Direction-Tracking Atomic Motions

A Direction-Tracking Atomic Motion is an algorithm that makes a vehicle track a given direction φ using a negative feedback control rule with a critical dumping response. When the vehicle’s present heading is θ, the vehicle turns φ – θ. We call φ – θ a turning angle. If φ – θ > 0, the vehicle turns counterclockwise (CCW); otherwise, it turns clockwise (CW). Any turning angle is allowed; thus, the vehicle may execute more than one complete turn of ±360º.

The input to a Direction-Tracking Atomic Motion is a pair of two real numbers: direction φ and smoothness σ. Its output is a pair of two real numbers: velocity v and path-curvature κ. Characterize Atomic Motions: [6] Responsiveness of Tracking-Type Atomic Motions describes the role of the smoothness σ.

The following five motions showcase the capacity and programmability of Direction-Tracking Atomic Motions:

[1.1] Petals by Science Robot (Math Mind)

This motion consists of
12 “petals,” each of which is created by
a Direction-Tracking
Atomic Motion of +210º.

[1.2] Squash by Science Robot

Math Mind bounces back at “boundary walls,” keeping the reflection angle
the same as the incidence angle.

A Direction-Tracking Atomic Motion creates these exact motions.

[1.3] Squash by the Swan Robot

The Swan robot executes a similar motion to the above [1.2] Squash motion, while the founder’s grandsons use “rackets” to determine reflection angles.

The Swan finds the racket’s normal direction in real time using the sonars and the least-fit algorithm.

[1.4] “Pull” by the Swan Robot

Daniel “pulls” the swan robot or
the robot follows him.

Direction-Tracking Atomic Motions
create this motion.

[1.5] “Push” by the Swan robot

Push” is a motion by the Swan robot, which backs off from
an approaching person.

Direction-Tracking Atomic Motions
also create this motion.

[1.6] “Push-Pull” by the Swan robot

The Swan can execute a combination of “push” and “pull” motions:

Andrew plays with the Swan robot
using a “push-pull” motion.

Direction-Tracking Atomic Motions
also creates this motion.