Impedance Control For A Prototype Of Golf Swing Robot (P2)
The experiment was implemented by a prototype of golf swing robot composed of an actuated joint driven by a direct drive motor (NSK MEGATORQUE) and a passive joint with a mechanical stopper. The stopper carries out the wrist cock action. A mechanical brake is used to stop the golf club after impact. An absolute resolver (feedback signal 51200 pulse/rev) and an incremental encoder (9000 pulse/rev) situated at the actuated and passive joints are utilized to measure the arm and club rotational angles, respectively. A 1-dimensional force sensor (KYOWA LCN-A-500N) and a 6-dimensional force sensor (NITTA IFS-67M25A50-I40) are adopted to obtain the reaction torque r N and reaction force r F from the club to arm, respectively. A flexible solid beam made of aluminium is used to replace the shaft, and it is clamped at the grip. The natural frequencies and vibration mode shapes of the golf club are obtained by numerical calculation and experimental modal analysis. The configuration of the experiment modal analysis system for the golf club is shown in Figure 5-4. Figure 5-5 shows the first and second mode shapes of the golf club used in our simulation (MAM), and those obtained from experimental modal analysis (EMA). It is evident that the mode shapes of the golf club applied in our simulation are consistent well with those obtained form experimental modal analysis.
The photograph of the robot system is shown in Figure 5-6. Table 5-1 gives the parameters of the robot system. The experimental control system is indicated schematically in Figure 5-7. A personal computer is used to implement the impedance control program and its sampling rate is 1KHz. By using the velocity control mode of the motor driver, the DD motor is controlled by the velocity (voltage) reference from a DA converter (CONTEC, DA12-16(PCI)). Here, JR3 is a DSP-based signal receiver for the 6-dimensional force sensor.
The obtainment of the reaction torque Nr is shown in Figure 5-8. Based on the figure, the reaction torque Nr can be calculated by
where Fn is the force measured from the 1-dimensional force sensor;bis the distance between the force contact point of the sensor and the wrist joint of the robot.
It is noted that not only the force measured from the 6-dimensional force sensor is needed to calculate the reaction force Fr , but also the inertia force of the sensor ft caused by the arm angular acceleration αr should be considered because the sensor is regarded as a part of hand-grip. The specific force analysis of the hand-grip is shown in Figure 5-9.
According to the figure 5-9, the following equations are obtained.