Motivation Physical Components

The algorithm consists of three components:1. Initialization – averages the target shapes2. Control to Match Targets – using a heuristic feedback

controller, actuates the current design to best match each target shape

3. Update Design – adds an actuator set (IPAM and jamming cells) where the error is greatest

Automatic Design Algorithm

Future Directions Acknowledgments

Deformable Model

This work was supported by U.S. Army Medical Research and Materiel Command (USAMRMC; W81XWH-15-C-0091) and by the National Science Foundation Graduate Research Fellowship Program.

References[1] A.A. Stanley, A.M. Okamura, “Controllable Surface Haptics via Particle Jamming and Pneumatics”, IEEE Transactions on Haptics, 2015. [2] E. Reichman, Emergency Medicine Procedures. McGraw-Hill Medical, 2013.

Model-Based Design of a 3D Haptic Shape Display

Margaret Koehler, Nathan S. Usevitch, and Allison M. OkamuraDepartment of Mechanical Engineering, Stanford University

Haptic shape displays render physicalenvironments for human interaction.Previous displays were primarily planar,2.5D displays [1]. We’ve developed a 3Dshape display and an automatic designalgorithm to display a set of target shapes.

We developed an iterative design algorithm fortwo reasons:

• To reduce the number of actuatorsrequired to reach particular shapes ofinterest. Many actuators are needed toreach an arbitrary shape, but we cansimplify the manufacturing process bylimiting ourselves to a small set of shapes.

• To take advantage of modernmanufacturing methods (like 3D printing)which admit arbitrary geometry and allowcustomization.

Spherical coordinates are used to compareshapes, and the number of actuators arespecified by the user.

To explore possible shapes and as a tool for the automatic design algorithm,we developed a mass spring model of our device.

• Shape sensing so the device could be used as both an input and output device• More sophisticated design optimization techniques as well as more complex shapes• Using different actuators or physical design components• Dynamic motion rather than a static target shape

• A silicone membrane provides the initial restshape as well as the surface with which the userinteracts. This closed membrane can be inflatedproviding a global shape actuator.

• Inverse Pneumatic Artificial Muscles (IPAMs) arepressure controlled linear actuators that controlthe distance between two attachment points onthe interior of the membrane.

• Particle jamming cells embedded in the surfaceprovide variable stiffness, which can be used forhaptics or for shape control.

Base Mesh

Initialization

Initial Design

Target Shapes

Control to

Match Targets

Reached Shapes

Update Design

New Design

Input

Process

Output

A cube prototype with 3 IPAMs and 6 jamming cells can reach different configurations depending on the actuation sequence.

The algorithm consists of three components:1. Initialization – averages the target shapes2. Control to Match Targets – using a heuristic feedback controller, actuates

(in simulation) the current design to best match each target shape3. Update Design – adds an actuator set (IPAM and jamming cells) where the

error is greatest in order to correct that error

IPAMs

Control to Match Targets

For each target shape, Tj

Input

Tj

Dynamic Simulation

Mass spring model

for 0.1 sec

Does m = mmax?

Is the model at

equilibrium and are

all controls within

their deadbands?

Output

Sij

Output

Sij + warning

yes

no

yes

Control Step

IPAM 3, push-pull

ΔPI,1 = cI(LT – L)

IPAM 2, push-pull

ΔPI,1 = cI(LT – L)

IPAM 1, push-pull

ΔPI = c(LT,m – Lm)

Main chamber

Δnair = (VT – Vm)*Pm/RT

Jamming Cell 3

ΔPI,1 = cI(LT – L)

Jamming Cell 2

ΔPI,1 = cI(LT – L)Jamming Cell 1

if κm ≤ min(κT,m, κm-1)

or κm ≥ max(κT,m, κm-1)

then: jam

Step count

m = m+1

Initial

Di

no

Symbol Meaning

Di

Design after the ith iteration of the design loop (has i linear actuators)

Tj Target Shape j

Sij Design i actuated to match Target j

mControl loop iteration count, indicates which quantities change each iteration

κ(?) Curvature heuristic, (T)arget curvature

L(?)

Actuator Length, (T)arget length, (N)atural length

P(?) Pressure, main (C)hamber or (I)PAM

V(?) Volume, (T)arget volume

c Actuator constant (not a spring constant)

RT Gas constant and constant temperature

Above: The heuristic feedback controller for the Control to Match Targets step. Below: An example with a cube and a heart shape and five IPAMs.

The Design Algorithm

Applications• Medical training simulators – model organs that change shape and

stiffness properties to display different healthy and diseased states• Haptic feedback for more immersive virtual reality.

Cardiac massage - a medical skill our device could help train.

Bending stiffness, crucial for jamming, is added via torsional dihedral springs.

IPAMs connect to triangle faces and are modeled as springs with controllable

natural length.

The silicone membrane is modeled as a triangle

mesh with a point mass at each vertex and a spring-

damper at each edge.

Input Target Shapes Output Shapes

Output Design

IPAM attachment points are blue. Jamming Cells

are pink.