(a) RAC with disturbance compensation (b) RAC without disturbance compensation

Fig. 13. Experimental results of discrete-time RAC with and without disturbance compensation

Next, experiments of discrete-time RAC with and without disturbance compensation of the base are done. To validate the performance of disturbance compensation, the feedback gains of the RAC are A = r = diag{0.3 0.3 0.2 0.2 0.2}. Using these values of the gains the basic control performance of the RAC becomes worse. The time constant of the filter for the disturbance compensation is Tf = 0.1 [s]. The experimental results of the RAC with and without disturbance compensation are shown in Figure 13(a) and (b), respectively. And Figure 14 shows the time history of the estimated disturbance. From Figures 13 and 14, it can be seen that the position and attitude errors of the base are reduced by using the disturbance compensation.

Finally, an experiment of avoidance of singular configuration is done. In this case, the basic desired position and attitude of the base (vehicle) is set as the initial values, and the threshold of the determinant of the Jacobian matrix is Js = 0.45 . And the feedback gains are A = r = diag{0.6 0.6 0.25 0.25 0.25}. The experimental result is shown in Figure 15. From Figure 15, we can see that the end-tip of the manipulator and base follow the desired trajectories avoiding the singular configuration of the manipulator and the tracking errors are very small.

In this chapter, our proposed continuous-time and discrete-time RAC methods was described and the both experimental results using a 2-link underwater robot were shown. For the continuous-time RAC method, experimental results showed that the RAC method has good control performance in comparison with a computed torque method and the RAC method with disturbance compensation can reduce the influence of the hydrodynamic modelling error. In practical systems digital computers are utilized for controllers. Then, we addressed discrete-time RAC methods including the ways of disturbance compensation and avoidance of singular configuration. Experimental results show that the control performance of the discrete-time RAC method is similar to the continuous version. Our future work is to carry out experiments in 3-dimensional space to evaluate the validity of the RAC methods.

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