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Tham khảo tài liệu 'advances in robot manipulators part 3', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 72 Advances in Robot Manipulators Fig. 23. Manipulability index - Wd 1 1 1 1 1 1 1 100 100 . In all three cases the manipulability measure was maximized based on the weight matrix. Figure 21 shows an improvement trend of the WMRA s manipulability index over the arm s manipulability index towards the end of simulation. Figure 22 shows the manipulability of the arm as nearly constant compared to that in Figure 23 because of the minimal motion of the arm. Figure 23 shows how the wheelchair started moving rapidly later in the simulation see figure 20 as the arm approached singularity even though the weight of the wheelchair motion was heavy. This helped in improving the WMRA system s manipulability. 6.2 Simulation Results in an Extreme Case To test the difference in the system response when using different methods an extreme case was tested where the WMRA system is commanded to reach a point that is physically unreachable. The end-effector was commanded to move horizontally and vertically upwards to a height of 1.3 meters from the ground which is physically unreachable and the WMRA system will reach singularity. The response of the system can avoid that singularity depending on the method used. Singularity joint limits and preferred joint-space weights were the three factors we focused on in this part of the simulation. Eight control cases simulated were as follows a Case I Pseudo inverse solution PI In this case the system was unstable the joints went out of bounds and the user had no weight assignment choice. b Case II Pseudo inverse solution with the gradient projection term for joint limit avoidance PI-JL In this case the system was unstable the joints stayed in bounds and the user had no weight assignment choice. c Case III Weighted Pseudo inverse solution WPI In this case the system was unstable the joints went out of bounds and the user had weight assignment choices. 73 A 9-DoF Wheelchair-Mounted Robotic Arm System Design Control Brain-Computer Interfacing and .
