Preliminary results on robust global localization: fault tolerance and robustness test on probabilis

Luca Carlone and Basilio Bona Member, IEEE

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PRELIMINARY RESULTS ON ROBUST GLOBAL LOCALIZATION: FAULT TOLERANCE AND ROBUSTNESS TEST ON PROBABILISTIC SHAPING ABSTRACT Interactive human-in-the-loop tasks in service or domestic robotics raise concerns about safety and dependability of localization systems. As physical redundancy is no longer suitable for low-cost-low-power applications, decisional mechanisms are required in order to assure reliable localization. We investigate the case of beacon-based positioning with particular emphasis on fault tolerance and robustness to environmental perturbations. We provide a model for range-only localization, called Probabilistic Shaping, that includes uncertainty on beacons’ position, noise on measurements and information from navigation sensors. Our approach is based on a closed-form probability distribution, called Radial Gaussian. We prove the robustness and the fault tolerance of our localization model in a simulation scenario, analyzing the response of the system in terms of accuracy and resilience. All relevant information on simulations are given in order to provide a virtual benchmark for dependable localization.

I. INTRODUCTION POSITION estimation is a crucial task for autonomous mobile systems. In service and domestic robotics, in particular, the knowledge of robot’s position is necessary to accomplish complex tasks in uncertain human-in-the-loop scenarios. The strong interaction with humans raises concerns about safety and dependability, requiring a deep insight of fault hypothesis and predicted response of localization system to adverse situations. We investigate the case of beacon-based localization in indoor environment. Many GPS-less localization problems are solved within an infrastructure of low-cost radio beacons inferring range information from received signal strength [1]-[2].

A widespread approach is to associate geometric lateration with Kalman Filter or model data through other probabilistic methods (Particle Filters, Grid localization etc.). Different algorithms, usually called non-linear sliding batch, use Gauss-Newton or Levenberg-Marquardt optimization to find the optimal path given all the data collected. The complexity of batch methods makes them unsuitable for online computation [3]. Few authors studied localization with radio frequency devices addressing the problem of sensor failures. In [4] a comparison of Monte Carlo methods and Kalman Filter can be found. Particular emphasis is put on response of probabilistic filters to extensive sensor silence. This work shows how traditional methods though being accurate in nominal situations, exhibit poor performances in adverse scenarios. Linearization errors in EKF framework lead to inconsistency as estimate diverges from true pose [5]. Similar problems could occur using Particle Filters when no particles are in the proximity of the true state (particle deprivation problem [6]).

In this context we propose a probabilistic model for beacon localization, called Probabilistic Shaping, and we test the robustness and fault tolerance

Manuscript received February 15, 2009. This work was supported in part by Regione Piemonte under MACP4log Grant (RU/02/26). L. Carlone is with CSPP, Laboratorio di Meccatronica, Politecnico di Torino, Torino, 10129, Italy (phone: +39-338-9072246; e-mail: luca.carlone@polito.it). B. Bona is with Dipartimento di Automatica e Informatica, Politecnico di Torino, Torino, 10129, Italy (e-mail: basilio.bona@polito.it).

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of the algorithm applied to a range-based positioning system. Our simulations are performed in a realistic scenario that can be a useful benchmark for performance evaluation and comparison. In the following section we introduce a general framework on robustness and fault tolerance in dependable systems, applying it to localization. In Section III we present our method, describing underlying assumptions and practical implementation.

Then in Section IV we show the results of simulation in a realistic scenario.

Conclusion are drawn in Section V.

II. ROBUSTNESS AND FAULT TOLERANCE Robustness and fault tolerance characterize the resilience of a system in delivering services despite adverse situations [7]. Robustness can be considered as a superset of fault tolerance but usually the following distinction is applied [8]: - Robustness is the capability of delivering the correct service when adverse environmental issues raise; - Fault Tolerance is the capability of delivering correct service despite faults affecting system resources.

