Our work includes analytical, simulation and experimental thrusts. The analytical work focuses on spatial dynamic modelling and passive dynamics analysis of highly articulated, variable compliance quadrupeds, and on robust nonlinear control methods for achieving given speeds in traversing known but varying environments, with stability and efficiency. A simulation environment provides a virtual testbed for testing alternative algorithms and designs. Finally, the experimental work focuses on designing and developing of novel quadruped robotic systems, capable of demonstrating the validity of the analytical results and achieving efficiently high speeds.