Autocalibration of a Mobile UWB Localization System for Ad-Hoc Multi-Robot Deployments in GNSS-Denied Environments
Carmen Martínez Almansa, Wang Shule, Jorge Peña Queralta, Tomi Westerlund
AAutocalibration of a Mobile UWB LocalizationSystem for Ad-Hoc Multi-Robot Deployments inGNSS-Denied Environments
Carmen Mart´ınez Almansa , Wang Shule ,Jorge Pe˜na Queralta , and Tomi Westerlund Turku Intelligent Embedded and Robotic SystemsUniversity of Turku, Finland { camart, shwang, jopequ, tovewe } @utu.fihttps://tiers.utu.fi Abstract.
Ultra-wideband (UWB) wireless technology has seen an in-creased penetration in the robotics field as a robust localization methodin recent years. UWB enables high accuracy distance estimation fromtime-of-flight measurements of wireless signals, even in non-line-of-sightmeasurements. UWB-based localization systems have been utilized invarious types of GNSS-denied environments for ground or aerial au-tonomous robots. However, most of the existing solutions rely on a fixedand well-calibrated set of UWB nodes, or anchors, to estimate accuratelythe position of other mobile nodes, or tags, through multilateration. Thislimits the applicability of such systems for dynamic and ad-hoc deploy-ments, such as post-disaster scenarios where the UWB anchors could bemounted on mobile robots to aid the navigation of UAVs or other robots.We introduce a collaborative algorithm for online autocalibration of an-chor positions, enabling not only ad-hoc deployments but also movableanchors, based on Decawave’s DWM1001 UWB module. Compared tothe built-in autocalibration process from Decawave, we drastically re-duce the amount of calibration time and increase the accuracy at thesame time. We provide both experimental measurements and simulationresults to demonstrate the usability of this algorithm.
Keywords:
Ultra-wideband · Localization · UWB · UWB Localization · Robotics · GNSS-Denied Environments · Multi-Robot Systems
The utilization of UWB radios for both localization and short-range data trans-mission started to gain momentum after the unlicensed usage legalization in2002 [1], and the IEEE standards released in 2007 [2]. Nonetheless, only in re-cent years UWB-based localization systems have seen wider adoption in therobotics domain, owing to their high accuracy, and often as a replacement toGNSS sensors in GNSS-denied environments [3]. UWB-based systems are now a r X i v : . [ c s . R O ] A p r Carmen Mart´ınez Almansa et al.
Anchor 0Anchor 1Anchor 2Anchor 3Anchor 4TagAutocalib.Tag Local.
Fig. 1: UWB localization and autocalibration concept. The circles are definedby the UWB-measured range between each of the anchors and the tag.The dotted lines represent the inter-anchor measurements taken duringthe autocalibration process. The number of tags and anchors is arbitrary,and only one tag is shown here for illustrative purposes.being utilized for communication and localization [4], or as short-range radarsystems for mapping or navigation, among other applications [5].UWB-based localization systems provide an inexpensive alternative to high-accuracy motion capture systems for navigation in application scenarios wherea localization accuracy of the order of tens of centimeters is sufficient [6]. InGNSS-denied environments, UWB-based localization systems can provide a ro-bust alternative to visual odometry methods [7], or other methods that relyonly on information acquired onboard mobile agents, such as lidar odometry [8],which present challenges in long-term autonomy. Therefore, UWB-based local-ization systems enable longer operations and tighter control over the behaviorof mobile robots. Moreover, accurate relative localization in multi-robot systemscan aid information control algorithms, such as those where only relative po-sition estimation is needed [9–11], or collaborative tasks requiring multi-sourcesensor fusion [12], such as cooperative mapping [13] or docking of unmannedaerial vehicles (UAVs) on mobile platforms [4].One of the main limitations of UWB-based localization systems, which theyshare with many other wireless localization systems based on active beacons, isthat they require a predefined set of beacons to be located in known positionsin the operational environment [14]. In UWB systems, these fixed radio nodesare often called anchors, while mobile nodes are called tags. Fixed anchors arerequired because only ranging information can be extracted from UWB signals.From a set of at least three anchor-tag distance measurements, the position utocalibration of a Mobile UWB Localization System 3 of a tag can be calculated from the anchors’ positions utilizing multilaterationmethods [15].Current systems, which mainly rely on a fixed set of anchors as a reference,require accurate calibration of the anchor positions, this significantly limitingtheir applicability. Motivated by this, we