Jawhar Ghommam

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

Hierarchical Fuzzy Cooperative Control and Path Following for a Team of Mobile Robots

In this paper, an intelligent cooperative control and path-following algorithm is proposed and tested for a group of mobile robots. The core of this algorithm uses a fuzzy model, which mimics human thought to control the robots velocity, movement, and group behavior. The designed fuzzy model employs two behaviors: path following and group cooperation. Hierarchical controllers have also been developed based on fuzzy and proportional integral derivative to instruct the robots to move in a group formation and follow specific paths. As the robots move along individual predetermined paths, the designed algorithm adjusts their velocities so that the group arrives at their target points within the same time duration regardless of the length of each individual path. The fuzzy rules applied to the robots are defined by the kinematics limitation, which is bounded by both linear and angular velocities and the length and curvature of the individual paths. The experimental results of three mobile robots traveling on different paths are presented to show the accuracy of obtaining control and cooperation by using the fuzzy algorithm.

Backstepping-based cooperative and adaptive tracking control design for a group of underactuated AUVs in horizontal plan

In this paper, we investigate new implementable cooperative adaptive backstepping controllers for a group of underactuated autonomous vehicles that are communicating with their local neighbours to track a time-varying virtual leader of which the relative position may only be available to a portion of the team members. At the kinematic cooperative control level of the autonomous underwater vehicle, the virtual cooperative controller is basically designed on a proportional and derivative consensus algorithm presented in Ren (2010), which involves velocity information from local neighbours. In this paper, we propose a new design algorithm based on singular perturbation theory that precludes the use of the neighbours’ velocity information in the cooperative design. At the dynamic cooperative control level, calculation of the partial derivatives of some stabilising functions which in turn will contain velocity information from the local neighbours is required. To facilitate the implementation of the cooperative controllers, we propose a command filter approach technique to avoid analytic differentiation of the virtual cooperative control laws. We show how Lyapunov-based techniques and graph theory can be combined together to yield a robust cooperative controller where the uncertain dynamics of the cooperating vehicles and the constraints on the communication topology which contains a directed spanning tree are explicitly taken into account. Simulation results with a dynamic model of underactuated autonomous underwater vehicles moving on the horizontal plane are presented and discussed.

Nonsingular Serret–Frenet Based Path Following Control for an Underactuated Surface Vessel

In this paper we develop a new control law to steer an underactuated surface vessel along a predefined path at a constant forward speed controlled by the main thruster system. The methodology is based on the Serret-Frenet formulation to represent the ship kinematics in terms of path parameters, which allows for convenient definition of cross and along track error. Furthermore, our approach for path following overcomes the stringent initial condition constraints. This paper also addresses the path following with environmental disturbances induced by wave, wind, and ocean-current. The proposed controller is designed based on the Lyapunov direct method and backstepping technique. The closed loop path following errors is proven to be uniform ultimate bounded. Results are demonstrated by high fidelity simulation.

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.

Coordinated path following for multiple underactuated AUVs

This paper addresses the problem of coordinated path following whereby multiple underactuated marine crafts are required to follow a prescribed paths while keeping a desired inter-vehicle formation pattern. We show how Lyapunov- based techniques and graph theory can be brought together to yield a decentralized control structure where the dynamics of the cooperating vehicles and the constraints imposed by the topology of the inter-vehicle communications network are explicitly taken into account. Path following for each vehicle consists of converging the geometric error at the origin. Vehicle coordination is achieved by adjusting the speed of each vehicle along its path according to information on the positions and speeds of a subset of the other vehicles of the group. We illustrate our design procedure for three underwater marine craft. Simulations results are presented and discussed.

Leader-follower formation control of nonholonomic robots with fuzzy logic based approach for obstacle avoidance

In this paper we investigate the leader follower motion coordination of multiple nonholonomic mobile robots. A combination of the virtual vehicle and trajectory tracking approach is used to derive the formation architecture. A virtual vehicle is steered in such a way it stabilizes to a shifted reference position/heading defined by the leader, the velocity of the virtual vehicle is then provided for further use in designing control law for the follower independent from the measurement of leaders velocity. Position tracking control is then constructed for the follower to track the virtual vehicle using the backstepping and Lyapunov direct design technique. Furthermore and to ensure the safety of robots while moving in a dynamic environment, obstacle avoidance scheme based on sensing the relative distance between follower robots and obstacles is introduced using fuzzy logic. Simulations are provided to show the effectiveness of the proposed approach.

Robust cooperative control for a group of mobile robots with quantized information exchange

Abstract In this paper we investigate the cooperative tracking control problem with quantized time delay information exchange for a group of wheeled mobile robots networked through a connected graph modeling the underlying communication topology. A cooperative controller is proposed using a combination of backstepping technique, graph theory and neural network radial basis functions. We show, using the small gain theorem, that the states of each mobile robot in the group converge to and remain inside a tube centered around its assigned trajectory to form a desired geometric pattern whose centroid is assumed to move along a predefined trajectory. Experimental results on a group of three mobile robots forming a triangular shape are presented to demonstrate the good performance of the proposed cooperative controller.

Three-dimensional distributed tracking control for multiple quadrotor helicopters

Abstract This paper deals with the cooperative tracking control of a team of underactuated quadrotors in three-dimensional space when the reference signal is not available to all the vehicles. Using the Backstepping and filtering design technique and results from graph theory, a distributed cooperative controller consisting of two interconnected blocks is proposed. The first block, which is based on local distributed controllers, guarantees that the centroid of the three-dimensional formation asymptotically follows a desired path corresponding to the desired formation trajectory. The second block ensures that the attitude dynamics of the quadrotor will converge asymptotically to their actual values, which are constrained within a predefined set, such that singularities are avoided in the quadrotor׳s dynamics. Due to the coupling property between the translational and rotational dynamics, the equilibrium point of the complete closed-loop system is shown to be asymptotically stable. Numerical simulations are illustrated to show that the theoretical conclusions are effective.

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.