# Impedance Control For A Prototype Of Golf Swing Robot (End)

** Results and discussion **

Figure 5-12 shows the results of a comparison of the arm and club rotational angles for the robot and different-arm-mass golfers. It is observed that the swing trajectories of the arm (Figure 5-12 (a), (c), (e)) and club (Figure 5-12 (b), (d), (f)) for H1, H2 and H3 are not the same. The comparison of the arm and club angular velocities for the robot and

different-arm-mass golfers is shown in Figure 5-13. It can be seen that the angular velocities of the arm (Figure 5-13 (a), (c), (e)) and club (Figure 5-13 (b), (d), (f)) are also different for three golfers. The maximum arm angular velocity of H3 is obviously larger than those of H1 and H2, and the increases are 2.86 rad/s and 1.16 rad/s as compared to H1 and H2, respectively. It is also clear that the club angular velocities are different for them and the maximum club angular velocity of H3 is larger than those of H1 and H2, and the increases are 5.16 rad/s and 2.30 rad/s, respectively. From Figure 5-12 (a), (c), (e) and Figure 5-13 (a), (c), (e), it can be seen that the swing motions of the arm of the

proposed golf swing robot agree well with those of the three golfers. As for the swing motions of the club, it shows that no substantial differences are found between the robot and golfers in Figure 5-12 (b), (d), (f) and Figure 5-13 (b), (d), (f). However, it is noteworthy to mention that the club swing motion differences between the robot and golfers will become large with the higher club angular velocity (For example, see Figure 5-12 (b), (f)). This can be explained from the fact that the higher club angular velocity causes a larger air drag force which retards the club in the swing experiment for the robot, and this retarding force, however, is neglected in the simulation of the swing motion for the golfer due to the complex dynamical modelling and practical measurement difficulty for this air drag force.

Through the above comparisons, it is shown that the swing motions of different-arm-mass golfers are not the same even if the shoulder input torques used by them are equivalent and the proposed golf swing robot using the impedance control method can emulate the swing motions of different-arm-mass golfers.

We should note that in our control method the control reference for the robot – arm angular velocity of a golfer is determined by the feedback signals such as the reaction force and torque from the club to the arm. Since the arm angular acceleration is approximated by the Euler method, the control reference in the nth sampling period is calculated by the feedback signals in the (n-1)th sampling period (Eq. (5-10)). Therefore, a sampling period time-delay error occurs. In order to solve this problem, we would have to adopt the relatively small sampling control period to limit the control error. In this study, the 1ms sampling control period was used and the satisfying results were achieved (Figure 5-12 and Figure 5-13). We are also expected to investigate whether a longer sampling control period such as 4 ms and 10 ms would lead to some good experiment results as compared to 1ms.

Figure 5-14 shows the results of a comparison of the arm and club angular velocities for the robot and different-arm-mass golfers while using the 4ms sampling control period. We note that the swing motions of different-arm-mass golfers still can be emulated by the robot with the 4ms sampling control period. But it is clear that the 10 ms sampling control period can not give the satisfying experiment results, in particular when the swing speed of the robot is increasingly high (Figure 5-15 (c) and Figure 5-15 (d)).

**Summary**

Various golfers can play different golf swing motions even though they use the same golf club. This phenomenon casts light on the significance of the dynamic interactions between a golfer’s arms and a golf club. Unfortunately, the influence of the dynamic interactions were not considered in the conventional control of a golf swing robot, though such interaction does result in different swing motions, even though the robot has the same input torque of the shoulder joint as the golfer’s. An impedance control method is thus proposed for a prototype of golf swing robot to emulate the swing motions of the different-arm-mass golfers in consideration of the dynamic interactions between arms and golf clubs. Based on the Euler-Lagrange principle and assumed modes technique, a mathematical model of golf swing, considering the bending flexibility and centrifugal stiffening of the golf shaft, is established to simulate the swing motions of different-arm-mass golfers. The impedance control method is implemented to a prototype of golf swing robot composed of one actuated joint and one passive joint. The comparison of the swing motions between the robot and different-arm-mass golfers is made and the results show that the proposed golf swing robot with the impedance control method can emulate the swing motions of the different-arm-mass golfers.