Graph Optimization Approach to Range-Based Localization

Abstract

In this paper, we propose a general graph optimization based framework for localization, which can accommodate different types of measurements with varying measurement time intervals. Special emphasis will be on range-based localization. Range and trajectory smoothness constraints are constructed in a position graph, then the robot trajectory over a sliding window is estimated by a graph based optimization algorithm. Moreover, convergence analysis of the algorithm is provided, and the effects of the number of iterations and window size in the optimization on the localization accuracy are analyzed. Extensive experiments on quadcopter under a variety of scenarios verify the effectiveness of the proposed algorithm and demonstrate a much higher localization accuracy than the existing range-based localization methods, especially in the altitude direction.Index Terms-Graph optimization approach, Range-based localization, 2-D and 3-D spaces, Ultra-wide band radio.

Robot Localization in Water Pipes Using Acoustic Signals and Pose Graph Optimization

“…Pose-graph optimization has been applied to localization of robots in pipes using vision [ 7 ], a fusion of IMU and tether cable information [ 17 ], and periodic radio wave amplitude [ 41 ]. Recent work in the use of acoustic echoes for localization in pipes [ 42 ] could be applied to pose-graph optimization; these acoustic measurements are range-only measurements of features, which have been used in pose-graph optimization in other applications [ 43 , 44 ]. As applied in many of these methods, the use of an approach based on the Levenberg–Marquardt method, such as general graph optimization [ 45 ], may be sufficient to find an optimal trajectory estimate given the dynamic information presented in this paper.…”

Critical Design and Control Issues of Indoor Autonomous Mobile Robots: A Review

“…Apart from these three techniques, another method named Pose Graph Optimization (PGO) has been popular in the last decade [112]. This method is mainly used for localization in graph-based slam techniques [113]. While a robot moves through the environment, its trajectory can be defined as a collection of its poses over time and these poses are joined together with edges creating some sort of graph.…”

3-D Multi-player Pursuit-evasion Game with a Faster Evader

“…where λ i = Vi Ve and λ j = Vj Ve are speed ratios. If the condition (21) holds at time instant t 0 , we have αi,j (t) < 0, t ≥ t 0 . The proof follows from that of Theorem 4.1 in the work [11].…”

“…The evader is said to be captured by a pursuer with non-zero capture radius d c > 0 if the distance between the evader and the pursuer is less than d c . [20][21][22]. The moving directions of the evader and pursuers are unknown to each other.…”

“…The initial positions of two pursuers are set as p i = (8, 5, 5) and p j = (10, −10, 0), and the initial position of the faster evader is set as p e = (0, 0, 0). Since this initial spatial distribution satisfies the sufficient capture condition (21), the evader will be finally captured by the pursuers. In the tenpursuer one-faster-evader game shown in Fig.…”