Open loop dynamic control of parts moving on an intelligent motion surface along paths comp

Abstract: In this paper we will derive an off-line sensorless (open loop) dynamic control algorithm for moving parts on an Intelligent Motion Surface (IMS), along paths composed of sequences of straight line segments. The algorithm uses a dynamic squeeze force field to move parts around the IMS, assuming the dynamic force field will abruptly stop at the end of each straight line segment. We assume the path is given a priori, being obtained using one of the several well-known path planning methods available in the literature. Initially, we will derive the algorithm assuming the part is a particle coincident with its center of mass. Later, we will relax this assumption, making the necessary modifications to the algorithm to take into account the part’s geometry. 1. Introduction The robotic community has been studying Intelligent Motion Surfaces (IMS) as an alternative for automatic parts assembly on both macro and micro scales. In the past few years, there has been a special interest in the application of IMS for micro assembly, for which several IMS prototypes where built and are being tested using a variety of technologies [2,5,8,9]. The IMS, an array of manipulators that in aggregate form a programmable motion surface, can be programmed to have the effect of inducing force fields on objects placed on it. The array is usually built from simple manipulators, each capable of moving in one single direction. The appropriate choice of force fields can move objects in manners that are suitable for mechanical assembly operations such as rotation, translation, orientation, alignment, parts feeder, and spatial filtering, among others [4]. We envisage the IMS being used as a workbench with several work cells, where parts are manipulated and assembled in each work cell, and are transported between work cells (see Figure 1.) Several sensorless manipulation strategies have been proposed to manipulate parts within a work cell using static force fields [4, 10], borrowing ideas from manipulation strategies using the well-known parallel jaw gripper [7]. However, most of them are based on quasi-static analysis, not being applicable for the case of dynamically controlling the movement of parts between work cells. In the latter case, the dynamics of the parts being manipulated must be taken into account if one wants to come up with a robust sensorless dynamic control algorithm that guarantees the part will be correctly moved between work cells.
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This work is sponsored by DARPA under Fort Huachuca Contract No. DABT-63-92-C-0052
center of mass. In section 6, we will relax this assumption, making the necessary modifications to the algorithm to take into account the part’s geometry. From now on, up to section 6, the words part and particle will be used interchangeably. 2. Using dynamic force fields to move parts between work cells Dynamic force fields have been introduced as a means of moving parts on an IMS [1]. A dynamic force field is a sub-region of the IMS that has its shape and/or position within the IMS changed on a time-varying basis. The idea is to put a force field around a part and move the force field in a continuous or discrete way, dragging the part along with the field (see Figure 1.) A realistic model of the movement of dynamic force fields was derived in [1], taking into account the discrete placement of the manipulators on the IMS surface. It was shown that the overall movement of the dynamic force field is not continuous, being limited to integer multiples of the length of the manipulators along the direction of movement. The derivation was made for the case of MEMS micromanipulators, but it is valid for the macro scale case as well. This overall movement constraint affects the dynamics of parts being manipulated and how fast we can move the dynamic force field without losing the part during the movement. This last problem is defined as the capture condition [1]. 3. Moving parts along a straight line segment using a squeeze force field A design goal of our algorithms is to maximize throughput. In order to achieve that, we need to move parts robustly and fast between work cells. Robustly implies that we will enforce the capture condition at all times. Fast implies that we will choose a particular dynamic force field and move it in such a way that the part will gain as much velocity as possible. In [1], we have derived a sensorless (open loop) dynamic control algorithm that enforces the capture condition while moving a part along a single straight line path, using a squeeze force field (see Figure 2.) The algorithm consists of moving the squeeze force field by a fixed distance d using non-uniform time steps. The time steps were computed in order to keep the part, as long as possible, entirely inside the squeeze region that has its force vector pointing on the same direction of the movement. The algorithm was designed for the abrupt stop case, in which the squeeze force field stops moving as soon as its center