**4.2 Experiment of vertical motion**

Even though we design the working depth of the vehicle to 10*m*, because the depth of experimental pool is only 1.2*m*, we can only make the experiments in shallow water. So we set the vertical motion time in a relatively small range. We also carried out two experiments: **Case 1**:

step 1. Set the top point of the spherical hull as the start point;

step 2. Move downward in Z axis for about 7*s* ;

step 3. Float up to the surface.

**Case 2**:

14 Will-be-set-by-IN-TECH

(a) *Vf* = 0.1*m*/*s*

(b) *Vf* = 0.2*m*/*s*

This experiment combines surge and sway together to verify the motion characteristics of the

Fig. 19. Propulsive forces with Different Control Voltages

vehicle in horizontal plane. We carried out three experiments:

step 1. Surge (Propeller I and II work together, propeller III powered off);

step 2. Brake (Propeller I and II powered off, Propeller III works to produce brake force). In case 1, timing of step 1 is about 10*s*, and step 2 takes about 12*s*. And timing of case 2 is relatively the same with case 1, because of the same hydrodynamics characteristics of turning right and left. In case 3, it takes 15*s* reaching a stable speed, and the brake effect happens in about 3*s* which is effective for low speed underwater vehicles. From Fig.20, we can see,

**4.1 Experiment of horizontal motion**

step 1. Surge (Move forward in X axis); step 2. Right steering (Turn right about 90*o*); step 3. Sway (Move forward along Y axis.)

step 1. Surge (Move forward in X axis); step 2. Left steering (Turn left about 90*o*); step 3. Sway (Move forward along Y axis.)

**Case 1**:

**Case 2**:

**Case 3**:

step 1. Set the top point of the spherical hull as the start point;

Based on the design of the vehicle, we introduced the principles of the water-jet propulsion system including the force distribution of three water-jet propellers, the working principles of different motions. And then we discussed about the modeling of one single propeller by identification experiments. For the modeling, the flow velocity and equivalent cross-section

Development of a Vectored Water-Jet-Based Spherical Underwater Vehicle 19

One experimental prototype of this spherical underwater vehicle is developed for the purpose of evaluation. Underwater experiments are carried out to evaluate the motion characteristics of this spherical underwater vehicle. Experimental results are given for each experiment, and

From the underwater experiments of the prototype vehicle, the availability of the design is proved, and the water-jet propulsion system can work well for different motions. But there are also some problems needed to be resolved. Firstly, the propulsive force of the water-jet propellers needed to be increased; secondly, the variation of water pressure on the propulsive force should be considered when building the dynamics model of propellers; thirdly, the gravity distribution should be re-regulated to improve stability; finally, from experiments, it is necessary to improve the accuracy of the dynamics model of the vehicle for precise control.

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**6. References**

step 2. Move downward in Z axis for about 7*s* ;

step 3. Stop the vehicle.

Fig. 21. Experimental Results of Vertical Motion

From Fig.21(a) and Fig.21(b), we can see, the experimental results does not fit well with simulation results very well, errors exceed 100%. When we analyze the reasons, we find that, the simulation experiment does not consider the variation of water pressure. The control voltage to the thrusters is 7*V* as a constant. That means, the propulsive force will not change. But with the increasing of depth, water pressure increases. As a result, the effective propulsive force are weaken by water pressure.

#### **4.3 Experiment of yaw**

We let the vehicle rotate about 90*<sup>o</sup>* then stop. From Fig.22(a) and Fig.22(b), the maximum error between simulation results and experimental results happens at about 2.8*s* where is nearly the maximum angular velocity. The reason of this result is that, we simplified the model of our vehicle, especially the hydrodynamic damping forces. Only linear damping force and quadratic damping force are taken into account in our case. But in the real experiment, there are many other velocity related hydrodynamic damping forces, therefore, when the angular velocity increasing, the damping effect of ignored forces become obvious.

Fig. 22. Experimental Results of Yaw

#### **5. Conclusions**

In this paper, we proposed a spherical underwater vehicle which uses three water-jet propellers as its propulsion system. We introduced the design details of mechanical and electrical system.

Based on the design of the vehicle, we introduced the principles of the water-jet propulsion system including the force distribution of three water-jet propellers, the working principles of different motions. And then we discussed about the modeling of one single propeller by identification experiments. For the modeling, the flow velocity and equivalent cross-section of the propeller are taken into account for dynamics model.

One experimental prototype of this spherical underwater vehicle is developed for the purpose of evaluation. Underwater experiments are carried out to evaluate the motion characteristics of this spherical underwater vehicle. Experimental results are given for each experiment, and the analysis are also given.

From the underwater experiments of the prototype vehicle, the availability of the design is proved, and the water-jet propulsion system can work well for different motions. But there are also some problems needed to be resolved. Firstly, the propulsive force of the water-jet propellers needed to be increased; secondly, the variation of water pressure on the propulsive force should be considered when building the dynamics model of propellers; thirdly, the gravity distribution should be re-regulated to improve stability; finally, from experiments, it is necessary to improve the accuracy of the dynamics model of the vehicle for precise control.
