## S

5.2 Disturbance compensation of vehicle

Discretizing the low pass filter, F( p) = 1/(Tfp +1), shown in Figure 3(b) (Godler et al., 2002), a digital version of disturbance compensation can be obtained. Figure 11 shows the digital version where h = e Tf /T .

Fig. 11. Digital type disturbance compensation

Fig. 11. Digital type disturbance compensation

### 5.3 Avoidance of a singular configuration

In much work on UVMS it is considered that the vehicle is keeping its initial state during the manipulation. In order to avoid the singular configuration of the manipulator in such case, the desired value of the vehicle is modified by using the determinant of the manipulator's Jacobian matrix J( k) = det J( k) (Sagara et al., 2006). The desired linear acceleration of the vehicle is defined as r0d (k) =

where pe is the desired linear velocity of the end-tip of the manipulator, and kaT and ksT are the time when | J(k) | becomes less or greater than a threshold Js , respectively, and naT is the acceleration time. 5 10

Fig. 12. Experimental result of discrete-time RAC

5.4 Experiment of discrete-time RAC

In this subsection, some experiments of the discrete-time RAC method described above are done for the underwater robot shown in Figures 1 and 4.

All experiments are carried out under the following condition. The desired end-tip position is set up along a straight path from the initial position to the target. On the other hand, the desired position and attitude of the base are set up the initial values. The sampling period is T = 1/60 [s] based on the processing time of video tracker.

First, a basic discrete-time RAC experiment is done. In this case, the feedback gains are A = diag{0.6 0.6 0.25 0.25 0.25} and r = diag{0.3 0.3 0.25 0.25 0.25}. Figure 12 shows the experimental result. From this figure, it can be seen that the discrete-time RAC method has good control performance and the performance is similar to that of the continuous-time version shown in Figure 7(b). Fig. 13. Experimental results of discrete-time RAC with and without disturbance compensation 