Discussion of results
The experiments demonstrate the necessary range of attitude control in yaw and pitch for the robot to adopt any attitude on the surface of a sphere with a zero radius turning circle. This freedom in attitude control allows Zero-G Class underwater robots to plan and optimise their missions in a three-dimensional manner in a way that has not been possible previously. Furthermore, the fast on the spot attitude control capabilities demonstrated are essential if Zero-G Class underwater robots are to be applied in geometrically complicated, cluttered and even enclosed environments where reorientations must be performed in confined spaces. The non-coincident centres of gravity and buoyancy cause an offset error in the static attitude response of the robot. It has been suggested in the previous chapter that this can be overcome by including an integral error term in the control law in future applications. However, the non-zero righting moment places a significant burden on the attitude control system. It is possible to sufficiently overcome this problem for practical applications by operating the flywheels at a higher rate to increase the momentum envelope. However, in a finite system the CMGs will eventually reach the boundary of their operating envelope when holding non-horizontal attitudes and it is important to take realistic measures to balance the internal moving parts and reduce the righting moment that forms the root of the problem.
9.2
Vertically pitched diving and surfacing in surge
This section demonstrates how a Zero-G Class underwater robot can plan and optimise its missions in a three-dimensional manner. Fig 9.7 shows an image sequence of the experiment taken by an underwater camera. This is the first time an underwater robot has performed vertically pitched diving and surfacing in surge. Video footage can be found in Appendix D.
Chapter Nine 9.2. Vertically pitched diving and surfacing in surge
The robot first adopts a horizontal attitude before pitching to 90o with its nose down and diving vertically in surge. It then holds a horizontal attitude before pitching to −90o with its nose up to surface vertically. Finally, the robot rights itself to complete the manoeuvre. The roll and yaw dynamics of the robot were not controlled during the experiment due to the unreliability of the attitude sensor’s measurements about these axes at near vertical pitch angles. Clearly the use of alternative sensors must be investigated. The CMG system exerts the necessary torques to reorientate the robot and actively stabilise its attitude as it propels itself through the water. The position data in Fig. 9.8 is computed in real-time by the robot using the dynamic model (3.12) with actual attitude and angular rate measurements. Using the length of the robot as a reference in the image sequence it can be seen that the simulated translational dynamics are reasonable.
Fig. 9.9 shows the attitude response of the robot during the experiment. The CMG system exerts a torque in the order of 0.2 Nm during the pitching manoeuvre to adopt a vertical pitch angle. As the robot propels itself at a vertically pitched orientation, the reaction to the torque exerted by the thruster causes the robot to roll. This can be seen in Fig. 9.7 and in the video footage in Appendix D. It follows that when the robot rights itself after having rolled when vertically pitched, its heading angle will have changed. This effect explains the large yaw angles observed and also accounts for the large yaw rate recorded by the sensor each time the robot rights itself. This can be overcome by actively stabilising roll motion using the CMGs or by using a contra-rotating propeller to actuate surge as discussed in Section 8.3.3.
Chapter Nine 9.2. Vertically pitched diving and surfacing in surge
a.) Attitude
b.) Angular rate
c.) Torque
Chapter Nine 9.2. Vertically pitched diving and surfacing in surge
Fig. 9.10 shows the steering response of the CMG system for a flywheel rate of ˙ψ= 10,000 rpm. The flywheels rotate 25% faster than in the vertical pitching manoeuvre described in the pre- vious section and so the gimbal rates required to generate the same magnitude torque are smaller. This results in smaller gimbal excursions during the manoeuvre and the system operates further within the momentum envelope and has a larger value of det(¯c¯cT).
Chapter Nine 9.2. Vertically pitched diving and surfacing in surge
Figure 9.11: Geometric representation of momentum vector during the diving manoeuvre The geometric representation in Fig. 9.11 illustrates the motion of the normalised CMG momentum vector to generate the required torques during the experiment. It can be seen that the momentum vector stays within the boundaries of the constrained workspace.
Discussion of results
This is, to the knowledge of the author, the first time an underwater robot has performed vertically pitched diving and surfacing in surge. The CMG system stores enough momentum at a flywheel rate of 10,000 rpm to adopt a vertically pitched attitude and overcome the non-coincident centres of gravity and buoyancy of the robot used in this experiment. The CMG system demonstrates a fast response and high resolution of control to actively stabilise the robot’s attitude as it propels itself through the water in vertically pitched surge. This clearly indicates that the CMG system is capable of stabilising any attitude on the surface of a sphere as the robot translates in surge.
The unrestricted attitude control capabilities allow the robot to take full advantage of its single thruster and perform three-dimensional manoeuvres that have not been possible previously. This is efficient in terms of both speed and power since the robot travels only in its principal mode of translation. The unrestricted attitude control and unique manoeuvring capabilities demonstrated in this experiment allow the missions of a Zero-G Class underwater robot to be planned and optimised in a fully three-dimensional manner.