The third phase of behavior prediction - 9. Lane change cost function

In the image above, the blue self-driving car (lower left) is trying to reach its goal (a gold star). Currently it is in the correct lane, but the green car is moving very slowly, so it considers whether it should perform a lane change (LC) or just keep lane (KL).

These options appear as light blue vehicles with dashed outlines. Identifying relevant variables is useful if we want to design a cost function that handles lane selection. In this case, we can define:

 

 

Before we define an actual cost function, let's consider some properties we want it to have...

1. Considering $\Delta d,\; would\; we\; ratherthe\; absolute\; value\; of\; \Delta d\; be\; larger\; or\; smaller?$

$a\; large$

$b\; small$

$2.\; Consider\; the\; impact\; of\; factor\; s\; on\; the\; cost\; function.\; Is\; the\; car-to-transform\; cost\; function\; correlation\; close\; to\; the\; target\; or\; far\; from\; the\; target?$

$a.\; far$

$b.\; near$

$We\; need\; a\; cost\; function\; that\; penalizes\; large\Delta dwhile\; penalizingsmall\; \Delta s.Furthermore,\; we\; want\; to\; ensure\; thatthemaximumcost\; of\; this\; cost\; functionnever\; exceeds\; 1,\; and\; theminimum\; valuenever\; falls\; below\; zero.$

$Which\; of\; the\; following\; recommendations\; meets\; these\; criteria?$

 

In this example we find that option 2 is correct, and if we call this scale X, we can use any function within the bounds of that function. These functions are useful when designing cost functions. These types of functions are called sigmoid functions