have developed an automatic calibra-tion method that allows these anchors to be mobile and hence to be used indynamic localization systems. The typical procedure to estimate the position ofa mobile tag based on the position of fixed anchors is depicted in Fig. 1, wherethe radius of each circle is defined by the distance to the tag estimated throughUWB ranging. The tag can locate itself by estimating the individual distancesto each of the anchors (solid line), while inter-anchor distances (dotted lines)can be utilized by the anchors themselves to calibrate their positions.In summary, our main objective is the design and development of a mobileUWB-based localization system that can be utilized for localization in multi-robot systems in GNSS-denied environments. This paper presents initial resultsin this direction. The DWM1001 UWB transceiver from Decawave has beenutilized and we have developed an autocalibration as part of wider UWB ex-periments reported in [15]. The code is made publicly available in our GitHubrepository , where we have released an initial version of the autocalibrationfirmware for Decawave’s DWM1001 development board. We utilize UWB ac-curacy measurements from our experiments to simulate the performance of amobile UWB-based localization system. This paper, therefore, focuses on theresults of those simulations to assess the viability and usability of the proposedsystem.The remainder of this paper is organized as follows. In Section 2, we re-view related works regarding the autocalibration of UWB localization systemsand provide a broad overview of their potential applications. Section 3 then in-troduces the details about the UWB calibration and localization process, withinitial results reported in Section 4. Finally, Section 5 concludes the work andoutlines future research directions. In this section, we first review existing autocalibration methods for UWB-basedlocalization systems. Then, we analyze in more detail the autocalibration methodincluded in the Decawave’s firmware, as well as its requirements and drawbacks.An early approach to automatic calibration of UWB radios in mobile robotslocalization systems was proposed by K. C. Cheok et al. [16]. The algorithm pro-posed by the authors is capable of determining the coordinates of four anchorsfrom UWB measurements estimating the distance between each pair of anchors.The algorithm relies on the following assumptions to calculate the anchor posi-tions: there must exist a known order of the four anchors such as anchor 0 definesthe origin of coordinates; anchor 0 and 1 define the positive x-axis direction; andthe plane x-y is defined by the first three anchors. TIERS UWB Dataset: https://github.com/tiers/uwb drone dataset Carmen Mart´ınez Almansa et al.
Another autocalibration UWB-based multi-robot localization system pre-sented by M. Hamer et al. is stricter in terms of assumptions [17]. In additionto the aforementioned conditions, in this second system it is also assumed thatanchor 2 lies on the positive y-direction, anchor 3 on the positive z-axis and allanchors are at fixed positions. Moreover, the system relies on clock synchroniza-tion, since the localization is based on time difference of arrival (TDoA).Several other works have presented on-board localization systems based onUWB technology for either one target [18, 19], or multiple targets [20]. In thesepapers, the anchors are situated on a mobile platform. The relative position ofthe tag, which is mounted on the target robot or person, is estimated from thedistances between itself and the anchors.Regarding Decawave’s UWB modules, a built-in calibration system is avail-able through their mobile application as part of Decawave’s real-time localizationsystem (DRTLS). This process. called auto-positioning, can be utilized with aminimum a priori knowledge of the anchor positions: it requires the anchors (upto four) to be arranged in a rectangular shape, at an equal or similar height, andin counter-clockwise order. In addition to this, we have found the calculationtime of this algorithm to be around 40 s and the error above 1 m in deploymentswhere the inter-anchor distance was less than 20 m. These characteristics makethe algorithm overly slow and inaccurate to be suitable for mobile settings. Thelack of accuracy is warned in the app itself, where it is recommended to measureand introduce the anchor positions manually since the autocalibration featuremakes the positioning less precise. Decawave devices are some of the most widelyused UWB ranging modules [21], and thus there is an evident need for faster andmore accurate autocalibration methods to enable faster ad-hoc and even mobiledeployments.
In this section, we first describe how distance can be estimated from the time offlight of a UWB signal, and then introduce our proposed autocalibration methodfor the anchors.
