In order to further evaluate the feasibility of the proposed HFNC in practical industry applications, this study has developed a 6-DOF robotic system for circular-path control of joint-space trajectory tracking within the workspace using the HFNC. The 6-DOF robot used in the experiment consists of a Mitsubishi Company 5-DOF robot type RV-MI with sliding track equipment at the robot base.  Each of the robot's joints are driven by a DC servo-motor.

Figure 10 demonstrates the experimental setup for the 6-DOF robotic control system. This robot incorporates an IBM PC Pentium IV 2.6 Ghz central processing unit to process all of the system input-output data as well as the control parameters. The interface is a PCI-8136 card with six digital-to-analog and six analog-to digital channels. The PCI-8136 also has 16 channels of digital-input and six decoding channels.  The card is manufactured by the ADLINK Company.

Figure 11 presents the defined coordinate system and the joint parameters for the 6-DOF robot using the Denavit-Hartenberg (D-H) method (Fu et al., 1987).  The joint parameters, defined in compliance with the rules established by the D-H representation, are listed in Table 2. The desired tracking trajectory in the workspace was a circular-path with radius of 10 cm. The corresponding reference joint trajectories of the robotic manipulator were calculated using inverse kinematics equations (Fu et al., 1987; Huang and Lian, 1997).

Table 1 lists the robot control fuzzy rules of the TFC and Table 3 presents the control parameters of the TFC as determined by the system’s dynamic characteristics.  Figure 12a demonstrates tracking trajectory responses for a circular-path workspace with a radius of 10 cm.  Both HFNC and TFC control results are plotted.   Because the tracking trajectory using the HFNC with two learning cycles is too close to the tracking trajectory with the TFC, they cannot be differentiated from one another.  Figures 12b and 12c show the 2nd and the 3rd robot joint errors in tracking trajectory using the HFNC and TFC for comparison in order to clearly observe their performance in controlling the robotic system.  Using the TFC to control the robot, the maximum angular errors and RMS errors were 0.168 and 0.053 degrees at the 2nd joint and 0.169 and 0.039 degrees at the 3rd joint (Figures 12b and 12c).  The maximum angular errors and RMS errors, however, were significantly reduced to 0.049 and 0.023 degrees at the 2nd joint and 0.033 and 0.012 degrees at the third joint when the HFNC with two learning cycles was applied.

Figure 13 depicts the tracking errors of positioning with respect to Cartesian coordinate axes X, Y, and Z for circular-path control of the robot using the HFNC with two learning cycles compared with errors of the TFC.  Table 4 summarizes the maximum errors and RMS errors of trajectory tracking based upon the results depicted  in Figure 13.  The findings indicate that the HFNC is clearly superior to the TFC in minimizing tracking errors of joint trajectories and of positioning for circular-path of the robot in the workspace.

In order to further evaluate the feasibility of the proposed HFNC in practical industry applications, this study has developed a 6-DOF robotic system for circular-path control of the joint-space trajectory tracking within the workspace, using the HFNC. The 6-DOF robot used in the experiment consists of a Mitsubishi Company 5-DOF robot type RV-MI, made by Mitsubishi Company,  and thewith sliding track equipment at the bottom of the robotrobot base.  Each of the robot's joints are  is driven by a DC servo-motor.

Figure 10 shows andemonstrates the experimental setup for of the 6-DOF robotic control system. This robot usedincorporates  an IBM PC Pentium IV 2.6 Ghz central processing unit to process all of the system input-output data as well as the control parameters. The interface is a PCI-8136 card comprising with six digital-to-analog and six analog-to digital with six channels, analog-to-digital with six channels,. The PCI-8136 also has 16 channels of digital-input with 16 channels, and six decoding channels.  The card was from theis manufactured by the ADLINK Company.

Figure 11 presents the defined coordinate system and the joint parameters for the 6-DOF robot,  using the Denavit-Hartenberg (D-H) indicated method (Fu et al., 1987).  The joint parameters, defined as per thein compliance with the rules established by the D-H representation, are listed in Table 2. The desired tracking trajectory in the workspace was a circular-path with radius of 10 cm. in the workspace. The corresponding reference joint trajectories of the robotic manipulator were calculated using inverse kinematics equations (Fu et al., 1987; Huang and Lian, 1997).

Table 1 lists the robot control fuzzy rules of the TFC and Table 3 presents the control parameters of the TFC, for control of the robot, according to as determined by the system’s dynamic characteristics. decided.  Figure 12a draws demonstrates tracking trajectory responses for a circular-path workspace with a radiusi of 10 cm.  Both HFNC and TFC control results are plotted.   for control of the robot in the workspace, using the HFNC and the TFC for comparison. Because the tracking trajectory using the HFNC with two learning cycles is too close to the tracking trajectory with the TFC, they cannot be differentiated from each one another.   Figures 12b and 12c show the 2nd and the 3rd robot joints’ errors in tracking trajectory, respectively,  using the HFNC and TFC for comparison in order to clearly observe their performance in controlling the robotic system, in order to clearly observe their performance in controlling the robotic system.  Using the TFC to control the robot, the maximum angular errors and RMS errors were 0.168 and 0.053 degrees at the 2nd joint and 0.169 and 0.039 degrees at the 3rd joint From (Figures 12b and 12c)., using the TFC to control the robot, the maximum angular errors and RMS errors are 0.168 and 0.053 degrees at 2nd joint, respectively and 0.169 and 0.039 degrees at 3rd joint, respectively.  The maximum angular errors and RMS errors, however, weare significantly reduced to 0.049 and 0.023 degrees at the 2nd joint , respectively, and 0.033 and 0.012 degrees, respectively at the third joint when the HFNC with two learning cycles wasis applied.

Figure 13 depicts the tracking errors of positioning with respect to Cartesian coordinate axes X, Y, and Z for circular-path control of the robot, using the HFNC with two learning cycles, compared with errors of the TFC.  Table 4 summarizes the maximum errors and RMS errors of trajectory tracking based upon the results depicted in in Figure 13.  The findings indicate that Tthe HFNC is clearly superior to the TFC, in minimizing tracking errors of joint trajectories and of positioning, for circular-path of the robot in the workspace.