Evaluating Tradeoffs for Swarm Reconnaissance With Autonomous Ground Vehicles

The capability and availability of self-driving cars have increased rapidly in the last decade [1,2]. The recent capability improvements of self-driving cars have largely been enabled by the development of machine learning algorithms [3]. However, despite recent advances, many challenges remain for self-driving vehicles. This is particularly true for self-driving in off-road terrain, which presents many challenges not encountered in highway and urban driving [4]. These include the absence of clearly marked travel lanes and the presence of vegetation, soft soil, rough surfaces, and negative obstacles.

The ability of a self-driving vehicle to traverse off-road terrain strongly depends on the characteristics of the vehicle like its size, weight, and tire properties [5]. Successful navigation of off-road terrain by a self-driving autonomous ground vehicle (AGV) requires the vehicle to measure the properties of the terrain with on-board sensing and compare the terrain properties to the vehicle capabilities in real-time. Despite advances in machine learning algorithms, this process of terrain perception is often limited by the range, resolution, and field-of-view of the sensors on the AGV—and this is especially true in the case of negative obstacles [6].

One potential method for mitigating perception limitations imposed by sensor range and field-of-view is to employ multiple autonomous agents viewing the terrain from different angles [7]. A team of multiple AGV cooperating independently is known as a swarm. While swarming concepts have been tested at fairly large scales for unmanned aerial vehicles (UAVs) [8], little work has been done to evaluate the effectiveness of AGV swarms in off-road environments.

In this work, an AGV swarm system for terrain exploration is presented with a focus on off-road mobility considerations and negative obstacle detection. A physics-based simulator, the Mississippi State University autonomous vehicle simulator (MAVS) [9], is used to demonstrate the swarm concept. MAVS was chosen for this work for two important reasons. First, MAVS is compatible with high-performance computing (HPC). Given that the main goal of this work was to simulate large-scale teaming of AGV, HPC was a requirement that no other publicly available simulator could easily meet. Second, MAVS provides detailed off-road environments, including geometrically detailed representations of vegetation, that give realistic results for lidar simulation that far exceed other simulators [9]. Using MAVS, a series of simulated experiments are conducted to evaluate the ability of the swarm to detect negative obstacles. These results are compared to the overall fuel consumption of the swarm system, failure rates, and mission completion time, arriving at an optimal number of AGV for terrain exploration and negative obstacle detection. This work presents novel contributions in both the size of the swarm (up to 100 robots) and the realism of the off-road terrain considered, as will be further shown in the following sections.

Simulation has become a critical enabler to the development and testing of AGV [10]. Simulation can be used early in the development phase to find critical bugs and optimize design considerations like sensor placement [11]. In the testing phase, simulation allows a large number of repeatable scenarios to be tested [12]. When it comes to multi-vehicle systems and swarms, the need for simulation is even greater because of the cost and logistics associated with maintaining a large fleet of AGV.

Some of the earliest work on robot teaming was performed by Burgard et al., who published a study of multi-robot exploration with a team of two robots in an indoor space [13,14]. Their system was evaluated using a purpose-built top-down 2D simulator. Similar early work was published by Rekleitis et al. [15], who performed multi-robot exploration experiments with a focus on collaborative localization using the robodaemon software [16]. Additional work on collaborative, team-based mapping was performed around this time by several groups [17–20].

Subsequent work developed methods for maintaining communication in distributed multi-robot networks [21], merging occupancy grids from teams of robots [22], and obeying constraints of wireless networks during exploration [23]. Research on optimizing exploration algorithms for robot teams also continued at this time [24,25].

Prior to the development and adoption of the robotic operating system (ROS) [26], much work was focused on developing interoperability between robots using custom-built simulators. For example, Brudnak et al. developed a real-time distributed simulator for up to 10 vehicles using high-level architecture [27]. Barnes et al. [28] developed a technique for controlling a group of small ground robots using potential fields and demonstrated the method experimentally. Saad et al. [29] developed a testbed for teams of up to a dozen small unmanned aerial vehicles (UAV) with a complementary 3D simulator based on a game engine.

