Jerome Jouffroy

Methodological remarks on contraction theory

Because contraction analysis stems from a differential and incremental framework, the nature and methodology of contraction-based proofs are significantly different from those of their Lyapunov-based counterparts. This paper specifically studies this issue, and illustrates it by revisiting some classical examples traditionally addressed using Lyapunov theory. Even in these cases, contraction tools can often yield significantly simplified analysis. The examples include adaptive control, robotics, and a proof of convergence of the deterministic extended Kalman filter.

Formation Control of Marine Surface Craft: A Lagrangian Approach

This paper presents a method for formation control of marine surface craft inspired by Lagrangian mechanics. The desired formation configuration and response of the marine surface craft are given as a set of constraint functions. The functions are treated according to constraints in analytical mechanics. Thus, constraint forces arise and feedback from the constraint functions keeps the formation assembled. Since the constraint functions are designed for a desired effect, the forces can be interpreted as control laws. Examples of constraint functions that maintain a formation are presented. Furthermore, the same approach has been applied with no major modification to position control purposes for a single vessel. An extension to underactuated vessels is given. Simulations with nonlinear models of tugboats illustrate the proposed method versatility and its robustness with respect to environmental disturbances and time delays

Some ancestors of contraction analysis

Contraction analysis is a recent tool for analyzing the convergence behavior of nonlinear systems in state-space form (see Lohmiller and Slotine [16] for the main reference). However, it seems that earlier results derived by mathematicians in the 1950s closely match some of the results of contraction analysis. In this paper, we review and place into perspective some references of this era, and relate them with contraction.

Formation Control of Marine Surface Craft using Lagrange Multipliers

We propose a method for constructing control laws for formation control of marine craft using classical tools from analytical mechanics. The control law is based on applying inter-vessel constraint functions which again impose forces on the individual vessels that maintain the given constraints on the total system. In this way, a formation can be assembled and stay together when exposed to external forces. A brief comparison with other control designs for a group of marine craft is done. Further, control laws for formation assembling (with dynamic positioning), and formation keeping during maneuvering is derived and simulated to illustrate the properties of the proposed method.

On algebraic time-derivative estimation and deadbeat state reconstruction

This paper places into perspective the so-called algebraic time-derivative estimation method recently introduced by Fliess and co-authors with standard results from linear state-space theory for control systems. In particular, it is shown that the algebraic method can essentially be seen as a special case of deadbeat state estimation based on the reconstructibility Gramian of the considered system.

An algebraic perspective to single-transponder underwater navigation

This paper studies the position estimation of an underwater vehicle using a single acoustic transponder. The chosen estimation approach is based on nonlinear differential algebraic methods which allow to express very simply conditions for observability. These are then used in combination with an integrator-based time-derivative estimation technique to design an algebraic estimator, which, contrary to asymptotic observers, does not require sometimes tedious convergence verification. Simple simulation results are presented to illustrate the approach.

Nonlinear dynamic positioning of ships with gain-scheduled wave filtering

This paper presents a globally contracting controller for regulation and dynamic positioning of ships, using only position measurements. For this purpose a globally contracting observer which reconstructs the unmeasured states is constructed. The observer produces accurate estimates of position, slowly varying environmental disturbances (bias terms) and velocity. The estimates are automatically adjusted to the present sea state by gain-scheduling the wave model parameters in the observer. Finally, the estimates are used in a nonlinear PID control law and the stability proof of the observer-controller is based on a separation principle for contracting systems in cascade.

Modeling and Nonlinear Heading Control of Sailing Yachts

This paper presents a study on the development and testing of a model-based heading controller for a sailing yacht. Using Fossens compact notation for marine vehicles, we first describe a nonlinear four-degree-of-freedom (DOF) dynamic model for a sailing yacht, including roll. Our model also includes two possible steering mechanisms: a conventional rudder and a simple moving mass system. Starting from this model, we then design, for both steering mechanisms, a nonlinear heading controller using the integrator backstepping method, which exponentially stabilizes the heading/yaw dynamics. By computing the equilibrium points of the system, the course is related to the heading angle, and course control is also achieved. A few simulation results are presented to illustrate the behavior of our control designs.

Real-time geo-referenced video mosaicking with the MATISSE system

This paper presents the MATISSE system: Mosaicking Advanced Technologies Integrated in a Single Software Environment. This system aims at producing in-line and off-line geo-referenced video mosaics of seabed given a video input and navigation data. It is based upon several techniques of image and signal processing which have been developed at Ifremer these last years in the fields of image mosaicking, camera self-calibration or correction and estimation of navigation data.

Underwater Vehicle Navigation Using Diffusion-Based Trajectory Observers

This paper addresses the issue of estimating underwater vehicle trajectories using gyro-Doppler (body-fixed velocities) and acoustic positioning signals (earth-fixed positions). The approach consists of diffusion-based observers processing a whole trajectory segment at a time, allowing the consideration of important practical problems such as different information update rates, outages, and outliers in a very simple framework. Results of contraction theory are used to prove that the observers are convergent, i.e., stable in the incremental sense. Simulation and experimental results are presented to illustrate the potential of application of the method.