  Building trajectories for biped robot walking is a complex task considering
all degrees of freedom (DOFs) commonly bound within the mechanical structure. A
typical problem for such robots is the instability produced by violent
transitions between walking phases in particular when a swinging leg impacts
the surface. Although extensive research on novel efficient walking algorithms
has been conducted, falls commonly appear as the walking speed increases or as
the terrain condition changes. This paper presents a polynomial trajectory
generation algorithm (PTA) to implement the walking on biped robots following
the cubic Hermitian polynomial interpolation between initial and final
conditions. The proposed algorithm allows smooth transitions between walking
phases, significantly reducing the possibility of falling. The algorithm has
been successfully tested by generating walking trajectories under different
terrain conditions on a biped robot of 10 DOFs. PTA has shown to be simple and
suitable to generate real time walking trajectories, despite reduced computing
resources of a commercial embedded microcontroller. Experimental evidence and
comparisons to other state-of-the-art methods demonstrates a better performance
of the proposed method in generating walking trajectories under different
ground conditions.