Indoor exploration by a team of three robots was studied by Wurm et al. [25] using the Carnegie Mellon Robot Navigation Toolkit [30]. Later, Atyabi et al. [31] created a custom simulator, Magician, to study heterogeneous teams of robots operating in urban environments. Like most of the simulators developed in these studies, Magician used a two-dimensional, top-down representation of the environment with simplified vehicle dynamics and sensor models. The primary focus of these early works was studying the theoretical framework for employing multi-robot systems. Further work in this area was done by Senthilkumar and Bharadwaj [32] and later Jezdimirović et al. [33], who created a simplistic 2D simulation environment for coordinated attack movements for groups of three or four vehicles. In addition, Krajzewicz et al. developed control algorithms for lane change maneuvers in groups of autonomous vehicles and tested the algorithms with the urban mobility simulator, SUMO [34]. Additionally, some recent work has used 2D, matlab-based simulators to study vehicle control and rollover mitigation [35,36].

With the widespread adoption of ROS, the availability of high-quality game engines, and the advancement of computing systems, multi-robot simulations have become more sophisticated in recent years. For example, Feierle et al. [37] simulated an autonomous and manned vehicle negotiating a single lane intersection, while Barciśet al. [38] simulated swarms of small robots in ROS2.

Many simulators using game engine technology have progressed beyond the 2D, top-down approach used in the past. Nieto-Granda et al. [39] evaluated a group of nine turtlebots cooperating to explore an indoor environment using the Stage simulator [40], while military autonomous convoy and leader-follower scenarios with up to four vehicles were simulated by Brabbs et al. [41] using the ANVEL simulator [42]. Barlow and Garratt [43] simulated a group of eight small ground vehicles moving collectively using CoppeliaSim [44]. In addition, multiple vehicles can be simulated in CARLA [45] using OpenScenario [46]. Lee et al. have used this feature to simulate V2X architectures in urban and highway environments [47].

The availability of high-performance computing (HPC) has also enabled new advances in swarm simulations, both in terms of realism and scale of team size. For example, Goodin et al. [48] simulated a four-vehicle team of high mobility multipurpose wheeled vehicle (HMMWV)-sized vehicles moving in biologically inspired formations using the physics-based virtual autonomous navigation environment simulator [49]. In contrast, Kuru and Kahn [50] developed an agent-level simulator for evaluating a framework for a “smart-city” for AGV navigation with up to 14,000 vehicles operating in the city environment.

This work extends these recent advances using a physics-based simulator to perform high-fidelity, off-road simulations of the vehicle sensors and dynamics. The simulation is scaled to large numbers of vehicles by distributing the vehicle simulation processes on HPC to create a simulation environment that exceeds previous efforts in both scale and realism for off-road environments. This work is the first of its kind to study large (>20) teams of AGV operating in realistic off-road environments.

The goal of the swarm system was to autonomously explore the area of operation and build a map of the obstacles in the mobility corridor. This was accomplished using a team of high-mobility light wheeled vehicles, composed of the Polaris MRZR-4 [51]. Each vehicle was equipped with a lidar sensor and localization sensor. The simulated lidar was a 64-beam Ouster OS2 [52] and the simulated localization sensor was a real-time kinematic corrected multi-band GPS receiver, the Swiftnav Piksi [53]. The lidar sensor was mounted on the front hood of the vehicle and tilted down at an angle of 25 deg in order to better scan the ground surface in front of the vehicle. The localization sensor was mounted on the roof of the vehicle, as shown in Fig. 1.

Each vehicle was equipped with its own autonomous control, capable of operating the vehicle independently of the swarm. The map collected by each vehicle was reported to the group through peer-to-peer communication. In the following subsections, the autonomy algorithms on each vehicle and the swarm control strategies are discussed in more detail.

The autonomy package for each vehicle consisted of three main modules: perception, path planning, and vehicle control. The perception module processed the lidar data to identify positive and negative obstacles. The path planning module selected a route for the vehicle from its current position to the goal point. And the control module calculated the appropriate throttle, steering, and braking commands to safely follow the desired path.

While many AGV use ROS to communicate data between the perception, planning, and control modules, ROS was not ideal for this application because of the relative difficulty of simultaneously operating dozens of individual systems in ROS, in addition to the difficulty of communicating between those systems with ROS. Instead, the MAVS simulator was embedded in a messaging architecture that used the message-passing interface (MPI) [54] to send messages between the AGV team agents.

