Tham khảo tài liệu 'humanoid robots part 14', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 318 Humanoid Robots If an axis Ag is defined where the moment is parallel to the normal vector n from the surface about every point of the axis then the Zero Moment Point ZMP necessarily belongs to this axis since it is by definition directed along the vector n. The ZMP will then be the intersection between the axis As and the ground surface such that - - Mg ZG X mg - ZG X maG - HG with Mg X n 0 52 53 where z represents the ZMP. Because of the opposition between the gravity and inertia forces and the contact forces mentioned before the z point ZMP can be defined by PZ n X Mpg Fg n 54 where P is a point of the sole where is the normal projection of the ankle. Fictitious zero moment point FZMP is an important expand of ZMP it can be used in stability control. In order to evaluate dynamic stability we use the ZMP principle. The ZMP is the point where the influence of all forces acting on the mechanism can be replaced by one single force. If the computed ZMP is the real ZMP this means the computed ZMP inside the real support polygon the biped robot can be stable. If the ZMP is not the real ZMP this means the computed ZMP is on the boundary of the support polygon the robot will fall down or have a trend of falling down. If the computed ZMP is outside the support polygon then the robot will fall down and in this case the computed ZMP is called fictitious ZMP. The link model of the humanoid robot is shown in Figure . Fig. 11. The link model of the humanoid robot. Walking Gait Planning And Stability Control 319 The projection of position vector of computed ZMP can be computed by the following equations E mi z g xi -E mixizi E M iy x i 1i 1_i 1 zmp 5 E mi i g i 1 E mi zi g y -E miyizi E M ix V ---------------------------------------- zmp 5 E mi z i g i 1 55 56 where mi is mass of every links xi yi zi is the coordinate of the mass center of the links Mx My T is the moment vector. If the ZMP is inside the support polygon and the
