Sharif Digital Repository

Dynamic gait planning for humanoid robots encounters difficulties such as stability, speed, and smoothness. In most of previous studies, joints' trajectories are calculated in 3D Cartesian space, then, introducing boundary conditions and using polynomials, the first and second derivatives of the motion are ensured to be continuous. Then, the stability of the motion is guaranteed using Zero Moment Point (ZMP) stability criterion. In this study, a trajectory planner is presented using the semi-ellipse equations of the motion; the continuity of the derivatives is preserved. Stabilization of motion is attained through using ZMP criterion and 3d inverted pendulum equations in three slope... 

Thermodynamic quantities such as proton affinity (PA) and molecular basicity (GB) for (CaO)n nanoclusters with n = 2–16 have been calculated using three computational models of the density functional theory (DFT) (Becke, 3-parameter, Lee-Yang-Parr (B3LYP), Minnesota 2006, Perdew-Wang 1991 (PW91), Coulomb attenuated method-B3LYP, and ωB97XD functionals); Møller-Plesset perturbation theory; and Hartree-Fock with the cc-PVNZ (n = D and T) basis set in the gas phase. Absolute deviation error (AAD%) indicates that obtained PA and GB values using DFT model and the B3LYP method with mean percentage errors of 0.77 and 0.90%, respectively, have the higher accuracy than the other methods and models....