Nowadays almost all the H-bridges are based on MOSFETs, but some time ago it was not always like that. Here some about old school electronics with relays.
Today any one is going to use a relay for a H-Bridge to control motors anymore. MOSFET transistor are far away better in all the aspects for switching than a relay can do.
The main advantage of the relays versus the transistors was that the voltage doesn’t fall down, and it doesn’t depend on the power used. Using relay commutation is utilice all the voltage of the bateries, but if you use mosfet H bridge it is not so important. Mainly the relays admite more power and they don’t heat up.
A basic schematic is:
The diodes are used for “eating” the intensity peaks at the moment that the motor changes the direction. This avoids the spark produced during the inductive component of the load in the commutation.
It doesn’t influence in the intensity, but it extends the lifetime of the relays. In small motors you cannot considerate it. Too fast diodes are not necesary, common diodes are enough.
If the intensity is important during the inversion, relays can be activated by sequence.