Controlling a biped robot with a high degree of freedom to achieve stable and straight movement patterns is a complex problem. With growing computational power of computer hardware, high resolution real time simulation of such robot models has become more and more applicable. This paper presents a novel approach to generate bipedal gait for humanoid locomotion. This approach is based on modifie...

Bipedal walking is a difficult task due to its intrinsic instability and developing successful controller architectures for this mode of locomotion has proved substantially more difficult than for other types of walking (Beer et al. 1998). This type of walking has been tackled from different directions that all of them have been divided to two major approaches of static walking (Kato et al. 197...

Biped walking by using all joint movements and DOFs in both directions (sagittal plane and coronal plane) is one of the most complicated research topics in robotics. In this paper, angular trajectories of a stable biped walking for a humanoid robot are generated by a Truncated Fourier Series (TFS) approach. The movements of legs and arms in sagittal plane are implemented by an optimized gait ge...

Knowledge of a truncated Fourier series expansion for a 2nperiodic function of finite regularity, which is assumed to be piecewise smooth in each period, is used to accurately reconstruct the corresponding function. An algebraic equation of degree M is constructed for the M singularity locations in each period for the function in question. The M coefficients in this algebraic equation are obtai...

Abstract. In examining the relationship between the number of points over Fp on certain Calabi-Yau manifolds and hypergeometric series which correspond to a particular period of the manifold, Rodriguez-Villegas identified 22 possible supercongruences. We provide a framework of congruences covering all 22 cases. Using this framework we prove one of the outstanding supercongruence conjectures bet...