How can you make a mechanical spider move left and right as opposed to just forward and back?

Question

My friend is building this robotic spider. The legs move in a circular motion so it can go forwards and backwards. However, he wants to figure out how he can make it walk side ways without putting the legs at an angle (there are 4 at the front and 4 at the back). He wants the spider as small possible so he says there isn't room to add extra parts or do anything fancy. I don't understand a lot of this stuff but sometimes the most obvious answer is the simplest one! Hopefully this is enough detail. Ask me if it isn't and i'll respond right away.

Answer 1

Rotate its head 90 degrees.

Answer 2

don't know about sideways butttt...

if you make the left side leggs stop moving while the right side leggs continue, the spider might turn left.

or reverse the leggs motion on one side to turn...

Answer 3

the obvious but useless method (because it doesn't change the true direction but only the apparent direction)

is to build a bulky (pseudo or let it contain the battery, controls etc) body (with attached head) above the legs mechanisms base and allow this to rotate  90 degrees left and right

to change direction one would have to have 2 separate drives for each sides' 4 legs and then change their relative speeds