In our case study the service required is localization: one or more robots, in general localization targets, estimate their own position using the information from on-board portable devices, later called readers, able to communicate with tags dispersed in the environment in known positions. The reader acquire range-only measurements from tags within the reading range. No prior information on robot position are available: the robot can only measure reader-tag distances and acquire motion information from its navigation sensors (IMU, gyros, odometry). The core of our localization system is the probabilistic model that performs estimation from data collected. Robustness and Fault tolerance are connected with both the infrastructure and the algorithm. In order to formulate our fault hypothesis we use a basic framework on dependability for autonomous systems, proposed in [8] and summarized in Fig. 1.

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When localization is performed the robot can compare its readings with nearest tags of the map, obtaining an indicator of missing readings for each tag. Given S$ (in a real situation can be found empirically) the probability of sensor fault, after K missing readings, is S$ K. Comparing the indicator of missing readings with a probability threshold, the system is able to detect anomalies. In our simulation sensor silence situations are always detected and no false alarm occurred. We stored missing readings indicator and fault probability of each tag in two vectors, called fault vectors. Through statistic on these vectors we are able to disambiguate normal conditions from fault situations. An example of fault vector is shown in Figure 7.

E. Robustness Results Perturbing tag positions we obtained the result shown in Table VI. Also in this case localization error remains upper-bounded within acceptable values.

In a real case, tag perturbation errors occur when operators place tags in inexact positions during system start-up. We simulated the case of uncertain positioning of all tags. Note that if a perturbation is limited to a single sensor, it can be similar to the case of sensor malfunction, because the bias in tag’s position causes an offset in distance measurement.

TABLE VI ROBUSTNESS TO TAG PERTURBATION

ıtag

Mean error (M)

Maximum error (m)

Standard deviation (m)

P P

During system start-up it is also possible that an operator places a tag in a completely wrong position. In this case the mismatch between real position and ideal one is so large that no reliable estimation is obtained when this tag is read. As consequence, the localization system detects the situation as sensor fault, allowing users to solve it. These are examples of design faults that can be solved within our method. In the case of kidnapped robot accuracy can not be used as metric for performance evaluation. When target is kidnapped, localization error explodes, because the robot is moving without any information to perform localization. In order to avoid catastrophic failure, when new measurements are acquired, the system has to recover with a time delay of the same order of magnitude of estimation period. Recovery time can be used for performance evaluation. In nominal conditions, recovery time for Probabilistic Shaping is less than 7H (only one estimation is completely wrong). In general it depends on the buffer length and on FIFO policy, since, in order to have a correct estimate, all measurements in the buffer should be relative to the new position. In our simulations, using a common personal computer, an estimation period is performed in 0.12 s.

V. CONCLUSION We proposed fault tolerance and robustness tests for beacon-based localization. Applying concepts of robust statistics, we provided a set of fault hypothesis and environmental perturbations, in order to study the response of localization systems to adverse situations. We tested our localization model, called Probabilistic Shaping, that performs global localization. The method stores measurements in a buffer and provide an estimate on demand, since estimation phase can be computed independently from measurement acquisition. This consideration implies that the only computational complexity is limited to estimation and no overhead occurs when localization service is not required. The method provides position-only estimates, so heading, when needed, can be derived from navigation sensors measurements. The outcome of the tests is that localization error remains upper-bounded within less than 2 m also when anomalies occur. Mean errors is inferior to 0.49 m in every simulation and maximum error occurred was 1.65 m (starting from range measurements with standard deviation 1 m and uncertain beacons’ position). Our model is able to assure fail-safe mode and to detect faults. Fault detection is performed through statistic on fault vectors, that contain information on missing readings and sensor malfunction. In all tests no catastrophic failure occurred. Probabilistic Shaping can also solve kidnapped robot problem assuring real-time system recovery. Robustness is achieved using a decisional mechanism, called judgement, that evaluates reliability of each estimate. Our probabilistic model is particularly suitable for localization based on radio beacons: it performs a spatial average of measurements, overcoming fluctuations and local biases, and can tolerate outliers without error explosion. Current work is focused on comparative study between classical Bayesian methods (Kalman Filter, Particle Filter) and the proposed model.

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Figure 7 . Fault vector in nominal condition simulation.

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