# 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.