## Navigation and Control of Underwater Robotic Vehicles

##### Doctoral thesis

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##### Date

2018##### Metadata

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- Institutt for marin teknikk [2756]

##### Abstract

The thesis considers navigation and control of underwater robotic vehicles, and is divided into two parts, with more emphasis on Part II. Part I considers stabilization of the end effector of an underwater vehicle-manipulator system using kinematic control, whereas Part II deals with aided inertial navigation for underwater vehicles by employing acoustic, depth and inertial measurements. Part I takes a more practical approach, in which a control scheme is suggested and tested experimentally, whereas Part II considers both theoretical analysis wrt. stability as well as experimental validation.
In Part I the problem of keeping the state (position and attitude) of the manipulator arm end effector of an underwater vehicle-manipulator system as close as possible to the desired state when the system is subjected to unknown time-varying disturbances is investigated. A common approach for keeping the end effector at a desired state is kinematic control, and a central assumption when applying kinematic control is that all reference velocities are followed perfectly. For underwater vehicle-manipulator systems it is argued that this assumption is not always accurate when subjected to time varying unknown currents, due to the large inertia of the vehicle body, thruster inaccuracies and the diffculty of obtaining highly accurate state estimates. A control scheme seeking to take the lower-level velocity tracking error in some of the less accurately controlled degrees of freedom of the system into account in some of the more accurately controlled degrees of freedom of the system is suggested. A simulation study and experimental validation is provided. In simulation, a significant improvement in accuracy is seen, whereas the difference in accuracy is less apparent in experiments. However, the proposed scheme results in improved accuracy for both simulation and experiments.
In Part II the problem of improving accuracy and robustness when estimating position, velocity, attitude, and system- and environmental uncertainties of underwater robotic vehicles is investigated. For a fully autonomous system it is of great interest to have state estimation schemes that are both as accurate as possible and that with certainty will not diverge from the true values. In more technical terms, this means estimation schemes that are optimal wrt. noise, and have proven stability. The newly developed eXogenous Kalman Filter principle has been applied in all estimation schemes in Part II, and is a principle that seeks to achieve exactly these two properties when estimating states in a nonlinear system: optimal noise properties and proven stability. This is done by generating a state estimate using an auxiliary estimator with proven stability, and using this state estimate as a linearization point in a Linearized Kalman Filter in a cascade structure. The noise properties of the observers using the eXogenous Kalman Filter principle are stated as close-to-optimal due to inaccuracies in linearization point and higher order linearization errors.
When performing acoustic ranging under water it is necessary to know the speed of sound in water. The underwater speed of sound can be varying over time, and should consequently be estimated online. Chapter 5 presents an observer estimating position, velocity and underwater speed of sound using acoustic ranges and depth measurements. The observer has a cascaded structure, and is proven to be globally exponentially stable. The cascade consists of three steps: An algebraic transformation along with solving an optimization problem if necessary, a linear Kalman Filter taking the algebraic transformation as measurements, and a Linearized Kalman Filter taking the output from the previous step as linearization point. A similar observer is first suggested in an earlier paper, and the contribution in this thesis is improving range measurement noise robustness compared to the previous observer. The observer is validated through a simulation study and experimentally. It converges quickly and has similar stationary performance as an optimal, benchmark observer.
Robust and accurate attitude estimation is important for several reasons. Thrust allocation during path following, knowing the camera direction during inspections and most importantly, to rotate accelerometer measurements given in the body-fixed coordinate frame in a strapdown system to the global coordinate frame for accurate positioning. The accelerometer is usually used to determine attitude, along with a measurement relating to the heading, usually provided by a magnetometer or a gyrocompass. Both of these heading sensors suffer from drawbacks, and it is of interest to investigate other ways of determining heading, both to increase robustness and for potential cost reductions. In Chapter 6 an observer estimating attitude and angular rate sensor bias using a position estimate along with acoustic range, angular rate, and accelerometer measurements is proposed. The heading estimate is based on measuring the difference in time of arrival of an acoustic signal for two or more receivers on the vehicle. The observer has a cascade structure, and is proven to be globally exponentially stable, except for known singularity points. The cascade consists of four steps: An observer generating a position and underwater speed of sound estimate, a step estimating the vectors between the receivers in the global coordinate frame, a non-linear observer generating a globally exponentially stable estimate of attitude and angular rate sensor bias, and a Linearized Kalman Filter using the output from the non-linear observer as linearization point. The observer is validated through a simulation study and experimentally. It converges quickly and has similar stationary performance as an optimal, benchmark observer.
When estimating accelerometer bias it is of interest to decouple the attitude estimate from the accelerometer measurements. This is usually not possible, as the accelerometer is very often central in determining attitude, but by employing several receivers on the vehicle, combined with angular rate sensor measurements, a fairly accurate attitude and angular rate sensor bias estimate can be achieved, using only acoustic ranging and angular rate sensor measurements. In Chapter 7 an observer estimating attitude and angular rate sensor bias using a position estimate and only acoustic and angular rate sensor measurements is suggested, which is globally exponentially stable except for known singular points. The observer is very similar to the previously described observer, except for the algebraic transformation and an assumption regarding the placement of the acoustic receivers. The observer is validated experimentally. It converges quickly and has similar stationary performance as an optimal, benchmark observer.
By combining the results obtained in Chapter 5 to Chapter 7, along with some additions, it is possible to design an observer estimating position, velocity, attitude, underwater wave speed, accelerometer bias and angular rate sensor bias using acoustic, depth, and inertial measurements. The observer is proposed in Chapter 8 and has a cascade structure, which is shown to be globally exponentially stable except for known singularities. The cascade consists of four steps: An observer generating a position and underwater speed of sound estimate, an observer generating an estimate of attitude and angular rate sensor bias with proven stability, an observer providing a rough estimate of accelerometer bias with proven stability, and a double Linearized Kalman Filter using the output from the non-linear observer as linearization point. Due to the availability of a full attitude estimate from the acoustic measurements, there is no demand of excitation of the system to estimate accelerometer bias accurately. The observer is validated experimentally. It converges quickly and has almost identical performance as an optimal, benchmark observer.
Finally, conclusions and further work is provided.