6. A racing robot has the following characteristics:
(1) The step length can be manually set to 0.1 meters, 0.2 meters, $\cdots$, 1.8 meters, or 1.9 meters:
(2) After the start command, the robot immediately takes the first step of the set length, and each step is completed instantaneously;
(3) When the step length is set to $a$ meters, the robot needs exactly $a$ seconds between each consecutive step.

Then the minimum time required for the robot to run 50 meters (allowing to exceed 50 meters) is
6.48.6 seconds.

Let $\lceil x$ denote the smallest integer not less than the real number $x$.
Let the step length be $a$ meters, $a \in\{0.1,0.2, \cdots, 1.9\}$. The robot takes $\left[\frac{50}{a}\right]$ steps to complete exactly 50 meters, and the number of intervals required is $\left\lceil\frac{50}{a}\right\rceil-1$. Therefore, the required time is
$$
f(a)=a\left(\left\lceil\frac{50}{a}\right\rceil-1\right) .
$$

Calculations yield $f(1.9)=49.4, f(1.8)=48.6$,
$$
\begin{array}{l}
f(1.7)=49.3, f(1.6)=49.6, \\
f(1.5)=49.5 .
\end{array}
$$

And when $a \leqslant 1.4$,
$$
\begin{array}{l}
f(a) \geqslant a\left(\frac{50}{a}-1\right)=50-a \\
\geqslant 48.6=f(1.8) .
\end{array}
$$

Therefore, when the robot's step length is set to 1.8 meters, the time required to run 50 meters is the shortest, at 48.6 seconds.