Faïçal Mnif

Asymptotic Backstepping Stabilization of an Underactuated Surface Vessel

This brief addresses the problem of controlling the planar position and orientation of an autonomous underactuated surface vessel. Under realistic assumptions, we show, first, that there exists a natural change of coordinates that transforms the whole dynamical system into a cascade nonlinear system, and, second, the control problem of the resulting system can be reduced to the stabilization of a third-order chained form. A time-invariant discontinuous feedback law is derived to guarantee global uniform asymptotic stabilization of the system to the desired configuration. The construction of such a controller is based on the backstepping design approach. A simulation example is included to demonstrate the effectiveness of the suggested approach

Cascade design for formation control of nonholonomic systems in chained form

This paper presents a constructive method to design a cooperative state and output feedback to steer a group of nonholonomic mobile robots in chained form to form a desired geometric formation shape. The control methodology divides the resulting tracking error dynamics into a cascaded of linear and time-varying subsystems. A basic consensus algorithm is first applied to the linear subsystem which makes the states synchronize exponentially to zero. Once this first linear subsystem has converged, the second cascade can be treated as a linear time-varying subsystem perturbed by a vanishing term from its cascade. A dynamic state and output feedback is constructed to achieve synchronization of the rest of the states. The proof of stability is given using a result from cascade systems. Since time delay appears in many interconnection networks and particularly in cooperative control, its effect on the stability of the closed-loop system is analyzed using Razumikhim theorem. It is shown that the established cooperative controller work well even in the presence of time delay. Numerical simulations are performed on models of car-like mobile robots to show the effectiveness of the proposed cooperative state and output-feedback controllers.

Robust control for constrained robot manipulators

In this paper, a robust control law for constrained manipulators with parametric uncertainties is derived. Two schemes are presented ; the first, based on The Corless-Leitmann approach, will guarantee ultimate uniform stability of the system, and hence uniform boundedness errors convergence. As a second approach, a class of continuous feedback controls is proposed to guarantee asymptotic stability of the uncertain system. The analysis is based on a theoretical result of asymptotic stability. In this approach, clue to the continuity of the control and asymptotic stability of the system, we can achieve acceleration convergence and, thus, constraint force convergence.

Nonlinear Formation Control of a Group of Underactuated Ships

This paper addresses a nonlinear formation control of a group of underactuated ship at a dynamic level of planar formation control, while holding a desired inter-ship formation pattern. In particular we propose a combination of the virtual structure and the path following approaches to derive the formation architecture. Ship coordination is achieved by adjusting the speed of each of the ships along its path, in the sense that the derivative of the path is left as a free input to synchronize the ships motion. The proposed controller is basically based on Lyapunov direct method and backstepping technique. Simulations illustrate the efficacy of the proposed approach.

Formation path following control of unicycle-type mobile robots

This paper presents a control strategy for coordination of multiple mobile robots. A combination of the virtual structure and path following approaches is used to derive the formation architecture. The formation controller is proposed for the kinematic model of two-degrees of freedom unicycle- type mobile robots. The approach is then extended to consider formation controller for its complete dynamic model. The controller is designed in such a way that the path derivative is left as a free input to synchronize the robots motion. Simulation results with three robots, are included to show the performance of our control system.

Set point stabilization of a 2DOF underactuated manipulator

Controlling an underactuated manipulator with less actuators than degrees of freedom is a challenging problem, specifically when it is to force the underactuated manipulator to track a given trajectory or to be configurated at a specific position in the work space. This paper presents two controllers for the set point regulation of 2-DOF underactuated manipulators. The first one is a cascade sliding mode tracking controller while the second one uses an inputoutput feedback linearization approach. The first algorithm builds on an observation that an underactuated manipulator can be treated as two subsystems. Consequently, a cascade sliding mode tracking controller has been designed. Firstly, a sliding mode surface is designed for both subsystems, these two sliding surfaces represent a first layer in the design architecture. A second layer sliding mode surface is then constructed based on the first layer sliding surface. The cascaded sliding mode controller is therefore deduced in terms of Lyapunov stability theorem. Robustness issues to bounded disturbances are then investigated. In a second stage of the paper, the input output feedback linearization (IOFL) control is presented. The latter, is then mixed to the sliding mode control scheme for robustness issues. Simulation results on 2-DOF whirling pendulum are presented to demonstrate the effectiveness of the proposed approach.

Observer design for euler lagrange systems: application to path following control of an underactuated surface vessel

This paper presents a practical method to design an output feedback controller for a general mechanical system described by Euler Lagrange equations. An application of such an observer is formulated to path following controller for an underactuated surface vessel moving in a horizontal plan. The surface vessel is underactuated in the sway direction and has only position and orientation measurement available. The control development is based on Lyapunov direct method and backstepping technique.

Radial-basis-functions neural network sliding mode control for underactuated manipulators

This paper presents a neural network (NN) sliding mode control (NNSMC) and indirect adaptive technique Neural Network sliding mode control (IANSMC) for underactuated robot manipulators. The adaptive NN based on Radial Basis Functions (RBF) is used as an estimators to approximate uncertainties of the problem formulation. Adaptive learning algorithms in NNSMC are derived from the Lyapunov stability analysis. Sliding mode control and indirect adaptive technique (IANSMC) are combined to deal with modeling parameter uncertainties and bounded disturbances. The stability of the mixed controller is then proved. A radial basis function Neural Network is used to estimate system parameters and to compensate the uncertainties in the design of the sliding mode control. Neural network parameters are tuned on-line, with no off-line learning phase required. Discussions and comparisons between proposed controllers are presented. Simulation results show that the NNSM and IANSMC are betters than the traditional SMC to control underactuated manipulators.

Formation control of multiple marine vehicles with velocity reference estimation-based passivity-control design

This paper addresses the problem of coordination path following control of multiple autonomous vehicles. Stated briefly, the problem consists of steering a group of vehicles along a specified path, while holding a desired inter-ship formation pattern. Path following for each vehicle amounts to reducing an appropriately defined geometric error to zero. We first show a passivity property for the path following system and, next, combine this with a passivity-based synchronisation algorithm to coordinate the vehicles along their paths. Vehicle coordination is achieved by adjusting the speed of each vehicle along its path according to information exchanged on the positions of a subset of the other vehicles, as determined by the communication topology adopted. We further assume the unavailability of the reference velocity to each vehicle; we consider the situation where this information is only available to a leader of this formation. Distributed observers are designed for the follower vehicles, under the assumption that the velocity of the leader cannot be measured in real time. Simulations results are presented and discussed.

Robust adaptive formation control of fully actuated marine vessels using local potential functions

We study the problem of formation control and trajectory tracking for a group of fully actuated marine vehicles, in the presence of uncertainties and unknown disturbances. The objective is to achieve and maintain desired formation tracking, and guarantee no collision between the marine vehicles. The control development relies on existing potential functions which fall at a minimum value when the vehicles reach the desired formation, and blow up to infinity when the vehicles approach collision. The combination of the potential functions, backstepping and variable structure based design technique allows us to handle time varying disturbances by ensuring a stable formation. Using the sliding-Backstepping technique and Lyapunov synthesis, a stable coordination tracking controller is designed. Uniform boundedness of the closed loop signals system is achieved.