ABSTRACT:
This paper describes a method to estimate the position of a mobile robot in an indoor scenario using the odometric calculus and the Wi-Fi energy received from the wireless infrastructure. This energy will be measured by wireless network card on-board a mobile robot and it will be used as another regular sensor to improve position estimation. The Bayes rule will be used to accumulate localization probability as the robot moves on. In this paper several experiments in a university building are shown. The two major contributions of the presented work are that the self-localization error achieved is bounded, and that no significant degradation is observed when the theoretical Wi-Fi energy at each point is taken from radio propagation model instead of an a priori experimental intensity map of the environment.
INTRODUCTION:
Localization in mobile robotics can be defined as the problem of determining the position of a robot. This information is essential for a broad range of mobile robot tasks, as long as the robot behavior may depend on its position. The aim of localization is to estimate the position of a robot in its environment, given a map of the environment and local sensorial data. Robot localization has been recognized as one of the most fundamental problems in mobile robotics.
The robot odometric sensors play a critical role to solve the localization problem in wheeled robots, as they provide information about robot movements. In that way, if the initial position is known, the current position could be calculated. Unfortunately, these sensors are noisy and accumulate errors over time. For instance, the use of landmarks of known position and Kalman filtering Without such beacons or environment tailoring, other sensors like sonar’s, laser and even vision sensors may provide some indirect information about robot position given a map. They have been successfully integrated in a probabilistic framework and offer good localization results. More recently sampling methods (Monte Carlo) have been introduced in the probabilistic approach to speed up the estimation, giving also good results.
APPROACHING TECHNIQUES:
Our approach is based in the use of the signal power level received from the wireless Access Points (AP) deployed nowadays across hotspots (airports, stations, etc.) of our cities. The main interest in the use of this information in indoor robotics research is based in the fact that they are a cheap and non intrusive method. The infrastructure has already been deployed (for instance most universities, as our, are endowed with wireless Access Points), it may cover big areas and does not require any additional hardware or environmental engineering to work.
There are also other works in the literature that have used Wi-Fi signal in localization problems. Some of these experiments have trusted the Wi-Fi signal so much, that they simply triangulate the position, translating power received into distance to the AP. However, these experiments have shown that using this method only poor resolution can be achieved; they have developed different statistical methods to calculate the location probability. These methods are based on models of the actions that the robot can perform (turn, going forward, etc.) and the predicted observation after these actions had been performed. This prediction is based on a-priori map of the Wi-Fi energy. The main difference between our work and these ones is that we are introducing the use a theoretical model of indoor propagation of the signal from the APs. This avoids the need of manually building a” wireless energy map” of the environment. Using this theoretical model we are getting localization error similar to the obtained with the energy map. And it results on an easier implementation.
PROBABILISTIC LOCALIZATION:
The aim of the experiments described in this paper is to locate a robot inside the indoor scenario shown in figure 1, populated with several access points used for wireless communication. We follow the probabilistic approach, a technique probed widely successful in robot localization with sensors as sonar’s or laser. In this approach the localization evidence is stored as the probability of being in each possible location, which generates a “probability grid.” Such probabilities are continuously updated with the information coming from sensor observations and movement commands. The Bayes rule is used to fuse new information with that already stored. The best position estimation is that of highest accumulated probability.
As stated in (equation 1), the probability of the robot be in the location x is defined as the conditioned probability of such location given all the past observations from robot sensors, which add some indirect position information. Considering only independent observations, at least Markovian independence (equation 2), and following the analysis, the probability can be expressed and computed in an incremental fashion (equation 3),
Figure 1: Indoor scenario with 3 access points (left) andr robot with wireless card (right)
P (x (t)) = p(x (t)/obs (t), obs (t − 1) ...) (1)
P (x (t)) = p(x (t)/obs (t)) _ p(x (t)/obs (t − 1), obs (t − 2) ...) ->>>(2)
P (x (t)) = p(x (t)/obs (t)) _ p(x (t − 1)) ->>>(3)
P (x (t)) = p(x (t)/mov (t − 1), x (t − 1)) _ p(x (t − 1)) ->>>(4)
The robot movements are integrated in the probability estimation following a given action model, as shown in (equation 4). That model stores the probability of being at position x if the robot was previously at position x (t − 1) and it makes the movement mov (t − 1) at time t − 1.In practice, the effect of such action model is an evidence displacement over the probability grid. Such displacement follows the robot movement, and in our work is computed from the encoder’s readings. Some Gaussian noise in translations and rotations in added to take into account slippages and encoders deviation from real movement. The noise blurs the evidence displacements.
The sensor observations also modify the probability grid. In (equation 3)
p(x (t)/obs (t)) represents the posterior sensor model, which contains all the position information carried by the observation, in a probabilistic way. Sometimes this sensor model can be inferred from the a priori sensor model, p (obs (t)/x (t)), which contains the probability to obtain the given sensor measurement obs (t) in time t if the robot were at position x at time t.
