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For Equation (38) reference joint-space acceleration is defined as qVef(t) = J#(t)|vVef(t)- J(t)J#(tK-ef(t)}. (39)

Based on Equations (34) and (39) actual control input is calculated by using the following equation:

where qVeS = qf + KvV (qf - qv ) + K pv (qf - qv ), (41)

and K^ and Kp are positive diagonal matrices.

Both simulations and 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 feedback gains are K^ = K^ = diag{10 10 10 10 10} and KPy = KPy = diag {100 100 100 50 50} . The initial relative joint angles are fo =-n/2 [rad], ^ =n/3 [rad] and fo = -5n /18 [rad].

(a) Computed torque method (b) RAC method

Fig. 6. Simulation results of computed torque method and RAC method

First, simulation results of the computed torque method and the RAC method are shown in Figure 6(a) and (b). From Figure 6 we can see that both control methods have similar performance.

Next, we show the experimental results. As a computer is used for a controller in experiments, the sampling period for the controller is set up to T = 1/60 [s]. Figure 7 shows the both experimental results. From this figure, we can see that the performance of the computed torque method becomes worse. Since the computed torque method only uses joint-space errors, the control performance of the end-tip of the manipulator depends on the robot base (vehicle) control performance. Therefore, if the acceleration and velocity relations between the end-tip and joints are inaccurate or the control performance of the vehicle is not better, good control performance of the end-tip cannot be obtained. On the other hand, from Figure 7 it can be seen that the RAC method has good control performance.

(a) Computed torque method (b) RAC method

Fig. 7. Experimental results of computed torque method and RAC method

(a) Computed torque method (b) RAC method

Fig. 7. Experimental results of computed torque method and RAC method

4.2 RAC method with disturbance compensation of vehicle

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 feedback gains are

KVv = diag{10 10 10 20 20} and KPy = diag{100 100 100 100 100} . The time constant of filter is Tf = 1 [s]. In this case joint velocity control type actuators are used.

Figure 8 shows the motion of the robot and estimated disturbance of the RAC with disturbance compensation, and Figure 9 shows the time histories of experimental results with and without disturbance compensation. Form Figures 8 and 9, it can be seen that the end-tip of manipulator follows the desired trajectory. Moreover, since the robot base position and attitude errors become small values using the disturbance compensation, the end-tip position error is also reduced.

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