tailieunhanh - Humanoid Robots Part 6

Tham khảo tài liệu 'humanoid robots part 6', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 118 Humanoid Robots without the slope. We utilize a simple inverted pendulum model to represent the complex dynamics of the humanoid robot. This paper is organized as follows It shows ZMP equation as the simplified model for the biped robot and arranges the relation of the ZMP and CoM in section 2. Three step modules are introduced for generating the ZMP and CoM trajectory in section 3 and we explain the procedure of generating the trajectory from footprints in section 4. Section 5 6 shows the results of simulations and experiment and we conclude this paper in section 7. 2. Linear Inverted Pendulum Model Fig. 1. Linear Inverted pendulum model The humanoid robot is designed like human for doing various behaviors and adapting to human s environment. For this purpose this robot consists of many links and joints. If the walking pattern took all dynamic properties of a number of links and joints into consideration the waking pattern could make good performance. However since it is difficult and complicated to calculate the walking pattern including all dynamic properties a simplified model is required to control the biped robot. Fig. 1 shows the inverted pendulum model as the simplified biped robot. In Fig. 1 p t and c t denote the ZMP and CoM respectively. The motion of the robot is designed by CoM trajectory instead of the full dynamics. For simplicity we use following assumptions 1. The time derivative of the angular momentum about the CoM is zero. 2. The difference of CoM and ZMP at z-axis is constant. 3. The acceleration of ZMP at z-axis is zero. Under these assumptions the relation between ZMP and CoM can be represented as follows. pW cW - Um 1 where a is VW I I1 . ZcoM Zzmp and g are the values of the CoM and the ZMP at the z-axis and the gravity separately. The walking pattern of the ZMP and the CoM is A Walking Pattern Generation Method for Humanoid robots using Least square method and 119 Quartic polynomial made with Eq. 1 . As mentioned above the CoM is .