PropEM-L: Radio Propagation Environment Modeling and Learning for Communication-Aware Multi-Robot Exploration

The communication challenges associated with multi-robot exploration have drawn increased attention [31, 26, 27, 34, 23]. These works are largely concerned with maintaining connectivity, which requires models for estimating and/or predicting connectivity. Existing work simplifies the inter-robot communication model to a deterministic communication radius [23], or predicts a probability of connectivity based solely on distance [31]. These simple models break down if, for instance, there is a metal wall within the communication radius which blocks the signal. For this reason, Miyagusuku et al. seek to capture the role of the environment through a learned model of signal attenuation [18, 19]. Their data-driven approach is well-suited for repeated operation in the same environment, but for exploration of an unknown and dynamic environment an online method is advantageous.

The authors of [12] demonstrate an online method for modeling RSS during single-robot exploration. While they present a model which captures the size and location of obstacles (for example, a 1m thick wall 4m from the transmitter), they defer the discussion of estimating these parameters. Quattrini Li et al. propose a Gaussian Process (GP)-based method to build a communication map from measurements taken by multiple robots [24]. These works also focus on 2D operations, and give little attention to the challenge of modeling the propagation environment given partial maps in the form of 3D point clouds.

Previous work in the ecology community has considered extracting relevant information from 3D point cloud data. The authors of [6] and [16] use point clouds to determine the location and thickness of trees in a dense forest, which could theoretically feed into the model presented in [12]. Recently, the authors of [10] extend this idea to use learning-based methods on 3D point cloud data to predict the affect of tree canopies on signals propagating between static wireless communication towers. Precise digital terrain models have also been used to inform signal propagation models. [11] extends a network simulator with awareness of the topography, while [29] validates terrain-aware signal strength models with experimental data. Recently, the authors of [17] demonstrate the capability of neural networks to learn from known digital terrain models to improve cellular network design. Our work extends this method to be suitable for a dynamic network of mobile, exploring robots.

To enable communication-aware multi-robot exploration in unknown environments, we propose Propagation Environment Modeling and Learning (PropEM-L), a framework for signal strength prediction which learns the effect of the environment on attenuation. The contributions and highlights of our work are:

1. 1.

   Propagation Environment Modeling: We propose PropEM, which leverages sparse 3D geometric representations of the environment (e.g. LiDAR point clouds) to extract features of the physical space which affect signal propagation, including line-of-sight visibility, shadowing due to obstacles, reflection, and diffraction.

2. 2.

   Learning: We validate PropEM in conjunction with conventional data-driven approaches to RSS prediction which rely on linear regression. We then propose a neural network-based approach, PropEM-L, which significantly improves prediction accuracy relative to a log-distance path loss model and can estimate RSS within a few decibels.

3. 3.

   Deployment: We evaluate the performance of PropEM-L experimentally on a dynamic network of 13 autonomously-deployed static radios, one base station, and six robots exploring an underground environment. Via online learning, we demonstrate that PropEM-L can adapt to challenging new environments and construct signal strength maps.

We performed extensive field testing in an underground limestone mine in Kentucky and captured about 80 minutes of autonomous exploration with 1 base station radio, 6 ground robots (3 legged Boston Dynamics Spot robots and 3 wheeled Clearpath Robotics Husky robots), and 13 communication relay radios which were autonomously deployed by the ground robots when signal-to-noise ratio (SNR) fell below a desired threshold. All radios were MIMO StreamCaster 4000-series radios from Silvus Technologies [15, 28]. Exploration spanned about 300 meters in each of the $x$ and $y$ directions, and we collected 1.3 million datapoints capturing transmitter position, receiver position, frequency, noise, transmitter power, RSS, SNR, loss rate, etc [1].

