Programmable vector fields can be used to
control a variety of flexible planar parts feeders.
These devices can exploit exotic actuation technologies such as
arrayed, massively-parallel microfabricated
motion pixels or
transversely vibrating (macroscopic) plates.
These new automation designs promise
great flexibility, speed, and dexterity - we believe they may be
employed to orient, singulate, sort, feed, and assemble parts. However, since
they have only recently been invented, programming and controlling
them for manipulation tasks is challenging.
When a part
is placed on our devices, the programmed vector field induces a force
and moment upon it. Over time, the part may come to rest in a
dynamic equilibrium state.
By chaining together
sequences of vector fields, the equilibrium states of a part in the
field may be cascaded to obtain a desired final state.
The resulting strategies
require no sensing and enjoy efficient planning algorithms.
This paper begins by describing our experimental devices. In
particular, we describe our progress in building the
M-Chip
(Manipulation Chip), a massively
parallel array of programmable micro-motion pixels. As proof of
concept, we demonstrate a prototype M-Chip containing over
11,000 silicon actuators in one square inch. Both the M-Chip,
as well as macroscopic devices such as transversely vibrating plates,
may be programmed with vector fields, and their behavior predicted
and controlled using our equilibrium analysis. We demonstrate
lower bounds (i.e., impossibility results) on what the devices
cannot do,
and results on a classification of control strategies
yielding design criteria by which well-behaved manipulation
strategies may be developed. We provide sufficient conditions
for programmable fields to induce well-behaved equilibria on every part
placed on our devices. We define composition operators to build
complex strategies from simple ones, and show the resulting fields
are also well-behaved. We discuss whether fields outside this class
can be useful and free of pathology.
Using these tools, we describe new manipulation algorithms. In particular, we improve existing planning algorithms by a quadratic factor, and the plan-length by a linear factor. Using our new and improved strategies, we show how to simultaneously orient and pose any part, without sensing, from an arbitrary initial configuration. We relax earlier dynamic and mechanical assumptions to obtain more robust and flexible strategies.
Finally, we consider parts feeders that can only implement a very limited ``vocabulary'' of vector fields (as opposed to the pixel-wise programmability assumed above). We show how to plan and execute parts-posing and orienting strategies for these devices, but with a significant increase in planning complexity and some sacrifice in completeness guarantees. We discuss the tradeoff between mechanical complexity and planning complexity.
