# Cooperative autonomous robots

Robot navigation-tracking towards an unpredictably moving object, obstacle avoidance, and cooperation between robots are some of the major research topics in robotics. Most methods suggested for navigation-tracking are either behavior-based or feature-based. Either modeling method makes it difficult to prove rigorously the validity of these approaches. To effectively address these difficulties, we introduce online model-based methods capable of solving the problem in real-time. We derive a mathematical model based on the integration of the relative kinematics equations and geometric rules. The resulting model consists of a system of nonlinear differential equations describing the motion of the moving goal in polar coordinates as seen by the robot. The control laws are derived based on the kinematics of the motion. Different techniques are used to solve the problem, namely, the pursuit, proportional navigation, parallel navigation, and line of sight techniques. In the line of sight control law, we define the notion of an observer, which supervises and controls the motion of the robot. For each control law, rigorous mathematical analysis is carried out. In the presence of obstacles, these control laws are integrated with classical obstacle avoidance methods, such as cell decomposition and polar histogram. Modeling and controlling a robot convoy is also considered. The robotic convoy is modeled using pairs of nonlinear differential equations, which capture the motion of the lead robot with respect to its following robot. Two control laws are derived for each following robot. It is proven that under our control laws, each following robot imitates the motion of its lead robot. The equations for the parallel navigation are used for collision course detection between robots. Cooperative real-time control laws for collision avoidance are then derived based on the collision course equations