TAILIEUCHUNG - Robot manipulators trends and development 2010 Part 10

Tham khảo tài liệu 'robot manipulators trends and development 2010 part 10', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 352 Robot Manipulators Trends and Development Fig. 16. Virtual impedance model for the mobile platform Fig. repulsion force The magnitude F obs a obs condition a obs Fobs is chosen to be Borenstein Koren 1991 -b b d t -d . where aobs and bobs are positive constants satisfying the 2 b d_- d dmax is the maximum distance between the robot obs max min and the detected obstacle that causes a nonzero repulsive force dmin represents the minimum distance accepted between the robot and the obstacle and d t is the distance measured between the robot and the obstacle dmin d t dmax Fig. 17 . Note that the bound dmax characterizes the repulsion zone. Which is inside the region where the repulsion force has a non-zero value. Desired interaction impedance is defined as the linear dynamic Trajectory Generation for Mobile Manipulators 353 relationship Zd Bds Kd where Bd and Kd are positive constants simulating the damping and the spring effects respectively involved in the robot obstacle interaction inside the repulsion zone. Simulation results Simulations are conducted in order to show the performance of the proposed methodology. The numerical example supposes the lengths of the arm are such that a a a and the initial configuration of the mobile manipulator is such that T p n 6 and qa a 4 - 2 jtt 4 The end effector is supposed to track the following straight-line trajectory ệ t ị 1 í ệ t i3 t J 1 y Furthermore we imposed the following additional tasks to the mobile platform . p t x t y t t t t n 4 . Fig. 18 shows the stance of the whole system when the end effector tracks the reference trajectory. The resulting trajectory of the end effector as well as that of the mobile plat form is depicted in Fig. 19. Figures 20 21 22 and 23describe the evolution of the angles of the arm and the orientation of the platform respectively. If the robot finds an obstacle at less than d__ 1m the impedance control is activated and the max .

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