We use the Wi-Fi energy measurements as the main sensor observations. In a typical indoor scenario there are several access points which provide wireless connectivity to the computers inside, mainly mobile ones.. We take advantage of such capability to use the wireless card as a Wi-Fi sensor. The Wi-Fi measurement is then defined as a vector with several components: number of visible access points, and signal and error energy levels for each one. In right picture of the figure 1 the wireless card of our robot is remarked.
Figure 2: Wi-Fi energy maps for Access Points 1 and 3
Nevertheless, if expected and observed readings are similar then the likelihood of the robot being at that position is high. Putting it in another way, the current Wi-Fi energy provided by the wireless network card will raise the probability of the locations with a similar expected energy and will low that of the locations with a very different energy value. We have tested two probabilistic models to add Wi-Fi data. The first one obtains the expected energy value from an a priori compiled energy map of the environment. Such map was built taking various measurements in all possible locations and collecting the energy received at each one. The second sensor model gets the expected energy value from a theoretical Wi-Fi propagation model. These two models are described in detail in the next two sections.
A PRIORI WI-FI ENERGY MAP:
The a priori energy map that the robot uses is in fact a set of maps, one for each access point, so we have three maps for our test scenario.
Figure 3: Breakpoint model function with exponent 3.5 after breakpoint
at 5 m.
Figure 2 shows those for access point 1 and 3.The energy tends to be lower at further locations from the access points, as it can be expected, however this attenuation was much lower than expected. The sensorial model used was p(x/obs (t)) = 1−d (t) _, where _ is an amplification factor and d (t) is computed as the percentage of energies from the sensor reading vector that fall close to its corresponding element in the expected vector. A given threshold is set to consider two energies as close enough.
The maps were built moving the robot through all possible positions and storing the measured WiFi energy values for each access point. When discredited the world into 2x2 meter square cells. This distance was chosen because there was no significant differences in the signal level for smaller distances.
WIFI PROPAGATION MODEL:
In the second WiFi sensor model the expected value was obtained from a propagation model for the WiFi energy. In particular it follows the equation 5, where distance function decreases exponentially with the diference in energy.
There have been a lot of research about propagation of radio signals in indoor environments; we have chosen the breakpoint model [1]. Our model will compute the signal level for each point as the equation 6. This is a free space loss model that takes only into account the distance from the emitter, and ignores any walls in between. Two different regions are used, before and after a given breakpoint, which was set at 5 meters for our experiments. The figure 3 shows the predicted energy level. It always follows the lower line, keeping a smooth drop for distances under the breakpoint, but falling down at higher rate further.
Signal level = 240 - (20 + 10 _ log(l))
if l<=5 meters
240 - (34 + 10 _ 3.5 _ log(l/5))
if l>5 meters (6)
Figure 4: Propagation models for AP1 and AP3
The use of the model for this experiment allows us to obtain the expected WiFi energies at every location of the grid without actually moving acquiring the data in a previous phase. This is very convenient as the map building phase is very tedious, and takes time. Figure 4 shows the appearance of expected energy readings for access points 1 and 3 according to the propagation model. In this case, we can easily calculate the energy map for the whole building, not just for the corridors as in the previous approach. We do not need explicit permission to enter private rooms, etc. In this way the experiments made using this approach use the whole map, which are harder conditions (larger grid and more possible errors) than in the previous approach; however, as we will point out in the next section, results are quite similar.
The localization performance of the probabilistic approach using the two different WiFi sensor models previously described was tested over a simulator.
Figure 5: Software architecture for the experiments
The module architecture of the software is shown in figure 5. We used the standard simulator of our Pioneer robot, SRI sim, which simulates the ejects of movement commands and gives the real location of the robot (ground truth position in figure 5), and the position computed from the encoders (odometer position in figure 5). It also provides the simulated sonar and laser readings, but they were ignored in our experiments. We have also coded a wireless module to simulate the WiFi readings using the measures taken by the robot to make the energy map described in section 2.1.Given the ground truth position, the WiFi readings are always taken from the experimental energy map, with some noise added to provide the observed energies (simulated wireless observations in figure 5).
The localization algorithm uses only such signal level from the WiFi sensor and the odometers readings to continuously compute its position estimate following one of the approaches described in last section. It also accesses the wireless table to get the theoretical wireless reading corresponding to each possible location.
CONCLUSION:
A probabilistic localization algorithm has been presented which uses a WiFi network card as another sensor in combination with odometric. The card measures the energy received from different communication Access Points in the environment. Experiments described in previous section have shown that, even though the wireless information isn’t very discriminative, it’s clear it helps in the robot localization task, improving the accuracy estimation over the odometric itself. In the near future we plan to repeat these same experiments using the real robot instead of simulator, in order to validate these preliminary conclusions.
REFERENCES:
[1] A. Clarke. A reaction dilution model for wireless indoor propagation.
[2] K.E.Bekris A.M.Ladd and A.Rudys. Robotics-based location sensing using wireless Ethernet.
[3] Sajid M. Siddiqi Gaurav S. Sukhatme Andrew Howard. Experiments in monte-carlo localization using WiFi signal strength.
[4] www.wikipedia.com
[5] www. robomovements.com
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