This paper deals with the problem of modeling, initialization, and control of mobile robots formation. We suggest to use a new family of methods that consists of a combination between classical guidance laws and kinematics rules. These methods allow modeling and controlling a dynamic robotic formation using sets of differential equations that give the relative motion between the robots. These differential equations give the range rate and the visibility angle between leaders and followers. Graph theory is used to store the relationship leader-follower and plan the formation by using three different matrices. The configuration of the formation is based on these matrices. Initialization of formation is also considered, where different approaches are suggested. Because of the nature of the kinematics laws, it is easy to model, initialize, and keep any formation shape. Simulation is provided to illustrate the method.

This paper suggests a method for autonomous wheeled mobile robots navigation under the nonholonomic constraint. The suggested method uses navigation functions that are based on the polar kinematics equations, where the steering angle and the orientation angle of the robot are included in an exponential function of the line of sight angle. Another control law is suggested for the robot's linear velocity to drive the robot to a desired position with a desired final orientation angle. The exponential navigation functions depend on various navigation parameters that allow to change the robot's path. This approach is combined with the collision cone technique to avoid collision. A Q-learning algorithm is suggested to select automatically the appropriate values of the navigation parameters. Simulation is used to illustrate the method.

In this paper, we introduce a new family of navigation laws which are based on analytic navigation functions derived using the kinematics equations. These navigation laws combine local and global aspects, and can be used for both indoor and outdoor navigation. The robot's kinematics model is represented in polar coordinates. The analytic navigation functions suggested here are functions of the line-of-sight angle between the robot and the goal, and depend on one or more navigation parameters. The navigation parameters allow us to control the navigation law and, thus, the path of the robot. The choice of the navigation function and its parameters is important, and must satisfy some conditions. Different paths are obtained for different navigation functions and different parameters. This property is used to avoid collision with obstacles. Under this formulation, the number of navigation functions allowing the robot to reach a given goal is infinite. An extensive simulation study shows the effectiveness of the method.

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