Just realized that I have put both sides to be channel A 
Also the transistors in the upper side of the bridge should switch their place with the ones from the lower side, and the Drain and Source terminals in the upper side must be switched between them, and some other details that won't make sense to discuss before fixing the schematic.
My advice is to search for a schematic of a "H bridge with complementary MOSFET" if that's what you want to use (search for images) and start from there.
About the question if an 1.8V I/O can control those MOSFET, no, it won't work, even after correcting the posted schematic. V
GS must be 1.8V or lower in order for a MOSFET to be controlled by an 1.8V signal. MOSFET transistors with low V
GS are sometimes called "Digital MOSFET" or so, so that would be a good term to search for, then look in the datasheets and pick some MOSFETs with V
GS 1.8V or lower.
Be careful with batteries and H bridges. Even when the design is OK they can still catch fire or explode, not kidding.
Always put a fuse in series with the battery, NEVER skip the fuse.