Target Tracking for Mobile Sensor Networks Using Distributed Motion Planning and Distributed Filtering

Abstract

The problem treated in this research work is as follows: there are N mobile robots (unmanned ground vehicles) which pursue a moving target. The vehicles emanate from random positions in their motion plane. Each vehicle can be equipped with various sensors, such as odometric sensors, cameras and non-imaging sensors such as sonar, radar and thermal signature sensors. These vehicles can be considered as mobile sensors while the ensemble of the autonomous vehicles constitutes a mobile sensor network (Rigatos, 2010a),(Olfati-Saber, 2005),(Olfati-Saber, 2007),(Elston & Frew, 2007). At each time instant each vehicle can obtain ameasurement of the target’s cartesian coordinates and orientation. Additionally, each autonomous vehicle is aware of the target’s distance from a reference surface measured in a cartesian coordinates system. Finally, each vehicle can be aware of the positions of the rest N − 1 vehicles. The objective is to make the unmanned vehicles converge in a synchronized manner towards the target, while avoiding collisions between them and avoiding collisions with obstacles in the motion plane. To solve the overall problem, the following steps are necessary: (i) to perform distributed filtering, so as to obtain an estimate of the target’s state vector. This estimate provides the desirable state vector to be tracked by each one of the unmanned vehicles, (ii) to design a suitable control law for the unmanned vehicles that will enable not only convergence of the vehicles to the goal position but will also maintain the cohesion of the vehicles ensemble. Regarding the implementation of the control law that will allow the mobile robots to converge to the target in a coordinated manner, this can be based on the calculation of a cost (energy) function consisting of the following elements : (i) the cost due to the distance of the i-th mobile robot from the target’s coordinates, (ii) the cost due to the interaction with the other N − 1 vehicles, (iii) the cost due to proximity to obstacles or inaccessible areas in the motion plane. The gradient of the aggregate cost function defines the path each vehicle should follow to reach the target and at the same time assures the synchronized approaching of the vehicles to the target. In this way, the update of the position of each vehicle will be finally described by a gradient algorithm which contains an interaction term with the gradient algorithms that defines the motion of the rest N − 1 mobile robots. A suitable tool for proving analytically the convergence of the vehicles’ swarm to the goal state is Lyapunov stability theory and particularly LaSalle’s theorem (Rigatos, 2008a),(Rigatos, 2008b). Regarding the implementation of distributed filtering, the Extended Information Filter and the Unscented Information Filter are suitable approaches. In the Extended Information 13