TABLE OF CONTENTS Table 1 summarizes fields and algorithms for manipulation tasks with programmable vector fields, and includes some additional recent results.
| task | field(s) | complexity | plan steps | |
|---|---|---|---|---|
| fields | planning | |||
| translate | constant | constant magnitude and direction |
| 1 |
| center | radial | constant magnitude, continuous directions |
| 1 |
| uniquely orient | seq. of squeezes | piecewise constant mag. and dir. | O( k 2 n 4) | O( k n 2) |
| inertial | smooth magnitude piecewise constant dir. | O(1) | O(1) | |
| uniquely pose | seq. of radial+squeeze | piecewise continuous mag. and dir. | O( k 2 n 2) | O( kn) |
| elliptic | smooth mag. and dir. | O(1) | O(1) | |
| UFO | continuous mag. and dir. |
| 1 |
Less difficult tasks such as translation can be achieved with relatively simple fields and without any planning. More complex tasks such as centering or unique orienting require increasingly complex fields. However, planning complexity is e.g. higher for sequences of squeeze fields, and lower for the more complex combined radial + squeeze fields (for a thorough discussion of these fields see [19]). This illustrates a tradeoff between mechanical complexity (the dexterity and controllability of actuator arrray elements) and computational complexity (the algorithmic difficulty of synthesizing a strategy).
Universal feeder-orienter (UFO) devices. Our research leads to the question about the existence of a "universal feeder-orienter" (UFO) device that uniquely poses a part without the need of a clock, sensors, or programming [19, 20]. It was shown in...
