Discontinuous gaits for walking machines offer great advantages over w
ave gaits, and they seem more adequate for following a path over irreg
ular terrain. This paper, focused on quadruped walking robots, address
es the problem of following an arbitrary path using both discontinuous
crab and turning gaits. First, the paper presents the algorithms to g
enerate these gaits as local motions and highlights their advantages i
n comparison with continuous gaits. This comparison considers stabilit
y, velocity, power consumption and terrain adaptability. The algorithm
s for tracking an arbitrary trajectory using these gaits are then intr
oduced, and some simulations and experimental results are reported.