Disturbance Rejection using Conditional Integrators: Applications to path manoeuvring under environmental disturbances for single vessels and vessel formations

Abstract

In this thesis, two main topics are discussed: the application of conditional integrators for disturbance rejection, and how to apply this to path following and trajectory tracking of single marine vehicles and vehicle formations.

Disturbance rejection using conditional integrators

The concept of conditional integrators is not yet well-known in the control community. An introduction to the topic is provided, along with a discussion on how we have extended the concept to reject external disturbances. We show that conditional integrators of the form proposed in this thesis can be superimposed to an already existing controller designed for the undisturbed system. Based on the stability and convergence properties of the undisturbed closed-loop system, we are able to guarantee similar properties for the disturbed closed-loop system. Hence if it is guaranteed that the system converges in the undisturbed case, it is guaranteed the system also converges to its desired state in the disturbed case. This simplifies the controller design for disturbed systems, as initially only the simpler undisturbed case needs to be taken into account.

Application to path manoeuvring for vessels

The disturbance rejection method using conditional integrator is used to add robustness against ocean currents (and wind) for marine vehicles. By modelling these disturbances as a constant force in the inertial reference frame, we can obtain accurate path following and trajectory tracking despite the influence of these unmeasured disturbances.

Single vehicle control

For autonomous vehicles often a choice is made between path following or trajectory tracking. The first concept focuses on the geometric task of reaching and following a predefined path irrespective of timing constraints; the latter concept focuses on the dynamic task of following a time-driven target which is moving along the trajectory. A third concept is path manoeuvring, which takes both the geometric and dynamic task into account. We propose a method that transforms any trajectory tracking controller into a path manoeuvring controller, by substituting the real time by a virtual time with certain state-dependent dynamics. By changing a single tuning parameter, the behaviour of the resulting controller can smoothly be adjusted from trajectory tracking via path manoeuvring to path following. This kind of flexibility has —to our best knowledge— not been presented in literature before.

Formation control and synchronisation

When considering formations of marine vehicles, several methods are possible to obtain manoeuvring along curved paths in a desired formation structure. In this thesis a method is described using a fixed formation structure, for which the formation centre follows a predefined trajectory. The desired positions of the individual vehicles will be constant in the path-fixed frame, a property which is exploited in the controller design. To obtain a pathfixed frame, often Serret-Frenet frames are used. This method excludes the set of trajectories having straight line segments or inflection points. It is shown that using a geodesic reference frame, also those trajectories can be followed by the formation.

The flexible path manoeuvring controller as developed for single vehicles is extended to formations, by adding a synchronisation term to the dynamics of the virtual time. The only information the vehicles in the formation need to exchange to obtain synchronisation, is their virtual time. Since this is a scalar value, only low bandwidth is needed to communicate this information, making it suitable for underwater applications.