Fethi Belkhouche

Reactive Path Planning in a Dynamic Environment

This paper deals with the problem of path planning in a dynamic environment, where the workspace is cluttered with unpredictably moving objects. The concept of the virtual plane is introduced and used to create reactive kinematic-based navigation laws. A virtual plane is an invertible transformation equivalent to the workspace, which is constructed by using a local observer. This results in important simplifications of the collision detection process. Based on the virtual plane, it is possible to determine the intervals of the linear velocity and the paths that lead to collisions with moving obstacles and then derive a dynamic window for the velocity and the orientation to navigate the robot safely. The speed of the robot and the orientation angle are controlled independently using simple collision cones and collision windows constructed from the virtual plane. The robots path is controlled using kinematic-based navigation laws that depend on navigation parameters. These parameters are tuned in real time to adjust the path of the robot. Simulation is used to illustrate collision detection and path planning.

Line of sight robot navigation toward a moving goal

In this paper, we consider the problem of robot tracking and navigation toward a moving goal. The goals maneuvers are not a priori known to the robot. Thus, off-line strategies are not effective. To model the robot and the goal, we use geometric rules combined with kinematics equations expressed in a polar representation. The intent of the strategy is to keep the robot between a reference point, called the observer, and the goal. We prove under certain assumptions that the robot navigating using this strategy reaches the moving goal successfully. In the presence of obstacles, the method is combined with an obstacle avoidance algorithm. The robot then moves in two modes, the navigation mode and the obstacle avoidance mode. Simulation of various scenarios highlights the efficiency of the method and provides an instructive comparison between the paths obtained for different reference points.

Modeling and controlling a robotic convoy using guidance laws strategies

This paper deals with the problem of modeling and controlling a robotic convoy. Guidance laws techniques are used to provide a mathematical formulation of the problem. The guidance laws used for this purpose are the velocity pursuit, the deviated pursuit, and the proportional navigation. The velocity pursuit equations model the robots path under various sensors based control laws. A systematic study of the tracking problem based on this technique is undertaken. These guidance laws are applied to derive decentralized control laws for the angular and linear velocities. For the angular velocity, the control law is directly derived from the guidance laws after considering the relative kinematics equations between successive robots. The second control law maintains the distance between successive robots constant by controlling the linear velocity. This control law is derived by considering the kinematics equations between successive robots under the considered guidance law. Properties of the method are discussed and proven. Simulation results confirm the validity of our approach, as well as the validity of the properties of the method.

Binary image encoding using 1D chaotic maps

Information security has become a major issue during the last decades where new algorithms based on algebraic methods or chaotic dynamics were suggested for encryption. This paper presents an algorithm for encoding binary images using one-dimensional chaotic maps. In order to perform pixel value permutation, the approach presented uses the diffusion property of chaotic maps, where local information is spread out. Comparison in terms of the correlation between the initial image and the transformed images is provided for different degrees of chaocity which corresponds to different values of positive Lyapunov exponent. Since images present a special kind of data where the size may be much larger than text data, an algorithm is suggested that emphasizes fast calculation in order to be implemented in real time for binary images encryption.

A method for robot navigation toward a moving goal with unknown maneuvers

This paper deals with a method for robot navigation towards a moving goal. The goal maneuvers are not a priori known to the robot. Our method is based on the use of the kinematics equations of the robot and the goal combined with geometrical rules. First a kinematics model for the tracking problem is derived and two strategies are suggested for robot navigation, namely the velocity pursuit guidance law and the deviated pursuit guidance law. It turns out that in both cases, the robots angular velocity is equal to the line of sight angle rate. Important properties of the navigation strategies are discussed and proven. In the presence of obstacles, two navigation modes are used: the tracking mode, which has a global aspect and the obstacle avoidance mode, which has a local aspect. In the obstacle avoidance mode, a polar diagram combining information about obstacles and directions corresponding to the pursuit is constructed. An extensive simulation study is carried out, where the efficiency of both strategies is illustrated for different scenarios.

Binary image transformation using two-dimensional chaotic maps

We present an algorithm for binary image transformation using chaotic maps. Because of its random-like behavior, chaos is a good candidate for encryption. We show that a two-dimensional discrete time dynamical system with one positive Lyapunov exponent allows the transformation of the image in an unpredictable manner. The suggested algorithm acts on the pixel position, where the diffusion property resulting from the sensitivity to the initial states is used to accomplish the transformation in a random-like way. The suggested algorithm uses three types of keys: initial state, external parameters and the number of iterations. Using the so-called Henon map as an example, we show that the algorithm produces almost uncorrelated images even when the keys are slightly changed, making it an attractive and fast method for image encryption.

Multi-robot hunting behavior

In this paper we consider the problem of hunting an unpredictably moving prey using a group of robots. We elaborate a mathematical model for the tracking-navigation problem based on geometric rules. This model consists of systems of two differential equations describing the relative motion of the prey with respect to the robots. The control laws are decentralized and the robots move in different modes, namely: navigation-tracking mode, obstacles avoidance mode, cooperative collision avoidance, and circle formation. In the tracking-navigation mode, we use the deviated pursuit strategy, which consists of a closed loop control law based on geometric rules. The properties of this strategy are explored briefly. For obstacles and cooperative collision avoidance, a collision cone approach is used. Our method is illustrated using simulation.

Chaotic gray-level image transformation

We deal with the applications of a class of nonlinear dynamic systems to image transformation and encoding whereby the nonlinear system presents a chaotic or hyperchaotic attractor. Several ways are possible to encode or transform the image using chaos. We develop algorithms for image encoding based on the permutation of the pixel value, position, or both. This approach enables the fast decorrelation of relations among pixels in the initial image in a random-like fashion. We illustrate the use of 1-D, 2-D, and 3-D maps for this purpose. We also use chaotic dynamical systems with a single or two outputs. A discussion of the sensitivity of the algorithms to the keys is followed by the illustration of the algorithms using example images.

Wheeled mobile robot navigation using proportional navigation

We present a method for wheeled mobile robot navigation based on the proportional navigation law. This method integrates the robots kinematics equations and geometric rules. According to the control strategy, the robots angular velocity is proportional to the rate of turn of the angle of the line of sight that joins the robot and the goal. We derive a relative kinematics system which models the navigation problem of the robot in polar coordinates. The kinematics model captures the robot path as a function of the control law parameters. It turns out that different paths are obtained for different control parameters. Since the control parameters are real, the number of possible paths is infinite. Results concerning the navigation using our control law are rigorously proven. An extensive simulation confirms our theoretical results.

Parallel navigation for reaching a moving goal by a mobile robot

In this paper, we present a method for robot navigation toward a moving object with unknown maneuvers. Our strategy is based on the integration of the robot and the target kinematics equations with geometric rules. The tracking problem is modeled in polar coordinates using a two-dimensional system of differential equations. The control law is then derived based on this model. Our approach consists of a rendezvous course, which means that the robot reaches the moving goal without following its path. In the presence of obstacles, two navigation modes are integrated, namely the tracking and the obstacle-avoidance modes. To confirm our theoretical results, the navigation strategy is illustrated using an extensive simulation for different scenarios.