The perception module identified obstacles geometrically using a combination of estimated slope and curvature to identify potential obstacles. In the first step of the perception, the point cloud from each successive lidar scan was registered to a global, static map using the transform provided by the real-time kinematic (RTK) localization sensor. A voxel filter was applied to the points, placing them into a 2D grid. In each grid cell, only the highest and lowest points were retained. For each cell, an “in-cell” slope was calculated by dividing the elevation difference between the highest and lowest points by the dimension of the cell. Cells with slope above a certain threshold (2.5 in this case) were flagged as obstacles. This is similar to the approach used by Rankin et al. [55].

The path planning module consisted of two stages. In the first stage, a global planner using A* [56,57] calculated a path through the map from the vehicles current position to the goal point. Since the terrains and maps were large, these paths could be several hundred meters long. In addition, the A* algorithm makes no consideration for the dynamics of the vehicle or the relative safety of the path. Therefore, in the second stage, a local planner calculated a near-field path that was feasible for the vehicle to follow. The local planner uses cubic splines and accounts for vehicle steering, collision avoidance, and minimizing steering changes [58], resulting in a smooth, drivable path.

The vehicle control module used the pure pursuit algorithm [59] to calculate steering based on the desired path output from the local planner. The throttle setting was calculated using a PID controller [60], which attempted to maintain a speed of 5 m/s for the vehicle. Throttle, steering, and braking commands were passed to MAVS using an array of three floats.

The swarm control model used in this work utilized a central authority to merge and manage the global map and assign goal points for each robot. In the initialization step, the central authority assigned a goal point to each agent. The goal points were distributed to ensure maximum exploration of the mobility corridor. Each agent independently and autonomously navigated to its goal point. At regular intervals, the robots sent their current map back to the central authority. The central authority generated the most up-to-date global map representation by combining the agents’ local representations and ensured that all agents had the current global representation by rebroadcasting the combined map. The global map was updated by the central authority at a rate of 10 Hz. Inter-AGV communication was enabled by MPI messaging with an array of floats for the state of each vehicle.

The maps were represented by a 2D occupancy grid. Figure 2 shows typical occupancy grids from the simulation, as well as the evolution of the map completeness over the course of a single mission. The top figure shows the map at the beginning of the experiment, while the bottom one shows the map near the end of the experiment.

The simulation environment used for this study was based on the MAVS software. The MAVS was integrated into an HPC-based distributed architecture that allowed dozens of vehicles to be simulated simultaneously. The following sections discuss the simulator and distributed simulation environment in more detail.

The MAVS was used to simulate the vehicles navigating in the off-road environments. The MAVS lidar simulation has been validated for use in dense vegetation [9] and rain [61]. The MAVS has also been used in a variety of studies related to lidar performance in autonomy including machine learning algorithms for classifying off-road terrain [62] and for detecting obstacles in dense vegetation [63]. The MAVS uses the Embree ray-tracing kernel [64] to accurately account for effects like lidar beam size, surface reflectance properties, and low-angle reflectance in lidar returns. For the RTK localization sensor simulation, MAVS uses an empirical model based on field measurements [53].

The vehicle suspension is simulated using a lumped parameter, independent linear spring damper model for each suspension element. This is similar to the approach used in Vehdyn [65], but extended to 3D using the Reactphysic3D multibody-dynamics library [66]. The tire is simulated with a radial-spring model [67] with the model extended to 3D by dividing the tire into multiple 2D slices. The tire–soil interaction is simulated with empirical models derived from the DROVE database for sand [68] and clay [69]. More information on the MAVS vehicle model can be found in recent works by Moore et al. [70] and Islam et al. [71].

To simulate the ad hoc communications of the simulated vehicles, a simple model consisting of binomial probabilistic links and a many-to-many propagation strategy is used [72]. Using a distance-based probability function, the probability of successful communication between every pair of vehicles is computed. These probabilities are then used to share vehicle data only via successful, direct links between vehicles. Over time, communication data will propagate throughout the vehicle network, dependent on the existing communication links.

This model allows coarse designing of a probability function with three major sections: a flat, high connectivity region within the nominal range followed by a region with gradually decreasing connection strength and a final, low connectivity region. While phenomenologically based, the posing of parameters in terms of desired behavior, ranges, and failure rates allows tuning of the model to capture specific network conditions irrespective of the broader, more complex environmental conditions that would predicate such conditions.

