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# Line-Tracking Atomic Motions

A Line-Tracking Atomic Motion is an algorithm that makes a vehicle track a given oriented line ((x, y), θ) under a feedback rule with critical damping response. The X-axis of the frame ((x, y), θ) in the positive direction is the oriented line to be tracked. A parameter called smoothness σ creates the feedback gain-set for the algorithm. [6] Responsiveness of Tracking-Type Atomic Motions (on Characterizing Atomic Motions page) thoroughly discusses the role of the smoothness σ.
Line-Tracking is the most-frequently used Atomic Motion type in the Swan programming.

The following six vehicle motions showcase the performance and programmability of Line-Tracking Atomic Motions. The first motion Polygon Medley demonstrates the powerful and flexible programmability of Atomic Motions accompanied with Symmetric Geometry:

### [2.1] Polygon Medley by Science Robot

This Polygon Medley creates
a sequence of pairs of
counterclockwise and clockwise
regular-polygonal motions
with n edges, where 3 ≤ n ≤ 10.

To make an n-gon,
Math Mind has to track n edges.
In the process, Math Mind repeats
the following operation pair n times:
(a) creating the next edge by composing the current edge and a transformation,
(b) switching from the current edge
to the next edge at the best timing.

Two medley motions demonstrate the effect of distinct smoothnesses that generate sharper (or smaller) turns and less sharp (or larger) turns.

### [2.2] Square by the Swan robot

The Swan robot creates a CCW Square motion, as Science Robot did
in [2.1] Polygon Medleys.

The Swan robot dynamically extracts linear features of the structure
using the sonar data and the least-squares-fit algorithm
and tracks that line
.

Motions [2.1] and [2.2] demonstrate that Atomic Motions are hardware independent; identical motions run in two different hardware robots, Science Robot and the Swan robot.

### [2.3] Structure Hugging by the Swan robot

Several line-tracking Atomic Motions create this structure-hugging motion.

The Swan robot dynamically extracts linear features of the structure using the sonar data and the least-squares-fit algorithm and tracks that line.

### [2.4] The Swan robot hugs sitting people.

It is hard to define the envelope of
this three-person object using a finite number of straight line segments.

However, Line-Tracking Atomic Motions reliably hugs this curving envelope with high-fidelity movement.

### [2.5] Science Robot climbs up and down staircases.

This Staircase motion demonstrates Atomic Motions’ programmability and high-fidelity motions.

### [2.6] The Swan robot passes through a Gate.

The Swan robot detects two cans’ positions,
computes their bisector, and follows it
using a Line-Tracking Atomic Motion.

If a vehicle needs to pass
between two close objects or
pass through a narrow alley,
the use of this kind of bisector tracking
is necessary and extremely useful.