PhD research

Robustness against constant external disturbances

The topic of my PhD research is cooperative control for autonomous underwater vehicles. Much work on this topic has been done by Even Børhaug; my predecessor as a PhD student of professor Kristin Pettersen. Based on his work, I continued by adding robustness to constant environmental disturbances, such as ocean currents and wind.

Initially the work focussed on straight-line path following, using line-of-sight (LOS) based control methods. In [ACC'09], we developed a solution based on adaptive control methods. Although theoretically sound, soon we realised that the method was difficult to implement due to the complex control law we obtained, which was not intuitive to tune. This resulted in a focus to find a solution with an easy tunable controller with a clear structure for implementation.

The answer we found in the use of conditional integrators; a control method developed by H.K. Khalil and his PhD students S. Seshagiri and A. Singh. Roughly this method behaves like sliding mode control when the error signals are large, and start acting as proportional-integral control for small error terms. Due to this it combines the positive properties of both methods, without inheriting their disadvantages; conditional integrators have
* bounded and smooth control signals
* build-in integrator anti-windup
* robustness against disturbances
* clear tuning rules

In [Oceans'09] we introduced this method, where the conditional integrators were adjusted to explicitly take into account external disturbances, which-in our particular case of marine vehicles, but also for aircraft and space structures-are constant in an inertial reference frame, while the control action is fixed to the body-fixed reference frame of the vessel. The stability analysis of this method is shown in [MCMC'09] for straight line path following for surface vessels.

Recently, our focus is on extending the idea to more general curved paths, motivated by the need for go-to-formation manoeuvres, which ensure collision-free arrival in a desired formation at a certain time. Obtaining such paths by means of optimization is the topic of the PhD research of Andreas Häusler; a fellow member of the FREEsubNET consortium. Go-to-formation manoeuvres rely on the vessels being on a specific place at a specific time (target tracking) in order to guarantee the absence of collisions between the vessels. In [IAV 2010] we show that using a constant-bearing guidance method for target tracking, augmented with a conditional integrator for adding robustness against ocean currents, we obtain global convergence and stability of the closed-loop system. The movie below shows the resulting performance of the method, where the white vessel is the target to be tracked, and the green vessel is the actual vessel following the path.

Curved trajectory tracking in the presence of constant ocean currents

Our claim of having clear tuning rules is supported by [Oceans 2010], where we explain the effects of changing the different tuning parameters, and discuss there effect on the performance of the system.