The simulation was distributed using a custom-designed hybrid memory model that used a shared memory approach, implemented with OpenMP [73], to simulate the individual sensors and vehicles and a distributed model, implemented in MPI [54], to facilitate communication between each vehicle.

The first step in the simulation loop is to update the state of each agent (AGV). This includes updating driving commands using the on-board autonomy, updating the dynamic state of the vehicle platform using those driving commands, and updating the sensors on the AGV. The vehicles are updated in a parallelized for-loop, meaning that all the vehicles can be updated simultaneously in parallel.

Following the vehicle update loop, the updated pose (position and orientation) of each vehicle is broadcast to all other vehicles using the MPI_Allreduce function. The AGV-to-AGV communication model presented in Sec. 4.2 is then updated with the revised vehicle positions.

In the next step, the occupancy grid of each agent is broadcast to all other agents using the MPI_Allreduce function. We note that this is not simulating a physical process—rather, the communication model is then used to calculate the transmission of each grid between robots to the central authority.

In the final step, the central authority checks to see if all agents have reached their final goal. If they have not, the central authority uses the grids it received to create a combined occupancy grid which is rebroadcast to all agents within the communication network. This loop repeats until the simulation is complete.

A reconnaissance scenario for an avenue of approach in a military context was constructed in order to evaluate the efficacy of the swarm concept. The goal of the reconnaissance is to select a mobility corridor that supports maneuver. According to Weigeshoff [74]:

Therefore, in this scenario, an avenue of approach that featured rolling terrain marked by both positive (trees) and negative (holes) obstacles was constructed. A new terrain was randomly generated for each trial with holes and trees at random locations. An example of one scene used in the simulated experiments is shown in Fig. 4. By completing many different trials of the experiment, each one in a randomly generated scene, the performance variables can be treated statistically rather than deterministically.

The surface mesh resolution was 0.25 m. The negative obstacles had a depth of 1.5 m, a radius of 2.5 m, and a parabolic shape. The vegetation consisted of sparse, mature trees of species consistent with the southeastern United States including oaks, pines, pecans, and magnolias.

To start the scenario, the vehicles were distributed in row across the western edge of the map. The vehicles were uniformly spaced in the north–south direction. Each vehicle attempted to navigate to a goal point at the eastern edge of the map while maintaining a speed of 5 m/s.

The number of robots (N_R) was the independent variable in this analysis. The vegetation density and surface roughness were varied randomly within a small range to introduce to randomness to the individual simulations. The number of robots was varied between 1 and 24, while the vegetation density was varied between no trees and approximately 10 trees/km².

For each trial, there were five dependent variables (metrics).

1. Time to complete (TTC)—the number of seconds it takes for all AGV to arrive at their goal point to complete the mission.

2. Failure rate (δ_f)—the fraction of trials that all AGV do not reach the goal point in the allotted mission time.

3. Fuel usage (f_v)—the total fuel usage for the AGV system.

4. Negative obstacle detection rate (δ_d)—the fraction of negative obstacles detected.

5. Fraction of terrain explored (δ_t).

The TTC metric is straightforward to measure—it is simply the amount of time in seconds it took for all vehicles to reach their goal.

For the failure rate metric, a trial was considered a “success” if all vehicles reached the goal point in the allotted time; otherwise, the mission was deemed a failure. The failure rate was the number of failures divided by the number of total trials for a given configuration. Therefore, the optimal failure rate is 0.0.

Negative obstacle detection rate was determined by counting the number of negative obstacles detected by the AGV team and dividing this by the total number of negative obstacles in the terrain. Therefore, the optimal detection rate was 1.0.

Fuel consumption depends on many factors like air temperature, tire inflation, and engine properties. While modeling the fuel consumption for the MRZR4 is beyond the scope of this work, Lee et al. [75] determined that fuel consumption is linearly related to throttle position. Therefore, for comparative purposes, the cumulative throttle position for all vehicles over the course of the mission was used as a proxy for the fuel consumption metric.

The fraction of the terrain explored is related to the occupancy grid. A grid cell is considered “explored” if there are at least three lidar returns within that cell. The fraction of the terrain explored is the total number of explored cells divided by the total number of cells in the map.

