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# Circle-Tracking Atomic Motions

A Circle-Tracking Atomic Motion is an algorithm that tracks an oriented circle given with its center (xc, yc) and radius r. If r > 0, the circle is regarded as counterclockwise (CCW); if r < 0, it is regarded as clockwise (CW). This motion adopts a feedback control algorithm with critical damping response; the vehicle exponentially converges to the circle.
There is another input parameter, smoothness, σ. [6] Responsiveness of Tracking-Type Atomic Motions (on Characterizing Atomic Motions page) discusses the role of the smoothness σ.

The algorithms for line-tracking and circle-tracking Atomic Motions are somewhat similar because if the radius r of a circle becomes larger and larger, the circle converges to a line. The following seven motions showcase the capacity and programmability of Circle-Tracking Atomic Motions:

### [3.1] Circle Medley by Science Robot

This medley motion consists of a series of Circle-Train motions with 2 ≤ n ≤ 10. For each n, Math Mind tracks n circles aligned on a line, slightly detached from each other.

The orientations (CCW or CW) of adjacent circles are opposite.

This motion consists of 2n-1 circle tracking and 2n-2 switchings.

### [3.2] Circle Train with n = 3 by the Swan robot

The Swan robot tracks three circles aligned on a line, slightly detached from each other.

Science Robot and the Swan robot are executing identical motions in [3.1] and [3.2],
demonstrating that Atomic Motions
are hardware independent.

### [3.3] Necklace by Science Robot

Math Mind sequentially tracks 17 small circles, aligned on a big circle
and slightly detached from each other.

Math Mind visits each small circle
twice before it finishes the round trip;
notice that the number 17 is odd.

### [3.4] Necklace (2) by Science Robot

This motion is similar to the previous [3.3], except that the radii of small circles vary.
These variable radii make the movement
more complicated and more artistic.

This motion demonstrates the flexibility and programmability of Atomic Motions.

### [3.5] Satellite by the Swan robot

In this “Satellite” motion, the Swan robot applies Circle-Tracking Atomic Motions to create circular motions detecting the position of the nearest object (person) as the circle center.

When the robot detects another person
while tracking,
Swan switches the target circle
with an opposite turning orientation.

### [3.6] Bubbles by Science Robot

Math Mind initially tracks a CCW circle with a given constant radius.

A mouse click provides its new circle center. Then, the circle center continuously moves from the former center to the new one.

A user can change the turning orientationfrom CCW to CW or from CW to CCW by clicking the Switch Orientation button.

### [3.7] Circular-Motion Creation through Mouse Clicking by Science Robot

A series of mouse clicks creates a path,
which Math Mind tracks.
A path segment to be tracked is a circular arc
determined by the latest three points.

If the path conflicts with an obstacle,
Math Mind automatically avoids it.
Math Mind reports a driving-skill index
at the end.

We discuss “Driving Skills” by Science Robot in Path Complexity and Driving Skills.
There we deal with the same motion from a different perspective.