Referring to the infantry specifically

In A popular game I play(Napoleon Total war) a lot of times you have to force your troops to literally run across the battlefield in order to secure a good position (Hill, farmhouse, etc) regardless if they are grenadiers, light infantry, or line infantry as marching your troops takes way longer in game than just making them run the whole time.. In some longer battles you'll be forced to do this many times over which got me thinking about how strange it must be to see these soldiers in an era of warfare where strict order and organised battlelines were so important, just running amok everywhere.

So we're soldiers of the Napoleonic wars ever expected to run extensively during a battle to perform maneuvers?

If so for how long and how fast were they expected to run?