The following subsection outlines the statistical techniques used in this work. While many analyses use statistical techniques appropriate for normally distributed data, much past work has shown that many performance metrics for ground vehicles are not normally distributed but rather follow binomial statistics or lognormal statistics. For convenience and clarity, these distributions and their application to AGV analysis are discussed in more detail in the following sections.

When conducting multiple tests and compiling TTC statistics, it is often illustrative to simply calculate the mean and variance of the TTC results. However, it is important to note that TTC do not follow the normal distribution. Rather, TTC are best fit by a lognormal distribution and the mean and confidence intervals should be calculated accordingly [78].

In this section, the results of two sets of simulated experiments are presented. In the first experiment, groups of 1–6 robots cooperatively explored a scene of 250 × 250 m² with 25 randomly placed negative obstacles. The vegetation density and surface roughness were varied randomly. A total of 100 trials were run for each number of robots for a total of 500 simulated experiments.

In the second experiment, groups of 1–24 robots cooperatively explored a scene of 500 × 500 m² with 100 randomly placed negative obstacles. Both the vegetation density and surface roughness were also randomly varied. A total of 100 trials each were run for 1, 2, 3, 4, 6, 8, 10, and 24 robots, for a total of 800 simulated experiments. It should be noted that the density of negative obstacles was the same for both experiments 1 and 2 (4 × 10⁻⁴ obstacles/m²), so the detection results are directly comparable.

The simulations were run on an Dell workstation with six Intel Xeon processors having 16 logical threads per processor for a total of 96 available threads. The simulations were run with eight threads per AGV. The 1400 simulations took a total of two weeks to complete. Results were saved to text files for each simulation, then compiled into a csv file for further analysis with python.

The results for experiment 1 are presented in this section. The results are summarized in Table 1. Negative obstacle detection rates, like failure rates, follow binomial statistics because each obstacle is either detected or not detected. Detection rates for each input configuration were analyzed using binomial statistics, and the results are plotted in Fig. 5.

Fuel consumption, like TTC, is a “statistical realization of the multiplicative product of many independent random variables, each of which is positive” [79]. Therefore, the fuel usage results are also analyzed using lognormal statistics. The results of the fuel usage for each configuration are plotted in Fig. 6.

Experiment 2 featured a larger terrain than experiment 1 (0.25 km² versus 0.625 km²) and more autonomous agents (up to 24 for experiment 2 versus only six for experiment 1). The purpose of this additional experiment was to determine if the size of the scene had an effect on the observed metrics.

The results for experiment 2 are summarized in Table 2. Detection rates for experiment 2 are plotted in Fig. 7. The results of the fuel usage for experiment 2 are plotted in Fig. 8.

One measure of performance of the overall simulation architecture is the scaling as more vehicles are added. Scaling tests were performed on Mississippi State University’s Orion high-performance computer. Orion is a Dell/EMC PowerEdge C6420 cluster composed of 1800 compute nodes, each with dual 20-core Xeon Gold 6148 processors (with a base processor frequency of 2.4 GHz) and a total of 345 TB of RAM. Eight of these nodes are large-memory nodes with 384 GB of RAM with the remaining 1792 nodes containing 192 GB of RAM. Each node is interconnected via Mellanox HDR100 InfiniBand (100 Gb/s).

Simulations were run on Orion’s regular nodes with 192 GB of RAM. The scene size was 600 × 1200 m. One goal was to see how large of a simulation could be reasonably run on Orion. The normal queueing system on Orion permits up to 10 nodes per job and up to 48 h of run time. The number of MPI processes per node (with one vehicle per MPI process) was limited primarily by the memory usage per process, so as the number of vehicles per simulation went up, additional nodes were added as necessary to provide the additional memory. Also it was insured that the number of processes was always less than or equal to the number of CPU cores. There were six simulations run with the resulting times, number of vehicles, and number of nodes used shown in Fig. 9.

The scaling results indicate that the communication architecture used between the vehicles does not scale well. Each vehicle had a copy of every other vehicles map in memory, and the communication simulation was used to evaluate how those maps were propagated through the communication network. This led to a drastic increase in the time for the MPI_Allreduce calls for the vehicle maps as the number of vehicles increased.