Although we can only collect signal strength data between pairs of radios which have connectivity, we have location estimate data for all radios. For pairs of radios which have certainly lost connectivity, meaning neither of the robots report RSS measurements at a given location for a two-minute period, we augment the dataset following the approach presented in [18], where the received signal strength is inferred to be the noise floor of the radios (here -94dB). To ensure synchronization between the location estimate and the signal strength measurement, we remove any data for which the two were observed more than one second apart. Additionally, we observe a limited number of outliers caused by localization failure which are easily removed for static radios whose location estimates should never vary more than a few meters.

As a preliminary step in validating PropEM, we note the correlation between the features PropEM outputs and the RSS measurements. Table I captures the Pearson correlation coefficient of data collected during field testing, which illustrates that signal attenuation is correlated with distance and the number of not-free voxels (occupied, maybe occupied, or unknown), followed by the additional loss predicted by the two-ray ground reflection model.

To demonstrate PropEM as part of an RSS prediction framework, and as baselines for comparison, we implement the standard log-distance path loss prediction model and several extensions of this model. Table II presents a summary of the accuracy of each model, and Fig. 6 offers a snapshot of their performance.

Simple Path Loss: Using linear regression, we fit the parameters of the simple path loss model given by Eq. 1. We abbreviate $PL(d_{0})_{dB}$ at $d_{0}=1$m to $PL_{d0}$ in this and the following sections. This regression gives $PL_{d0}=14.84$ and $\eta=4.73$.

Visibility: Motivated by the distinctly different curves observed in the data, as demonstrated in Fig. 5, we implement a model which incorporates visibility. We use linear regression to fit two distinct lines to Eq. 1 depending on whether there is line of sight, which gives $PL_{d0}^{\textrm{LOS}}=36.5$, $\eta^{\textrm{LOS}}=2.75$, $PL_{d0}^{\textrm{nLOS}}=13.72$ and $\eta^{\textrm{nLOS}}=4.81$.

Shadowing Heuristic: Considering not just visibility but the amount of occupied space, we use linear regression to approximate the dB of attenuation per meter of not-free voxels. Similar to the approach presented in [4], this model adds an additional attenuation of 0.16 dB/m to the output of the path loss model with LOS parameters.

Two-Ray: This ground reflection model subtracts $RL_{dB}$, given by Eq. 5, from the simple path loss model using LOS parameters.

Knife-Edge: This diffraction model subtracts $DL_{dB}$, given by Eq. 7, from the simple path loss model using LOS parameters.

Reflection-Diffraction: As presented in [11], this model combines the effects of two-ray ground reflection and knife-edge diffraction. For a maximum $v\leq-0.8$, the Fresnel zone is considered clear and this model reduces to the two-ray model. Otherwise, the diffraction loss is subtracted from the two-ray model with the modification that any constructive reflective interference is ignored.

Of these models, the visibility model achieves the most accurate prediction, as shown in Fig. 6 (top). The two-ray, knife-edge, and reflection-diffraction models are very sensitive to small differences in antenna height, distance between transmitter and receiver, and precise location of neighboring walls. Because PropEM relies on sparse point clouds, uncertain location measurements, and discretized space (voxels are up to 1.5m wide), we see rapid changes in the predicted diffraction loss as new voxels are explored or the robot’s position changes even slightly. This sensitivity is likely the reason the more parsimonious models actually perform better.

As implemented, the conventional models make a few simplifying assumptions: the simple path loss model assumes no obstacles, the visibility and shadowing heuristic models assume all obstacles have the same material properties, the two-ray model assumes a flat reflective terrain, and the knife-edge model assumes the worst-case from obstructions. While these models have the advantage of being interpretable and grounded in the physics of how radio signals propagate, non-linear combinations of these features, learned via stochastic gradient descent, can capture subtleties in the environmental dependence which are inadequately captured in the simpler models.

We introduce five fully-connected neural networks (NN), each with the same simple structure: an input layer, a sixteen-unit hidden layer with restricted linear activation function, and an output layer which predicts attenuation $PL_{dB}$. Each NN learns to minimize the L2 loss between the predicted attenuation and the measured attenuation, using the Adam optimizer to train for 100 epochs or until convergence. The field test data from the limestone mine is normalized such that all features have zero-mean and unit standard deviation. 30% of the data is withheld from training, and the remainder is divided randomly into batches of size 2048.

