# Path Complexity or Driving Skills

### [1] Evaluating Path Complexity

We consider a vehicle path that includes frequent turns to be “more complex” than a straight-line path. MotionLab possesses *an equation* that *quantitatively evaluates the complexity* of a given path. Let us take two slalom sample paths, A+B-C+D-E- and A+B-C+D-E+; *MathMind* computes each of their complexity in a single number, which we call *path complexity* or *motion complexity*. (We already discussed these sample motions in Path Classes and Their Symbolic Representation [2].) A path with *a larger path complexity* means the path is *more complex*.

A user inputs

“A+B-C+D-E-”

for this *Slalom* motion.

The *Motion Complexity* field reports

**1.0114** at the end.

A user inputs

“A+B-C+D-E+”

for this *Slalom* motion.

The *Motion Complexity* field reports

**1.0887** at the end.

We intuitively expect that the former path class “A+B-C+D-E-” is less complex than the latter “A+B-C+D-E+.” This intuition is confirmed by the *path complexity* numbers shown in the demonstrations.

### [2] Evaluating Driving Skills

The same equation used for complexity evaluation can assess a driver’s driving skills as well. In this case, we call the number the *driving-skill index*:

A user drives a car using mouse clicks

in *Math Mind* motion *8.1 Driving Skills*.

In this performance, *Math Mind* returns

a *driving-skill index* of **2.3928**.

A smaller* index* means a better skill.

If this user tests the same *Driving Skills* program again, he or she will obtain a different motion-skill index.

Motions created by a novice driver may contain unnecessary windings; the driving-skill index reports the result quantitatively. Any vehicle can install this driving-skill-evaluating capacity, not only in self-driving cars. This equation has a wide variety of potential applications. A driver can check his or her skills as a reference, and the index would indicate how much a driver’s skills have improved. This capacity can also be used to compare performances of two self-driving algorithms.