EVALUACIÓN DEL DESEMPEÑO PROFESIONAL DE LOS DOCENTES

This section compares these three different assembly methods by their performance on several example structures. Relevant quantities are the time necessary for structure completion, and the amount of communication required. The latter factor includes both messages passed within the structure (that is, between blocks which are physi-cally connected), and messages passed from the structure to robots moving along its surface.

As in two dimensions, the physical presence of robots will be an implementation-dependent restriction on possible structures: any deliberate infoldings of the surface need to leave enough room for robots to move over the surface freely. The size and geometry of robots will also affect how close they can get to one another. In these experiments I do not explicitly consider the physical presence of robots; a robot carrying a block takes up the same space (one grid cell) as a block alone. The effect is equivalent to self-mobile blocks. Blocks are allowed to move in any direction along the structure surface, and to approach each other as closely as to occupy two adjacent sites.

Experiments proceed as follows. A structure begins with a seed block in an empty workspace. Ten robots carrying blocks are placed at random a constant distance away. Each moves inwards until it reaches the growing structure, then moves along its surface according to one of the three approaches discussed above. At each step adjacent to the surface, a robot receives a message from neighboring blocks about whether it can legally attach at that site; with the gradient approach, direction infor-mation is communicated as well. Additional communication may take place within the structure, as blocks are added and allowed attachment sites change, and (when applicable) as gradient information is updated. The simulations implement the algo-rithms in a centralized way, but calculate at each step the approximate number of messages that would be sent in a decentralized implementation. Each time a robot finishes attaching a block, it moves instantaneously back to a random position at the original distance from the seed, holding a new block. Messages travel infinitely fast compared to the speed of robot movement. Movement updates are asynchronous.

Figure 7-4 shows experimental results, averaged over ten runs each for various structures, for the total distance robots move along the surface of the structure during assembly, the number of messages sent to robots from the structure, and the number of messages passed within the structure.

1. The random walk approach requires more robot travel than do the other ap-proaches. This difference increases for structures with greater surface area.

S M1 M2 0

1 2 3 4 5 6x 10⁴

S M1 M2

0 1 2 3 4 5 6x 10⁴

S M1 M2

0 1 2 3 4 5 6x 10⁴

S M1 M2

0 1 2 3 4 5 6x 10⁴

S M1 M2

0 2 4 6 8 10x 10⁵ Random movement

Systematic search Gradient−based

Figure 7-4: Performance comparison for the three movement approaches, for various structures. S: Steps taken along surface. M1: Messages passed to robots from structure.

M2: Messages passed within structure.

2. The systematic search eliminates a great deal of repeated movement and guar-antees that robots will reach every allowed site in bounded time.

3. With the gradient-based approach, robots travel distances an order of magni-tude smaller still, as they are directed straight to the closest available site. How-ever, the cost is at least an order of magnitude more communication within the structure, to establish and maintain the gradient. Additionally, the (fewer) mes-sages sent to robots from the structure will need to contain more information, specifying movement direction in addition to whether attachment is allowed.

These costs may be bearable in practice for the sake of the speedup in con-struction, since communication between blocks which are physically connected should be rapid, unambiguous, and reliable, and hence of low cost compared to movement or less direct communication.

FromNarbonic 2000 Shaenon Garrityc www.narbonic.com Used with permission.

Chapter 8

Other extensions

This chapter discusses other extensions to the approach described in previous chapters. Section 8.1 discusses how temporary structures could be disassembled by the same robot construction team. Section 8.2 discusses recovery from failures (of the blocks, robots, or marker). Section 8.3 discusses building structures with de-liberate holes. Section 8.4 discusses the isomorphism of this approach using square or cubic blocks to a “Tinkertoy”-style approach using rods and hubs to build open lattices. This chapter describes these issues in two dimensions, but three-dimensional extensions are straightforward.

8.1 Disassembly

Many applications will involve structures intended to be temporary. If block at-tachments are reversible, a swarm construction system like those described here can dismantle a structure following its use and reuse its parts for another structure. Disas-sembly can be accomplished by having robots follow the structure perimeter, removing any blocks they find that satisfy the following criteria:

1. The block has at most two neighbors, bordering adjacent sides; i.e., if that site were unoccupied, it could physically accomodate a block.

2. If it does have two neighbors along adjacent sides, then the other site which those two neighbors border is occupied by a block (Figure 8-1).

2 3

4 X

5 1

Figure 8-1: A structure in the process of disassembly. Numbered blocks can be removed. The block marked X meets criterion 1 in the text but not 2; if removed, it would split the structure into two parts.

Also, if the application involves a marker which acts as a tether and/or a beacon to let robots find the structure, then the marker must be the last block removed.

The first criterion assumes that physical constraints on block motion are the same for disassembly as they are for assembly. The second criterion ensures that throughout disassembly, the structure remains one contiguous piece. Violating this rule can result in part or all of the remaining structure becoming isolated. In a system where robots follow a beacon to reach the structure, a disconnected component will be lost to perimeter-following robots. If the structure is physically tethered to some anchor point via the marker (as would likely be the case, e.g., in underwater or space-based applications), then violating those criteria would mean that blocks could drift off and be lost in a more literal sense.

Care must also be taken with multiple robots that two blocks not be chosen for removal at the same time such that each block considered alone satisfies the criteria, but would violate criterion 2 if the other block were removed. Blocks 1 and 3 in Figure 8-1 illustrate such a pair.

Either blocks or robots may be responsible for determining whether blocks satisfy these criteria, according to whether communicating or noncommunicating blocks are involved.