Relative Localization Problem Research Articles

Asymptotically Efficient Estimator for Range-Based Robot Relative Localization

This study investigates the 2-D relative localization problem, which estimates the relative orientation and position between two moving robots using inter-robot range measurements. We propose a novel formulation and a robust weighted semidefinite relaxation solution for the relative localization problem in the presence of range measurement error and robot state transition error. Theoretical analysis and simulations show that the weighted semidefinite relaxation solution achieves Cramér–Rao lower bound performance when the measurement noise and the odometry uncertainty follow Gaussian distributions with moderate noise power. Demonstrations using data from a laboratory environment validate the promising and robust performance of the weighted semidefinite relaxation method. The root-mean-square errors in estimating the orientation and position are <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$3.97^\circ$</tex-math></inline-formula> and 0.22 m with affordable hardware.

A distributed relative localization approach for air-ground robot formations with onboard sensing

In a multi-robot system, diversity in the sensing and motion models of robotic entities can improve the overall performance. While such heterogeneous systems offer peculiar advantages in terms of robustness and resiliency, positioning and situational awareness of individual robots in these systems remain a challenge. In this paper, the problem of relative localization in a system composed of a drone and multiple unmanned ground vehicles which are desired to move in formation is addressed. By utilizing a leader–follower formation graph, a distance-based relative localization algorithm based on an extended Kalman filter is proposed for online estimation of the relative positions among the ground vehicles. The necessary conditions to satisfy the observability of the unmeasured states are provided. In the proposed framework, the robots exchange a limited amount of information only and do not rely on an external infrastructure, GPS, or magnetometer. Furthermore, an application of the proposed localization framework integrated to custom formation control schemes is proposed. The performance of the proposed approach is evaluated through a set of simulation and real life experiments, and its advantages and limitations are discussed by means of a comparative study.

3-D Inter-Robot Relative Localization via Semidefinite Optimization

In this letter, the 3-D inter-robot relative localization problem is addressed using noise-corrupted odometric and distance measurements. Unlike the existing solutions, we are devoted to providing a relative localization method that has an “overall best performance,” which means that the tradeoffs between the estimation accuracy (EA), the number of measurements (NoMs), and the computation efficiency (CE) are considered. We demonstrate that an existing formulation of the 3-D relative localization problem, the square distances weighted least square (SD-WLS), can be equivalently reformulated as a non-convex quadratic constrained quadratic programming (QCQP) problem. Further, to handle the non-convex nature of the QCQP problem, we adopt the semidefinite programming (SDP) relaxation approach, which drops the rank constraint and recovers the solution of the QCQP via an eigenvalue decomposition strategy. Finally, a refinement step is introduced to solve the problem that the quadratic constraints might not be satisfied due to the SDP relaxation. The simulation and experiment results show that, compared to existing methods, our method has the best overall performance when the three factors, i.e., EA, NoMs, and CE, are important for a relative localization application.

TOA-Based Relative Localization With Reflecting Signal Paths Assisted: Algorithm and Performance Analysis

This letter investigates a communication node relative localization problem based on time-of-arrival (TOA), where both the distances in direct signal paths and reflecting signal paths are measured. A wireless sensor network model of distance measurements and node locations is established, and a new two-step localization iterative algorithm is proposed. Simulation results illustrate the performance of the proposed algorithm, which is compared with Cramer–Rao lower bounds (CRLBs) and genetic algorithm (GA)-based algorithms.

Approaches, Challenges, and Applications for Deep Visual Odometry: Toward Complicated and Emerging Areas

Visual odometry (VO) is a prevalent way to deal with the relative localization problem, which is becoming increasingly mature and accurate, but it tends to be fragile under challenging environments. Comparing with classical geometry-based methods, deep learning-based methods can automatically learn effective and robust representations, such as depth, optical flow, feature, ego-motion, etc., from data without explicit computation. Nevertheless, there still lacks a thorough review of the recent advances of deep learning-based VO (Deep VO). Therefore, this paper aims to gain a deep insight on how deep learning can profit and optimize the VO systems. We first screen out a number of qualifications including accuracy, efficiency, scalability, dynamicity, practicability, and extensibility, and employ them as the criteria. Then, using the offered criteria as the uniform measurements, we detailedly evaluate and discuss how deep learning improves the performance of VO from the aspects of depth estimation, feature extraction and matching, pose estimation. We also summarize the complicated and emerging areas of Deep VO, such as mobile robots, medical robots, augmented reality and virtual reality, etc. Through the literature decomposition, analysis, and comparison, we finally put forward a number of open issues and raise some future research directions in this field.

