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Control >> Finding object/goal >> Chain formation
Chain formation
Robotic chains can be described by five characteristics.
First, robots can form a chain by following simple rules relying on
locally perceived information only. Second, in particular for open
environments, a chain of robots has the advantage that it keeps a
connection to a base station, thereby limiting the risk of robots to
get lost. Third, a robotic chain can establish connections between
different locations, in this way allowing other robots to exploit these
connections in order to navigate along them. Fourth, the distance
between such locations can be bigger than the perceptual range of one
robot. Thus, the group of robots forming a chain can collectively
overcome the limitations of a single robot. Finally, the approach of
robotic chains is scalable to large groups of robots without the need
of a more complex control strategy, a quality that is fundamental to
swarm robotics.
Combining these characteristics, robotic chains can be
clearly distinguished from other exploration strategies. For instance,
planner based systems, which often rely on map-learning and
path-planning strategies, may enable a robot to memorize important
features of the perceived environment, thereby avoiding that the robot
gets lost and possibly enabling it to navigate between distant
locations. On the other hand, for a robot to create an internal map
representation of its environment, complex control strategies are
required that rely on idiothetic/proprioceptive sensors which provide
internal information about the robot's movements. As such idiothetic
sensors involve an integration process, they are subject to cumulative
error. Their quality accordingly decreases continually. Furthermore,
the control complexity increases rapidly when applied to groups of
robots. At the other end of the control spectrum, purely reactive
approaches to exploration may enable the use of simple control
strategies, and are often scalable to large groups of robots, but they
are neither able to avoid the risk for a robot to get lost in open
environments, nor do they provide a mechanism to navigate between
distant locations.
Experimental setup
Our basic goal is to let the s-bots form visually connected
chains, where each s-bot aggregated into a chain has to activate an
appropriate colour such that a chain becomes a directed structure that
can be used for navigation purposes. We realize this by using a
behaviour based architecture to control the s-bots. This controller
results in the execution of a particular behavioural set, which may
differ in time depending on the state of an s-bot. There are four
simple behaviours:
- Adjust distance (AD): attraction/repulsion with respect to
one given object. The AD behaviour depends on the perceived distance
and direction to the respective object, and on a distance constant
d(aa) that represents the desired distance.
- Move perpendicular (MP): executed with respect to one
given object. When executed in combination with the AD behaviour it
results in turning around a certain object. The MP behaviour depends on
the perceived direction to the respective object only.
- Adjust angle (AA): executed with respect to two given
objects; results in moving between those two objects. The MP behaviour
depends on the perceived directions to the respective objects.
- Avoid obstacles (AO): repulsion from each object that
causes an activation of the proximity sensors.
Each of the behaviours computes a two dimensional vector that
represents the desired direction of movement (direction of the vector)
and the desired speed (length of the vector). While for the AD, MP and
AA behaviours the required information is taken from the camera, the AO
behaviour uses the proximity sensors. In each state the vectors of the
respectively active states are added and the resulting vector is used
to determine the activation of right and left wheel. The following
three states can be distinguished:
- Explorer: The intial state for each s-bot at the beginning
of an experiment. An explorer searches an existing chain and, in case
it finds one, moves to its end to eventually connect itsself to the
chain. In order to connect to a chain the s-bot has to reach a certain
distance from the chain and then activate its LED ring with the
appropriate colour. The active behaviours are AD, MP and AO.
- Chain member: We distinguish three different control
strategies when an s-bot is aggregated into a chain:
- Static Strategy: The control for a static chain member
is very simple. The chain member keeps its position and does not move
until it disaggregates from the chain. As no movement is required, no
behaviour is active.
- Aligning Strategy: A chain member aligns itsself with
respect to its two neighbouring chain members. This is realized by
adjusting the distance to the previous neighbour and moving between the
previous and the next neighbour. The last member of a chain, which only
perceives a previous but no next neighbour, only adjusts its distance
with respect to the previous neighbour. The active behaviours are AD,
AA and AO.
- Moving Strategy: The moving strategy only differs from
the aligning one by the behaviour of the last member of a chain. In
addition to adjusting the distance a perpendicular movement is executed
so that the last member of a chain moves around its previous neighbour.
As all other chain member align themselves, this strategy results in
the coordinated movement of a chain as a whole. All four behaviours are
active.
- Lost: When a robot cannot perceive any chain member it
enters the lost state and does not move until a chain is perceived
again. No behaviour is active.
A switch from the explorer to the chain member state is
probabilistic. At each control time-step (100 ms) there is a
probability P(expl->chain) for an explorer to become a chain member,
and a probability P(chain->expl) for a chain-member to become an
explorer.
Results
Figure 1 displays the number of formed chains for a group
size of 10 s-bots and the three control strategies when varying the two
control probabilities.
Figure 1. Number of chains, 10 s-bots.
Looking at the graphs, we can recognize that for all control
parameters and all strategies, the system forms in average between 1
and 3 chains. The results for the static and the aligning strategy are
very similar. A maximum number of roughly three formed chains is
reached for P(chain->expl) close to 0, and P(expl->chain) close
to 1. For the moving strategy, the number of formed chains is in
general lower than for the other two strategies. Usually, no more than
two chains are formed, and for a wide area of parameter combinations
there is just one. Thus, it is possible to control the structure of the
formed chains by varying the two control parameters.
References
Control >> Finding object/goal >> Chain formation
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