After many overly complex failed efforts, I have made a pneumatic biped. The walking mechanism is completely automatic. Just apply air pressure. It can only walk forwards. No turning. 

Pneuma-Ped uses two pistons for the hips and two pistons for the ankles. The hip pistons are cross connected so that under no load conditions the pistons state should be opposite of each other. This means that when the left hip piston expands, the right hip piston contracts, and visa versa. The ankle pistons are also cross connected.

The hip pistons control the forward/backward movement of the legs. The ankle pistons control the right and left lean of the robot. 

The right hip and right ankle are hooked together in a pneumatic timer circuit nicely described by Eric Brok . My configuration of the timer circuit is shown in this schematic. The timer circuit makes the right hip and right ankle go through this sequence: 

CC Leaned right, right foot forward 

XC Leaned right, right foot back 

XX Leaned left, right foot back

CX leaned left, right foot forward 

where C means contracted and X means expanded.

When Pneuma-ped leans to the right, its center of gravity is over the very large right foot. When leaning to ther left, its center of gravity is over the very large left foot.

Pneuma-ped's stride is 3 3/8 inches (8.5 centimeters). I provide pressure to it using a super hand pump invented by my friend Sam Hanes. He put 5 large pumps on a 2x10 plate, and then ran a #12 axle through the knobs in the top. I takes about 2 compressions to make it through then entire leg cycle. This means that it would take about 10 compressions with a single pump. 

Pneuma-ped is by far the most stable and agile biped I've made yet. He can easily walk on carpet, and even clear a thick throw rug on top of the carpet.

When pumping aggressively, Pneuma-ped has a pretty even gate and walks with a slight curve to the right. When pumped slowly, he turns more severly to the right due to asymetries in his design. One asymetry is that the right foot weighs more, because of the pneumatic valve assembly on the right foot. The biggest asymetry is due to the fact that the left piston and left ankle's movement is tied to the right leg and ankle's valves.

My next pneumatic biped will have two valves per piston configured so that the progression through the leg sequence depends on both side's pistons states. This way the pneumatic circuit will not advance until both the right and left pistons have hit their extreme.