Multirobot Active Target Tracking With Combinations of Relative Observations

Abstract

Abstract-In this paper, we study the problem of optimal trajectory generation for a team of mobile robots tracking a moving target using distance and bearing measurements. Contrary to previous approaches, we explicitly consider limits on the robots' speed and impose constraints on the minimum distance at which the robots are allowed to approach the target. We first address the case of a single sensor and show that although this problem is non-convex with non-convex constraints, in general, its optimal solution can be determined analytically. Moreover, we extend this approach to the case of multiple sensors and propose an iterative algorithm, Gauss-Seidel-relaxation (GSR), for determining the set of feasible locations that each sensor should move to in order to minimize the uncertainty about the position of the target. Extensive simulation results are presented demonstrating that the performance of the GSR algorithm, whose computational complexity is linear in the number of sensors, is indistinguishable of that of a grid-based exhaustive search, with cost exponential in the number of sensors, and significantly better than that of a random, towards the target, motion strategy.

Selected Open Problems in Discrete Geometry and Optimization

“…For instance, in location-aware networks-which support a host of services such as emergency response [14], mobile advertising [18], and target tracking [23]-wireless nodes that are deployed in an area of interest must be able to localize themselves using distance measurements obtained from direct communications with their neighbors. Another example can be found in biochemistry, where the positions of atoms in a molecule-which provide important information about the properties and functions of the molecule-are typically determined from a set of geometric constraints that include a subset of the interatomic distances [6].…”

Target Tracking with Limited Sensing Range in Autonomous Mobile Sensor Networks

“…In addition, the authors also account for the velocity constraints on mobile sensors. Different from precious work [8], the authors [9] impose constraints on the minimum distance at which the mobile sensors are allowed to be close to the target. Besides, the authors adopt measurements extend to a mixture of relative observations, including distance-only, bearing-only, and distance-and-bearing measurements.…”

Formation control driven by cooperative object tracking

“…Recent formation control methods go beyond simply stating the desired geometry for the formation by providing some meta-specifications (e.g., for velocity matching, connectivity maintenance and containment control among the formation members [6,7]) but often give little or no relevance to the requirements imposed by target localization and/or tracking to the formation geometry, so as to improve the target detection and tracking quality (e.g., accuracy). Active cooperative perception methods in sensor and robot networks [8] concern precisely this problem: how to actively move mobile sensors so as to improve the accuracy of target detection by the network, as the result of (spatially and temporally) fusing the information from all the static and mobile sensors which observe the target during a step sequence. In this paper we propose an integrated solution of the ''target localization and tracking by a vehicle formation'' problem, supported on the following novel contributions:…”

“…Recent approaches for active cooperative target tracking by a robot team formation such as [8] rely on computationally heavy optimization processes. By introducing the Gauss-Seidel relaxation in an iterative algorithm to detect the next best sensing location for the mobile sensors, the authors in [8] achieve a linearly growing computational complexity over methods like grid-based exhaustive search which have similar tracking accuracy but where the complexity grows exponentially with the number of sensors.…”

“…By introducing the Gauss-Seidel relaxation in an iterative algorithm to detect the next best sensing location for the mobile sensors, the authors in [8] achieve a linearly growing computational complexity over methods like grid-based exhaustive search which have similar tracking accuracy but where the complexity grows exponentially with the number of sensors. The novelty in our approach of integrating the controller and estimator modules to achieve a formation that minimizes the joint uncertainty covariance of the tracked target lies in the fact that the controller module of each robot performs an optimization over an already fused target posterior which makes the computational complexity of the optimization process constant with respect to the number of mobile sensors in the team.…”