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# 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. The following five types form the set of Atomic Motions (AMs):

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

The table below shows 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 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, …):