  We present a solvable biped walking model based on an inverted pendulum with
two massless articulated legs capable of walking on uneven floors and inclined
planes. The stride of the two-legged robot results from the pendular motion of
a standing leg and the articulated motion of a trailing leg. Gaiting is
possible due to the alternating role of the legs, the standing and the trailing
leg, and the conservation of energy of the pendular motion. The motion on
uneven surfaces and inclined planes is possible by imposing the same maximal
opening angle between the two legs in the transition between strides and the
adaptability of the time of each stride. This model is solvable in closed form
and is reversible in time, modelling the different types of biped motion.
Several optimisation results for the speed of gaiting as a function of the
robot parameters have been derived.
