tailieunhanh - Humanoid Robots - New Developments Part 4

Tham khảo tài liệu 'humanoid robots - new developments part 4', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Dynamic Simulation of Single and Combined Trajectory Path Generation and Control of A Seven Link Biped Robot 97 v4 -ZO0O sinfX qf - Z1 1 sin 62 -1 - Z202 sinO -02 ty Z3ã3 sin ớ3 - Ằ Zc404 sin ớ4 - Zj0j cos ớj - ty ZOãO cos ptrt qf - Z2â2 cosO - 02 ty -Z3ã3 cos ớ3 -2 - Zc4ã4 cos ớ4 - K V5 Z- O sin PM qf -Z1 SĨsii -ty -Z2S2 sin T-02 Z Z202 sinệ 3 -ty Z4Ô 4sin 4 -ty L stymv2-ty Pmt -qty Z1 SĨ cos 1 -2 Z0 0cos i Oi Ịf -Z2 2c0s T-02 2 -Zty cosp-ty -l cosft -Ấ Z5 c Ĩ5cos r 2-2 s c -qb K v. H o sin 5Lt qf ZA sin 1 - Z2Õ2sin --62 ty Z orũ tor sinậ 2-0tor -2 ÕịZi c s Z -ty Zoâocos ỉtot qf -Z2 Ỉ2 cos --62 ty Z OrS tOr cOs ĩ 2-0tOr -2 K 27 28 29 Accordingly the linear acceleration of the links can be calculated easily. After generation of the robot trajectory paths with the aid of interpolation process and with utilization of MATLAB commands the simulation of the biped robot can be performed. Based on the all above expressed relations and the resulted parameters and subsequently with inserting the parameters into the program the simulation of the robot are presented in simulation results. 3. Dynamic of the robot In similarity of human and the biped robots the most important parameter of stability of the robot refers to ZMP. The ZMP Zero moment point is a point on the ground whose sum of all moments around this point is equal to zero. Totally the ZMP mathematical formulation can be presented as below n n n mi gcosẤ ii xt mi gsin xi zi Ipi 30 Xmp ----- Zm gcos2 z- Í 1 Where x. and z. are horizontal and vertical acceleration of the link s mass center with respect to where 0 is the angular acceleration of the links calculated from the interpolation process. On the other hand the stability of the robot is determined according to attitude of ZMP. This means that if the ZMP be within the convex hull of the robot the stable movement of the robot will be obtained and there are no interruptions in kinematic parameters Velocity of the links . The convex hull can be imagined as a .