# Atomic Motions

A driverless car’s entire software system outputs two degrees-of-freedom (2-DOF) motion, (*v, κ*) = (translation velocity, path curvature) to control the car. MotionLab has succeeded in dividing the entire system into the following two subsystems:

*The Decision-Making Subsystem**The Motion-Creation Subsystem*

Further, MotionLab has invented well-structured motion-creation algorithms that make up the Motion-Creation Subsystems.

We call the algorithms *Atomic Motions *(or *Minimal Motions*)*, *which we categorize into five types:

*Direction-Tracking*Atomic Motions: the vehicle tracks a direction ‘*α*‘ with a negative-feedback rule.*Line-Tracking*Atomic Motions: the vehicle tracks an oriented line ‘L’ with a negative-feedback rule.*Circle-Tracking*Atomic Motions: the vehicle tracks an oriented circle ‘C’ with a negative-feedback rule.*Curvature-Defined*Atomic Motions: the vehicle creates a motion using a curvature*κ*=*κ(s),*where*s*is arc length, 0 ≤*s*≤*S*, and*S*a positive total arc length.*Park*Atomic Motions: the vehicle moves forward or backward from the start frame ((0, 0), 0) to a target frame ((*x, y*),*θ*) minimizing the path complexity.

The table below lists the geometric object that is input for each type. These inputs are the narrow-bandwidth interface from the Decision-Making Subsystem to the Motion-Creation Subsystem:

**Input for Atomic Motion (AM) Types **

1. Direction-Tracking AM | Direction α, smoothness σ |

2. Line-Tracking AM | Frame ((x, y), θ); smoothness σ |

3. Circle-Tracking AM | Center (x, y), radius r, smoothness σ |

4. Curvature-Defined AM | Curvature function κ = κ(s), 0 ≤ s ≤ S, S > 0 |

5. Park AM | Frame ((x, y), θ) |

The dimension of each variable, where *L* means the length (its unit is 1 cm, 1 m, 1 foot, …):

*α, θ*: 1 (radian)

*x, y, r, σ, s, S: L*

*κ: L ^{-1}*

Thus, the units of all interface items are geometrical entities; 1, *L* or *L ^{-1}*.

The Decision-Making Subsystem may be dealing with a formidable amount of sensor data, big data, and AI methods, but it needs to output only a couple of geometric elements for the Motion-Creation Subsystem.