9.3
Implications for underwater robot research
The application of CMGs to Zero-G Class underwater robots has several important impli- cations for underwater research using AUVs. The unrestricted attitude control and unique manoeuvreing capabilities allow Zero-G Class underwater robots to approach their missions in a truly three-dimensional manner, optimising the use of their thrusters, sensors and power supply in a way that has not been possible previously. In addition to improving AUV effi- ciency, this opens up new fields of research where AUVs can be applied. This section discusses the implications of CMG technology on Zero-G design and provides suggestions for the types of missions in which this new class of underwater robot could be applied.
9.3.1 Zero-G design
The freedom in attitude control offered by CMGs allows Zero-G Class underwater robots to manoeuvre freely in any direction whilst travelling only in their principal mode of translation. This is often seen in nature and is efficient both in terms of performance and design. Since the robot can adopt and maintain any attitude it only requires a single thruster to actuate surge. Having just a single mode of translation minimises the number of sensors required for navigation and obstacle avoidance as in principal, the robot only requires perceptional sensors in the direction of travel. Since the CMG system is contained within the body of the robot, it is physically protected and does not exert any external forces that may agitate loose surfaces or small creatures. This highly integrated form preserves the hydrodynamic integrity of the hull and allows for simple and elegant design.
The idea of using the flywheels as a mechanical battery was introduced in Section 7.3.4. As stated it may be possible to perform short missions with no chemical battery at all. Specifically in the case of CMGs, this combines energy storage and attitude control in a single device, known as an Integrated Power and Attitude Control System, or IPACS, as suggested by Will [74] in 1974. This, together with the highly efficient three-dimensional approach to missions, minimises the necessary number of components and indicates that Zero-G Class underwater robots can be considerably smaller than conventional AUVs.
9.3.2 Zero-G missions
The concept of minimal redundancy is central to the design philosophy of Zero-G Class underwater robots. This not only applies their physical design, but also extends to their missions. It is envisaged that Zero-G Class AUVs will perform 20-30 minute inspections of targets that have been located prior to deployment. The short mission time suggests that the robot would not require any source of power other than the energy stored in their flywheels. These can be accelerated to their operational speed in a matter of minutes and this can be performed on board a support vessel using an external power source immediately prior to each deployment. Since no gases are produced this can be performed without opening the pressure hull. This combined with the ease of handling for deployment and recovery due to the small size of the robot, allows for a rapid turnaround that would allow a number deployments to be made in quick succession when inspecting large, or multiple targets.
Chapter Nine 9.3. Implications for underwater robot research
The small size and highly integrated design combined with the high manoeuvrability at low speeds allows for manoeuvring in confined spaces, making Zero-G Class AUVs ideal for operation in geometrically complicated, cluttered and even enclosed environments. This allows Zero-G Class AUVs to perform missions that have so far eluded AUVs. Potential applications include tracking the dives of marine animals such as whales, turtles and even penguins and ranges to visual surveys of man-made structures such as oil rigs, subsea oil wells, submerged ruins and even the inside of sunken wrecks. It is hoped that the increased agility and operational envelope will ultimately lead to an increase in the commercial and scientific value of AUVs.
Chapter 10
Conclusions and future work
The aim of this research has been the development of a new class of Zero-G underwater robot that is capable of approaching its missions in a fully three-dimensional manner. This requires the ability to perform on the spot rotations to adopt and maintain any attitude on the surface of a sphere as if in a zero gravity environment and the ability to actively stabilise any attitude while translating in surge. To achieve this CMGs have been introduced as a new type of underwater actuator and a novel control scheme has been developed based on internal momentum exchange.