Each NN takes a subset of the features which PropEM outputs, as described below:

• •

  NN-vis uses logarithmic distance and LOS, which is broken into two boolean input features: strictly visible indicates all the voxels between the transmitter and receiver are free; strictly not visible indicates there is at least one occupied voxel.

• •

  NN-vox uses logarithmic distance and the number of occupied, maybe occupied, free, and unknown voxels.

• •

  NN-ref uses logarithmic distance and reflection loss.

• •

  NN-diff uses logarithmic distance and diffraction loss.

• •

  NN-all combines the features of NN-vox, -vis, and -diff.

Table II compares the performance of each NN model, and Fig. 7 depicts the probability density function of errors observed using each model. NN-all saw the best performance of any method with an average error of only 3.72 dB, and is less likely to produce errors above 10dB. To contextualize this performance, the standard deviation of $PL_{dB}$ for a pair of static radios (at a constant distance) observed in the limestone mine was up to 3.43 dB, indicating that errors in this range may be attributed to inevitable channel noise.

To adapt to drastically different environments, PropEM-L can perform online learning to leverage the partial 3D geometric representations available during exploration. Note that for simplicity we assume in this section RSS measurements from all radios are available at the base station immediately, ignoring any networking latencies.

Linear regression: Using the visibility model and re-fitting the parameters $\eta^{\textrm{LOS}},PL_{d0}^{\textrm{LOS}},\eta^{\textrm{nLOS}},PL_{d0}^{\textrm{nLOS}}$ every $k$ minutes, we can achieve a mean absolute error of 10.99dB (21% improvement over the offline-learned model) on day 1, 12.47dB (12% improvement) on day 2, and 11.89dB (5% improvement) on day 3 for $k=1$. These improvements are due to the fact that the model updates the attenuation it associates with a given number of occupied voxels between a transmitter and receiver. This reflects a change in the model’s belief about the RF properties under identical geometries.

Perhaps more notably, the final path loss parameters learned via linear regression can shed insight on the environment itself. The learned $\eta^{\textrm{LOS}}$ in the new environment was between 1.59-1.94, which indicates indoor areas and is significantly lower than the initial estimate of 2.75 which is typical for outdoor urban environments. Without any other information about the map, we can conclude the competition environment was more confined. Similarly, re-fitting the heuristic model increased our approximation of attenuation over not-free space from 0.16 to 0.43-0.66 dB/m. This lets us infer that the competition environment had material which blocked radio waves on average up to 4 times more than expected. This interpretability is an advantage of the conventional linear regression models over the NN models.

Neural Networks: To train the neural network component of PropEM-L online during exploration, every 60 seconds we train for 10 epochs (selected empirically) on data collected in the last minute. The number of samples used to retrain is on average 2644 (with a minimum of 498 and a maximum of 5414). Starting with the model trained offline prevents overfitting to initial measurements, while over time the new environment is learned. Fig. 9 shows how the mean absolute error decreases and converges over time. Over the entire duration of the competition run (day 3), NN-vox trained online can achieve a mean absolute error of 7.28 dB, improving performance over the simple path loss model trained offline almost two-fold.

PropEM-L can predict the strength of a signal received by a robot at any arbitrary location from one or multiple nearby radios. Given the location of static radios and their transmit powers, we can use our framework to construct a signal strength map, as shown in Fig. 1. PropEM-L can update this map as areas are explored or the network topology changes. Connectivity maps have a number of uses in communication-aware exploration: robots can autonomously identify areas to deploy additional relay radios [28], prioritize exploring new areas which are expected to offer connectivity, or navigate to areas with strong signal to prioritize data transfer and improve situational awareness for the human supervisor [8].