The two main methods for UWB ranging measurements, also applicable to otherwireless ranging technologies, are time of flight (ToF) and time difference ofarrival (TDoA).ToF is a method for estimating the distance between an emitter and a re-ceiver node multiplying the time of flight of the signal between a single pair oftransceivers, usually an anchor and a tag, by the speed of light in air [22]. It’s atwo-way ranging (TWR) technology, requiring transmissions in both directions.In single-side TWR (SS-TWR), a transmitter, or initiator, sends a poll messagewhich then receiving node replies to. By measuring the total time until it obtainsa response, the initiator can then estimate the distance that separates it from utocalibration of a Mobile UWB Localization System 5
Fig. 2: Decawave’s DWM1001 Development Board, which has been utilized inthe experimentsthe node that replied to the message. In this situation, the antenna delays andthe fixed time required to process the poll message and send the response atthe receiving node must be known and taken into account when estimating thedistance. Double-side TWR (DS-TWR) eliminates the need for calibration byadding an additional response, or final message.TDoA is another widely-used method for locating a mobile node by detect-ing the time difference of arrival (TDoA) of the same wireless signal received atmultiple interconnected anchors [23]. In this algorithm, the anchors need to besynchronized, and the hyperbolic branch is drawn for each anchor pair from thedifference between the reception time of the main anchor and other anchors [22].The point where all the hyperbolic intersections occur is taken as the approxi-mate location of the tag. TDoA ranging is also called hyperbolic ranging.
The aim of our work is to develop a UWB-based localization system with built-inautocalibration, which could be used for the localization of multi-robot systemsin dynamic scenarios. Our customized autocalibration method relies on a seriesof assumptions for the first measurement, in order to localize the system inthe space. These initial assumptions are similar to those in the related worksdescribed in the previous section: – The first anchor (Anchor 0) is situated at the origin of coordinates. – The direction from Anchor 0 to Anchor 1 defines the positive x-axis. – All other anchors lie in the half-plane with positive y-coordinate.Based on these assumptions, the initial calibration step estimates the positionof each of the anchors based on the measured distances to the first two anchorsdefining the origin of coordinates and the positive x-axis direction. Then, the po-sition of all anchors is adjusted by minimizing the error between the inter-anchordistances and the UWB ranging measurements with a least squares estimator(LSE). After the initial calibration step, the only assumption we make is that theposition anchor 0 defines the origin. The reason behind this relaxed conditions
Carmen Mart´ınez Almansa et al. regarding the x and y axis is that our experiments have shown that the rota-tional error is negligible. This implies more flexible conditions than in previousworks [17] and [16].In our autocalibration process, every anchor behaves as initiator and respon-der in turns. The anchor that defines the origin is the first initiator. The processis initiated by a start command sent to the corresponding anchor through theUART interface. This first initiator, henceforth referred to as Anchor 0, calcu-lates the distances to each of the other anchors. The distances are estimatedbased on the time of flight (TOF) using SS-TWR. The communication is donein pairs, only after receiving the distance measurement from one responder andbroadcasting it, the initiator will start communication with the following one.Once the initiator has gathered the distance values to every other anchor,it will send a message to the following one, according to the counter-clockwiseorder established, and will change its mode to responder. The recipient of themessage will become initiator and start the cycle again. When the last anchor inthe network finishes its measurements, it will send the message to the Anchor 0,which will become initiator again, and await the next start trigger. Calibrationsshould occur periodically whenever the inter-calibration positioning error at theanchors exceeds a certain error threshold. The inter-calibration positioning canbe done with other on-board methods, such as visual or lidar odometry.Table 1: Latency of the Autopositioning method from Decawave’s DRTLS com-pared to our self-calibration method for anchors.
LatencyRTLS Autopositioning s ± s Custom Calibration (x50) . s ± . s Custom Calibration (x5) . s ± . s Table 2: Accuracy of the Autopositioning method from Decawave’s DRTLS com-pared to our self-calibration method for anchors.
Covered RTLS Autopositioning Our AutocalibrationArea
Min. Err. Max. Err. Min. Err. Max. Err.1 m m m
163 cm 219 cm 135 cm 182 cm
This autocalibration process has been implemented in C and the firmware forDecawave’s DWM1001 Development board, illustrated in Fig. 2, has been madepublicly available in Github. Table 2 shows the difference in calibration accuracy utocalibration of a Mobile UWB Localization System 7 between our firmware and Decawave’s DRTLS autopositioning system, the latterbeing a process that is triggered through the DRLTS mobile application. In ourimplementation, every time the autocalibration occurs, multiple measurementsare taken and the average and standard deviation are shared with all otheranchors to estimate each other’s positions. In Table 1, we show the latency whenwe take 5 or 50 measurements for each pair of anchors. M e a s u r e d D i s t a n ce ( m ) Linear fitRaw data0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.00.40.60.81.01.21.41.61.82.0 Real Distance (m) M e a s . D i s t a n ce ( m ) Linear fitRaw data
Fig. 3: Experimental measurements and fitted line utilized for the simulations.The offset created by the responser delay has been already adjusted inthe raw data measurements.
