Several mundane armor modifications were released with Pathfinder Chronicles: Faction Guide
Deflecting
Whenever an opponent strikes at the wearer with a bludgeoning or slashing melee weapon and misses by 5 or fewer, the wearer gains a +1 circumstance bonus on his next melee attack roll against that opponent. This attack must be made in the next round or the bonus is lost.
In addition to increasing the armor’s base cost and weight, this upgrade reduces the wearer’s speed by 5 feet; the Slow and Steady dwarven racial ability enables dwarves to ignore the associated speed penalties. The listed costs are for including this modification to nonmagical armor; increase the cost by 50% if adding to a suit of magical armor.
Cost: +1,000 gp; Weight: +10 lbs.
Jarring
Whenever an opponent with a melee weapon strikes at the wearer using the Power Attack feat and misses by 5 or fewer, he must make a Fortitude save or be sickened until the end of his next turn. The save DC is 10 plus the bonus that Power Attack would have applied to the damage roll if the attack been successful.
In addition to increasing the armor’s base cost and weight, this upgrade reduces the wearer’s speed by 5 feet; the Slow and Steady dwarven racial ability enables dwarves to ignore the associated speed penalties. The listed costs are for including this modification to nonmagical armor; increase the cost by 50% if adding to a suit of magical armor.
Cost: +1,000 gp; Weight: +20 lbs.
Vital Guard
Whenever an opponent scores a critical threat against the wearer, treat the wearer’s armor bonus as +2 higher than normal for the confirmation roll.
In addition to increasing the armor’s base cost and weight, this upgrade reduces the wearer’s speed by 5 feet; the Slow and Steady dwarven racial ability enables dwarves to ignore the associated speed penalties. The listed costs are for including this modification to nonmagical armor; increase the cost by 50% if adding to a suit of magical armor.
Cost: +500 gp; Weight: +15 lbs.
How do the speed reductions work with the Fighter class Armor training?
Does armor training mitigate the movement penalty?
As far as I can tell, no. Dwarves ignore these penalties though.
I agree. The fighter armor training only allows you to ignore the speed reduction from wearing medium and heavy armor. This is something else, which actually specificies how to avoid it (being a dwarf).