10.1
Original contributions and summary
This is the first application of CMGs to underwater robots and so it has been necessary to develop a dynamic model of a rigid body, containing an arbitrary system of single gimbal CMGs, that is free to translate and rotate in a viscous fluid. This has been derived using Kirchhoff’s equations of motion, which is more concise than the Newtonian derivations of previous works. This is the first time that the translational dynamics of a CMG system have been modelled and that the coupled effects of translation have been accounted for in the rotational dynamics. Furthermore, the hydrodynamic interactions of the body have also been included in the form of added mass, added inertia and viscous drag together with the effects of other actuators. The equations have been restricted to a body with coincident centres of gravity and buoyancy as this concept is central to this research. However, for completeness, a method to incorporate gravity effects into the model has been presented. In order to describe any orientation, the attitude of the body is converted to the inertial frame using quaternions since they contain no singularities in their description of motion.
The freedom in attitude control offered by having coincident centres of gravity and buoy- ancy raises questions concerning the stability of the system. This has been assessed based on energy considerations of the complete CMG, body and fluid system using Lyapunov’s direct method. The results of this analysis forms the basis of a globally asymptotically stable feed- back attitude control law that determines the torques necessary for the robot to adopt and maintain any attitude in roll, pitch and yaw. In contrast to all previous CMG applications, the control law developed in this research takes into account the effects of translation, the added inertia and the viscous hydrodynamic interactions of the body as well as the coupled dynamics of the CMG and body system.
Chapter Ten 10.1. Original contributions and summary
The greatest challenge in the application of single gimbal CMG systems is the inherent and serious problem of singular orientations that can result in a momentary loss of control authority. This research has presented a method to geometrically represent the singularities of a CMG system based on previous work by Kurokawa [64]. A new method has been developed to classify escapable and inescapable singularities based on the Gaussian curvature of null motion that is determined using the eigenvalues of a characteristic function. This is more simple and direct than the method presented by Kurokawa that indirectly deduces escapability using a number of different conditions. A comprehensive geometric study of a minimally redundant CMG pyramid has been performed and the graphical assessment is the first such study to explicitly distinguish between escapable and inescapable singularities for the complete singular surface. The study has demonstrated why no exact, real-time steering law can guarantee singularity avoidance over the entire workspace. The implications of this on attitude control have been discussed and it was concluded that a steering law for application to AUVs must be applicable in real-time and must remain exact, guaranteeing that the torque developed by the CMG system is always equal to that demanded by the control law. A global steering law that satisfies these conditions has been formulated based on the method of workspace restriction developed by Kurokawa. This research has presented a formal method to derive the appropriate algebraic constraining condition, filling in gaps in the logic of the previously mentioned work that pioneered this technique, based on global considerations of the inverse kinematics of attitude control.
The underwater robot IKURA, developed as part of this research, is the first prototype of the Zero-G Class and is the first application of CMGs to underwater robots. Practical considerations of its mechanical and electrical design have been discussed and a series of dry- land and underwater experiments performed to verify the associated theoretical developments. In particular, the actuation capabilities of the CMG system and the exactness and real-time applicability of the steering law have been verified by physical measurements of the torque generated. The dynamic equations for the complete CMG, body and fluid system have been verified in a series of underwater experiments, though difficulties were encountered due to the tether and the non-coincident centres of gravity and buoyancy of the robot used. The control law developed has demonstrated robustness to certain types of unmodelled disturbances, such as the effects of non-linear bearing friction and vibrations of the system. However, problems were encountered due to the hydrostatic righting moment of the body and the presence of a tether that caused a small, bounded offset in the robot’s closed-loop attitude response. It has been suggested that this can be overcome by adding an integral error term in the control law, though this remains to be verified experimentally. Despite these problems experiments have demonstrated that the control law developed in this research takes advantage of the coupled behaviour of the CMG, body and viscous fluid interactions to make a more efficient use of the system, achieving a superior control response for 20% less overall control activity in yaw and 30% less activity in pitch than two alternative control laws that neglect the dynamics of the system and the fluid interactions of the body respectively. Finally, the ability of the system to actively stabilise the passively unstable, unsteady self-propelled translational dynamics of a Zero-G Class underwater robot has been verified experimentally.