In order to test the accuracy and usability of the autocalibration algorithm, wereport two different types of results. First, we have measured the accuracy ofUWB ranging with the DWM1001 transceiver, and the maximum error in whichour autocalibration firmware incurs has been shown in Table 2. Second, we haveutilized this data to study the localization accuracy in a simulation of a mobiledeployment with multiple anchors and tags.Regarding the measurements with the DWM1001 development board, wetested our autocalibration firmware to measure its latency and accuracy. The
Carmen Mart´ınez Almansa et al. A n c h o r P o s i t i o n E rr o r A1A2A3 (a) Error in the estimated position of anchors. The UWB calibration happens everyten simulation steps. T ag P o s i t i o n E rr o r Tag1Tag2Tag3 (b) Error in the estimated position of the tag during the simulation. The position ofthe tag is always calculated from the anchor positions based on UWB ranging. X - A x i s P o s i t i o n ( m ) Tag1 Tag2Tag3 A0A1 A2A3 (c) Paths followed by the anchors and tags over the simulation. The paths haveindividual random components.
Fig. 4: Simulation results for a system with four anchors and three tags. Thefigures show the error and paths over time of the anchors and tags. Theposition estimation of the anchors between calibrations are defined witha random error at each simulation step. utocalibration of a Mobile UWB Localization System 9 deployed network consisted of four anchors, one of which was placed in line ofsight at different distances, ranging from 0.5 m to 22 m. The distances measuredby the UWB modules during this experiment are depicted in Fig. 3. The resultsyielded from this experiment served to characterize the modules’ error.In the simulation, we have also utilized 4 anchors. A minimum of three an-chors is needed, but four anchors increase the system robustness in case one ofthe ranging measurements fail or the error is significant [15]. In addition, threetags were situated within the figure formed by the anchors to be localized. Themovement of the anchors and the tags was generated following a constant di-rection with added random Gaussian noise. In every step, a random value inthe interval ( − . m, +0 . m ) was added to each anchor’s position, representingthe error of the on-board position estimation utilized between calibrations. Thisrange of values was chosen in order to have a significant error accumulated be-tween calibrations and test the ability of the autocalibration process to bring theerror down. The anchors’ calibration was performed every ten steps in the sim-ulation. Both the calibration of the anchor positions and the positioning of thetags are done utilizing a least squares estimator, except for the initial positioningstep before the movement starts.The results of our simulation are shown in Fig. 4. Subfigures 4a and 4bshow the error in anchors and tags positioning over 55 steps, respectively. It canbe observed how calibration, performed every 10 steps, reduces significantly theanchors’ positional error. The number of steps shown in this figure is reduced forvisualization purposes. We have carried out multiple simulations with hundredsof steps and observed the same behavior.Finally, Fig. 5 shows the distribution of translation and rotation errors. Thetranslation error was calculated for both anchors and tags and is illustratedin subfigure 5a. The rotation error in subfigure 5b shows the error in the anglecalculated between the x-axis and the line crossing the origin and Anchor 1. Notethat Anchor 1 does not necessarily lie in the x-axis after the movement starts.In cases where the distance between these two anchors is enough this error issmall. Therefore, the assumption that Anchor 1 defines the x-axis is only neededbefore the movement of the anchors starts. Motivated by the limitation on the applicability of UWB-based localization sys-tems on dynamic scenarios, we have presented a mobile UWB-localization systemwith built-in autocalibration that can be deployed within a multi-robot system.The UWB anchors can be placed on mobile ground vehicles to support, for in-stance, the operation of UAVs and other robots in GNSS-denied environments.The key advantage of the proposed system is the periodic built-in self autocali-bration of anchor positions. This allows for the localization error to stay withina certain tolerance even if the anchors are moving.In future work, we will experiment with real multi-robot systems and providea more exhaustive analysis of the usability of the proposed system in complex . . . . E rr o r ( m ) (a) Translation Error X Axis-0.020-0.0100.0000.010 E rr o r ( r a d ) (b) Rotation Error Fig. 5: Translation and rotation error distribution for the anchors and tags. Therotation error refers only to the X-axis, defined as the direction betweenthe origin anchor and the first one in the counter-clockwise direction.scenarios. We will also extend the calibration and localization approaches mod-elling the robots’ dynamics and their odometry algorithms.
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