Ultra-wideband based cooperative relative localization algorithm and experiments for multiple unmanned aerial vehicles in GPS denied environments

This article puts forward an indirect cooperative relative localization method to estimate the position of unmanned aerial vehicles (UAVs) relative to their neighbors based solely on distance and self-displacement measurements in GPS denied environments. Our method consists of two stages. Initially, assuming no knowledge about its own and neighbors’ states and limited by the environment or task constraints, each unmanned aerial vehicle (UAV) solves an active 2D relative localization problem to obtain an estimate of its initial position relative to a static hovering quadcopter (a.k.a. beacon), which is subsequently refined by the extended Kalman filter to account for the noise in distance and displacement measurements. Starting with the refined initial relative localization guess, the second stage generalizes the extended Kalman filter strategy to the case where all unmanned aerial vehicles (UAV) move simultaneously. In this stage, each unmanned aerial vehicle (UAV) carries out cooperative localization through the inter-unmanned aerial vehicle distance given by ultra-wideband and exchanging the self-displacements of neighboring unmanned aerial vehicles (UAV). Extensive simulations and flight experiments are presented to corroborate the effectiveness of our proposed relative localization initialization strategy and algorithm.

Observability Analysis of Relative Localization Filters Subjected to Platform Velocity Constraints

This research study performs an observability analysis of the relative localization problem related to multirobotic systems. The study considers different constraints related to the availability of relative position measurements and platform velocity measurements. Constraints related to these measurement sources arise due to several reasons such as, sensing limitations especially in aerial platforms, field of view limitations of sensors, and communication bandwidth limitations that may affect the available measurement rate. Although numerous observability studies are reported for localization of multirobot systems, most of these studies do not investigate the problem under constraints related to platform velocity sensing capabilities, and moreover, these do not investigate the global uniqueness of its results. This paper analyzes observability of the relative localization problem in detail for multiple practical scenarios having limited measurement sources and then extends the study with a global uniqueness analysis of the results. The paper establishes theoretical limitations and design recommendations relevant to relative localization frameworks, which are validated through numerical and experimental evaluations using a multirobot system equipped with relative positioning sensors.

An Observability Metric for Underwater Vehicle Localization Using Range Measurements

The paper addresses observability issues related to the general problem of single and multiple Autonomous Underwater Vehicle (AUV) localization using only range measurements. While an AUV is submerged, localization devices, such as Global Navigation Satellite Systems, are ineffective, due to the attenuation of electromagnetic waves. AUV localization based on dead reckoning techniques and the use of affordable motion sensor units is also not practical, due to divergence caused by sensor bias and drift. For these reasons, localization systems often build on trilateration algorithms that rely on the measurements of the ranges between an AUV and a set of fixed transponders using acoustic devices. Still, such solutions are often expensive, require cumbersome calibration procedures and only allow for AUV localization in an area that is defined by the geometrical arrangement of the transponders. A viable alternative for AUV localization that has recently come to the fore exploits the use of complementary information on the distance from the AUV to a single transponder, together with information provided by on-board resident motion sensors, such as, for example, depth, velocity and acceleration measurements. This concept can be extended to address the problem of relative localization between two AUVs equipped with acoustic sensors for inter-vehicle range measurements. Motivated by these developments, in this paper, we show that both the problems of absolute localization of a single vehicle and the relative localization of multiple vehicles can be treated using the same mathematical framework, and tailoring concepts of observability derived for nonlinear systems, we analyze how the performance in localization depends on the types of motion imparted to the AUVs. For this effect, we propose a well-defined observability metric and validate its usefulness, both in simulation and by carrying out experimental tests with a real marine vehicle during which the performance of an Extended Kalman Filter state observer is shown to depend on the types of motion imparted to the vehicle.

Relative localization for wireless sensor networks with linear topology

Sensors can be deployed along a road or a bridge to form a wireless sensor network with a linear topology where nodes have a spatial ordering. This spatial characteristic indicates relative locations for nodes and facilitates such functions as object tracking and monitoring in the network. We attempt to derive this ordering with RSSI (Received Signal Strength Indicator) as the only input, which does not require attaching extra hardware to the sensor nodes. This requires a method for translating RSSI into spatial constraints. There are two candidate methods in the literature. The first method uses connectivity information among the nodes to calculate their relative locations. But analysis of real-world trace data indicates that it does not work well in reality. The second method assumes that closer nodes receive higher RSSI. However, we have proved that the relative localization problem is actually NP-hard under such an assumption. Fortunately, the problem turns out to be efficiently solvable if we adopt a new observation slightly different from the above-mentioned closer-higher RSSI assumption. This observation that the closest node always receives the highest RSSI is verified by the analytical results of the same real-world trace data. We then propose a spatial ordering method based on the observation, and evaluate it through various field experiments. Results show that the proposed method achieves an accuracy of over 99%.

Odometry and Laser Scanner Fusion Based on a Discrete Extended Kalman Filter for Robotic Platooning Guidance

This paper describes a relative localization system used to achieve the navigation of a convoy of robotic units in indoor environments. This positioning system is carried out fusing two sensorial sources: (a) an odometric system and (b) a laser scanner together with artificial landmarks located on top of the units. The laser source allows one to compensate the cumulative error inherent to dead-reckoning; whereas the odometry source provides less pose uncertainty in short trajectories. A discrete Extended Kalman Filter, customized for this application, is used in order to accomplish this aim under real time constraints. Different experimental results with a convoy of Pioneer P3-DX units tracking non-linear trajectories are shown. The paper shows that a simple setup based on low cost laser range systems and robot built-in odometry sensors is able to give a high degree of robustness and accuracy to the relative localization problem of convoy units for indoor applications.