Detecting a Target Location Using a Mobile Robot With Range Only Measurement Gaurav Chaudhary Systems and Control Engineering Indian Institute of Technology, Bombay Mumbai, India Email: gauravch@sc.iitb.ac.in Arpita Sinha Systems and Control Engineering Indian Institute of Technology, Bombay Mumbai, India Email: asinha@sc.iitb.ac.in Abstract—This paper addresses the problem of guiding a mobile robot to a point of interest or the target point using only range sensors. The bearing information is not available. The target point can be the source of some gas leakage or nuclear radiation or it can be some landmark or beacon. A control strategy is proposed that can bring the robot arbitrarily closed to the target point. It is shown analytically that this strategy works for any initial condition of the robot with respect to the target point. Simulations are carried out to validate the results obtained in this paper. I. INTRODUCTION Strategy for autonomous robots to capture a stationary or a moving target using range only measurement has attracted special attention in field of robotics (see e.g. [1], [2], [3] and references therein). The objective of the paper is to find a strategy to capture a target with range only measurement. We can use this strategy in applications such as finding the point of leakage of some gas by only knowing the intensity of gas at the robot position or in pursuit evasion problem using only distance information between the pursuer and the evader. Several target tracking approaches are proposed in the litera- ture that uses only the range information to capture a stationary or moving target. In [1], a sliding mode control strategy is proposed using which the robot follows the target with constant speed while maintaining the predefine range margin from the target. In [2], guidance algorithms for following both steady and moving targets are proposed and the guidance methods have the property that the robot follows a trajectory that is close to a certain curve called equiangular spiral. A switched logic- based control strategy to solve the pursuit problem for target tracking is shown in [3]. This problem is solved in discrete time in [4] where the target position is estimated at each instance of time and the robot moves towards the estimated target position in discrete steps. In [5], local observability requirements are developed for target tracking and are verified by evaluating the performance of a state estimator. Problem of target motion analysis from range and range−rate measure- ments is investigated in [6]. Range only Extended Kalman Filter (EKF) is utilized to track the trajectory of the moving target in [7] and several different estimation based techniques are discussed in ( [8]–[12]) for tracking of target using range only measurement. For a team of mobile robots tracking a moving target using distance-only measurements, Zhou et al. ( [13], [14]) have proposed algorithms for determining the set of feasible locations that each robot should move to in order to collect the most informative measurements, that is, the distance measurements that minimize the uncertainty about the position of the target. A strategy for searching the source of gas using mobile robot is discussed in [15]. When the presence of gas is detected, the robot turns in the direction of the airflow that carries the gas and looks for any suspicious object. In [16], the robot is driven by the concentration gradient generated by a gas leak. In this paper, we propose a generalized guidance strategy for detecting a stationary target using only range and range- rate information. The problem in continuous time is addressed. A single robot is used for the detection. The strategy does not involve any estimation of states. The robot can reach arbitrarily close to the target from any initial position. This paper is organized as follows: The problem is define in Section II. In Section III, the mathematical analysis for locating the target is discussed. Simulation results for different cases are presented in Section IV. Section V concludes the paper. II. PROBLEM STATEMENT Consider a mobile robot that can measure the distance and the rate of change of distance from a given point. The problem is to guide the robot to that point. We consider an unicycle model for the robot, the kinematics of which is given by ˙ x r = v 1 cos(α) (1) ˙ y r = v 1 sin(α) (2) ˙ α = u (3) where (x r ,y r ) is the instantaneous position of the robot, v 1 is the linear velocity of the robot and u is the control input to the robot. Thus, the angular velocity of the robot is controlled while the linear velocity is constant. We are considering a stationary target point that the robot has to locate. Let the target point be at (x t ,y t ) with respect to some reference frame and while the robot is at (x r (t),y r (t)) at time t. This is shown in Figure 1. Let the distance between the robot and the target, that is, the line-of-sight (LOS) distance be R and the LOS angle be θ. The robot can measure R and ˙ R, but not θ. Thus, u is some function of R and ˙ R. We determine the conditions that this function needs to satisfy so that it can 28 978-1-4577-2119-9/12/$26.00 c 2011 IEEE