Characterizing Atomic Motions
We are discussing Atomic Motion’s characteristics and advantages that are common to all of the five types:
 Atomic Nature
An Atomic Motion is a vehicle-motion creation algorithm. We cannot divide any Atomic Motion into two or more simpler algorithms.
By installing in standard object-oriented programming languages, Atomic Motions create car-motions with any complexity the same way Lego blocks construct a large castle. The Swan robot and the Science Robot app present all sorts of motions powered by Atomic Motions.
Atomic Motions are installed in the Swan vehicle using the Java® language and are installed in the Science Robot app using the Xcode®.
 Unique Personality of Each Type
Each Atomic-Motion type possesses a unique “personality.” One Atomic-Motion type cannot replace another. For example, even though Direction-Tracking and Line-Tracking Atomic Motions look similar, they are never interchangeable. This uniqueness of Atomic-Motion types firmly supports Hypothesis K2 below.
 Hypothesis K1: Necessity and Sufficiency
MotionLab has experienced that Atomic Motions create any vehicle motion we need; the set of Atomic Motions are sufficient to create any vehicle motion for any purpose in any situation.
Further, the set of all the Atomic-Motion types is necessary to create motions for various purposes in various situations. This fact is confirmed by the videos presented in the five Atomic-Motion pages under the Atomic-Motion menu. To date, we have found no counterexample of this fact.
Thus, we claim this Hypothesis K1:
“The set of Atomic Motions is necessary and sufficient to create vehicle motions.”
 Hypothesis K2: Accurate Response
Moreover, we found that there is no situation where two Atomic Motions respond with the same accuracy. That is, there exists only one Atomic Motion that accurately responds to a given situation, and this brings us to the second Hypothesis K2:
“One and only one Atomic Motion exists that accurately responds to a given situation.“
Hypothesis K2 is stronger than the first, K1. To date, we have found no counterexample of this statement.
 Responsiveness of Tracking-Type Atomic Motions
There are three tracking-type Atomic Motions:
- Direction-Tracking Atomic Motions (Click here to know more)
- Line-Tracking Atomic Motions (Click here to know more)
- Circle-Tracking Atomic Motions (Click here to know more)
These Atomic Motions work under feedback control rules that produce exponential convergence with critical damping responses for each target, direction, line, or circle. Each Atomic Motion has a single input parameter σ, which controls the spatial responsiveness (this is related to vehicles’ static, geometrical trajectories). We call the parameter a smoothness. The smoothness σ works in the motion responsiveness as follows:
- A smaller smoothness σ makes convergence quicker and its transition part smaller.
- A larger smoothness σ makes convergence less quick and its transition part larger.
Let us show sample Science Robot motions with two distinct smoothnesses. The following motions are a part of Line-Tracking Atomic Motions, [2.1] Polygon Medley:
A smaller σ generates a quicker response.
A larger σ generates a less quick response.
While driving in a lane on a highway, if the lane is straight, the vehicle uses a Line-Tracking Atomic Motion to keep the lane. Otherwise, the vehicle uses a Circle-Tracking Atomic Motion instead.
In case the car wants to switch to the next lane, the target of each Atomic Motion will change to a next oriented line or circle. The smoothness σ controls how, geometrically, quickly the car transitions lanes. For a quicker response, use a smaller smoothness σ; otherwise, use a larger one.
- With a too small σ, the car responds too quickly and may frighten people.
- With a too large σ, the car responds too slowly and may not entirely switch in time.
Choosing an appropriate smoothness for these Atomic Motions in a given situation is essential for the car to acquire trust from people.
 Installing A New Vehicle-Motion Simulator
A firm can optionally build its vehicle-motion simulator, which is similar to Science Robot in the firm’s IDE with a MotionLab’s full support. The simulator will become a motion-creation reference and a useful tool for the firm’s software-development projects. It saves time and money.
 Mathematics Lasts
Because Atomic Motions are based on the rock-solid Symmetric Geometry, we will not need to modify Atomic Motions for decades, possibly forever. Coding done today might be unambiguously understood by colleagues 20 years later.