Additional simulations were run with a fixed number of vehicles, 32 in this case, on the big memory nodes (384 GB RAM) while increasing the number of nodes. Increasing the number of nodes adds more cpu cores and more memory but would likely add latency in the communication inter-node compared to intra-node. This is also due to the large amount of shared map data being stored in memory in this particular simulation architecture. Figure 10 shows the results.

Taken together, experiments 1 and 2 reveal several interesting trends. The general trends show that as the number of robots increases, the amount of fuel used also increases and the fraction of obstacles detected increases. The results also show that the assumption of lognormal TTC statistics is reasonable.

The best value of α for each dependent variable is found through fitting the linearized data. The results of these analyses are presented in more detail in the following sections. In the following subsections, it will be shown that this approach can be used to produce an analytical relationship between the probability of negative obstacle detection and overall fuel usage for a swarm of AGV. This approach for deriving the mathematical relationship will be generally applicable for all swarm-based systems and presents a method for evaluating one relative tradeoff for AGV teaming—that is, the value of adding more robots to a team versus the relative fuel cost incurred by adding more AGV. Tradeoff models of this nature are essential for optimizing complex systems like AGV teams.

One way to interpret the observed trend for the negative obstacle detection rate is to compare to the “expected” rate based on the predictions of an analytical model. For many obstacles, the probability of detection by a particular sensor, p_d, is a function of the range (R), that is, p_d(R).

For analyzing the fuel usage from the combined data from experiments 1 and 2, it is found that $αfv=1$ yields the best fit. The results are plotted in Fig. 12.

For the negative obstacle detection rate, it is found that the combined data are best fit by $αδd=−1.55$⁠. The results of this fit for the combined data are shown in Fig. 13.

This model is specific to this particular AGV team and detection tasks. However, the basic steps followed to derive this model from the data are applicable to any AGV swarm. These steps include (1) developing a linearized model for detection rate of the target of interest which relates the AGV team areal density to the probability of detection for the system, (2) developing a model for fuel usage as vehicles are added to the swarm, and (3) relating these two models based on the intended problem size to develop a prediction for the performance tradeoff, as presented in Eq. (23).

In Sec. 5.2.2, it was stated that TTC statistics follow a lognormal distribution, as opposed to a normal distribution. While many works mistakenly use normal statistics to analyze results, in this section it is shown why proper statistical treatment is necessary. Figure 14 shows the probability distribution of finish times in the 10 vehicle scenario of experiment 2. This subset of data features 98 TTC points, excluding the two failed tests which did not complete the scenario.

Figure 14 compares the fit to the data using lognormal statistics (solid line) versus normal statistics (dashed line). Clearly, the lognormal statistics used in this work fit the observations better, reproducing the asymmetrical tail of the observed distribution better than the symmetric normal distribution. This observation is typical for TTC data where the symmetric normal distribution overestimates the number of observations below the mean and underestimates the observations above the mean. Noting that the other measurements of experiments 1 and 2 also fit this trend, the choice of lognormal statistics is validated by observation.

In this work, a simulation framework for testing of large-scale, off-road swarms of passenger-sized of autonomous vehicles was presented. This framework presented several key developments, including the use of a high-fidelity, physics-based simulation tool to analyze swarm robotics in realistic off-road terrain, the utilization of distributed simulation, and the development of appropriate metrics and statistical analysis techniques for swarm robotics.

By using negative obstacle detection as a performance metric, a clear relationship between performance and fuel use was found as a function of the number of vehicles in the swarm. Additionally, the statistical approach for evaluating performance was validated by the observations. This work was the first of its kind to study large (>20) numbers of AGV operating collaboratively in realistic off-road terrain.

Future will focus on developing more advanced coordination algorithms for the swarm, including biologically inspired algorithms. The MPI communication architecture for shared map data will be improved to improve scaling, and additional AGV performance metrics will also be evaluated.

The research described and the resulting data presented herein, unless otherwise noted, were funded under PE 0602784A, Project T53 “Military Engineering Applied Research,” Task 11.3 under Contract No. W56HZV-17-C-0095, managed by the U.S. Army Combat Capabilities Development Command (CCDC) and the Engineer Research and Development Center (ERDC). The work described in this document was conducted at the Center for Advanced Vehicular Systems, Mississippi State University. Permission was granted by ERDC to publish this information.

There are no conflicts of interest.

The datasets generated and supporting the findings of this article are obtainable from the corresponding author upon reasonable request.