randolph, M. Finch, J. M. Van Verth, and R. M. Taylor II. Adding Force Feedback to Graphics Systems: Issues and Solutions. In Proc. of ACM SIGGRAPH, 1996.

W. A. McNeely, K. D. Puterbaugh and J. J. Troy. Six Degree-of-Freedom Haptic Rendering Using Voxel Sampling. In Proc. of ACM SIGGRAPH, 1999.

D. C. Ruspini, K. Kolarov, and O. Khatib. The Haptic Display of Complex Graphical Environments. In Proc. of ACM SIGGRAPH, 1997.

C. Zilles and K. Salisbury. A Constraint-based God Object Method for Haptic Display. In Proc. of IEEE/RSJ Int. Conference on Intelligent Robots and Systems, 1995.

M. C. Lin

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