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Nothing about the estimation or control framework relies upon the sensor modality, so long as we are able to create detection, measurement, and clutter models for the sensor. To verify this, we conduct a nal series of simulation experiments in which robots are equipped with noisy, range-only sensors.

Sensor Models

The range-only sensor parameters used in this case are not based on a particular physical sensor, but rather seek to capture the general behavior of an RF-based range sensor. Fig- ure 64 shows the detection model for the sensors, pd(x | q), which decays steadily with

distance. The measurements have zero-mean Gaussian noise, soz ∼ N(|x−q|, σ2), where

σ= 1 m. The measurement noise is relatively high compared to the bearing-only sensor, so

we expect the rate of information gain to be lower. Clutter detections occur uniformly over the sensor footprint, with a clutter PHD c(z) = µ/rmax, where µ= 0.1 is the clutter rate

and rmax= 5 mis the maximum range of the sensor.

Results

Most of the simulation parameters are kept constant: a team of 3 robots begin at location 1 in Levine, and use planning mode 2 with the same length scales as the bearing-only sensor. The termination criterion is = 4 to account for the much coarser localization that the range-only sensor is able to achieve, due to the high measurement noise.

X (m) Y (m) 1 10 20 30 40 50 5 10 15 20 25 30 35 40 45 50 55 (a) Floorplan Completion time [s] 0 500 1000 1500 2000 2500 3000 3500 (b) Completion times % of exploration Expected # targets 0 0.2 0.4 0.6 0.8 1 0 20 40 60 80 100

(c) Average expected cardinality as a func- tion of normalized time

% of exploration Entropy [nats] 0 0.2 0.4 0.6 0.8 1 0 100 200 300 400 500 600 700

(d) Average target set entropy as a function of normalized time

Figure 41: Plots of the performance for a team of three simulated robots exploring a second en- vironment using planning mode 2. (a) Shows the oorplan of the complex, indoor environment used in simulations. The robots begin in room 1 in the upper left corner. (b) Shows the spread of time to completion. (c) Shows the mean (solid lines) and standard deviation (shaded regions) of the expected cardinality across runs as a fraction of the total time with the true cardinality shown (dashed black line). (d) Shows the mean (solid lines) and standard deviation (shaded regions) of the entropy across runs as a fraction of the total time with the ideal value shown (dashed black line).

Figure 42 shows the resulting completion times, cardinality estimates, and target set entropies, as well as an example localization result. As is expected, the system takes longer to complete the localization task, and the resulting target estimates are not as precise as with the bearing-only sensor. The team is able to discover the approximate locations of all of the targets, though there are a number of false positive targets that appear in the nal PHD estimate. In particular, it is dicult for the team to eliminate the false target near (15, 18) m as this is only observable from several meters below and there are true targets nearby at very similar ranges to the false target. Despite the errors in target localization, the team is still able to accurately estimate the true target cardinality.

4.6 Conclusion

In this chapter, we proposed a novel receding-horizon, information-based controller for ac- tively detecting and localizing an unknown number of targets using a small team of au- tonomous mobile robots. The robots are equipped with unreliable sensors, failing to detect targets within the eld of view, returning false positive detections, and being unable to uniquely identify true targets. Despite this, the PHD lter simultaneously estimates the number of targets and their locations, avoiding the need to explicitly consider data asso- ciation and providing a scalable approach for various team sizes, sensor modalities, and environments.

The controller, which maximizes the mutual information between the target set and the future binary measurements of the team, hedges against highly uninformative actions in a computationally tractable manner. We provide several variations on the controller: concurrently or sequentially planning across robots in the team and length scales of actions, planning in a decentralized fashion, and comparing the performance of the PHD and CPHD lters. The PHD lter, somewhat counterintuitively, outperforms the CPHD lter when the sensor has a nite footprint, with the CPHD lter performing poorly in terms of the cardinality estimation. The eectiveness of our control strategy is demonstrated through a series of hardware experiments with small teams of ground robots exploring an indoor oce

Range [m] Probability of detection 0 1 2 3 4 5 0 0.2 0.4 0.6 0.8 1

(a) Range-only detection model Completion time [s] 0 200 400 600 800 (b) Completion times % of exploration Expected # targets 0 0.2 0.4 0.6 0.8 1 0 5 10 15 20 25 30 35

(c) Average expected cardinality as a func- tion of normalized time

% of exploration Entropy [nats] 0 0.2 0.4 0.6 0.8 1 0 50 100 150 200 250

(d) Average target set entropy as a function of normalized time X [m] Y [m] 5 10 15 20 25 2 4 6 8 10 12 14 16 18

(e) Estimated target locations

Figure 42: Plots of the performance for a team of three simulated robots equipped with range-only sensors exploring the Levine environment using planning mode 2. (a) Shows the detection model used in the simulation trials. (b) Shows the spread of time to completion. (c) Shows the mean (solid lines) and standard deviation (shaded regions) of the expected cardinality across runs as a fraction of the total time with the true cardinality shown (dashed black line). (d) Shows the mean (solid lines) and standard deviation (shaded regions) of the entropy across runs as a fraction of the total time with the ideal value shown (dashed black line). (e) Shows the true (red diamonds) and estimated (blue dots) target locations, with dot size proportional to the number of targets at that location.

environment. A series of simulated experiments show that the proposed approach performs well in a variety of settings: with low and high target cardinality, in multiple environments, and with multiple sensor modalities. The proposed control law also signicantly outperforms a random walk through the environment without signicantly increasing the computational load. The team is able to autonomously cease exploration once their condence in the target estimates is suciently high.

Chapter 5

Active Detection, Localization, and

Tracking of Moving Targets

Target tracking is a fundamental problem in robotics research and has been the subject of detailed studies over the years. In this chapter, consider the problem of tracking an unknown and dynamic number of mobile targets with a team of robots. We present a greedy algorithm for assigning trajectories to the robots that maximize submodular objective functions and prove that this is a 2-approximation. We examine two such objective functions: the mutual information between the estimated target positions and future measurements from the robots, and the expected number of targets detected by the robot team. We provide extensive simulation evaluations using a real-world dataset. The research in this chapter was originally published in [28].

5.1 Introduction

Target detection, localization, and tracking has many applications including search-and- rescue [36], wildlife tracking [98], surveillance [42], and building smart cities [63]. Conse- quently, such problems have long been a subject of study in the robotics community. Target tracking typically refers to two types of tasks: estimating the trajectories of the targets from the sensor data, and actively controlling the motion of the robotic sensors to gather

the data. We address both types of problems for the case of multiple, moving targets. Unlike most existing work, we study the case of tracking an unknown and varying number of indistinguishable targets. This introduces a number of challenges. First, we cannot maintain a separate estimator for each target, since the required number of estimators is unknown. Second, we must account for the fact that targets appear and disappear from the environment. Third, we cannot maintain a history of the target positions because we cannot uniquely identify individual targets, making prediction dicult. Finally, the system must be capable of handling false positive and false negative detections and unknown data association in addition to sensor noise. Despite these challenges, we present positive results towards solving the problem.

An important consideration for target tracking is the motion model for the targets. A number of parametric motion models have been proposed in the literature (see [61] for a detailed survey). We employ a data-driven technique to extract the motion model, instead of assuming any parametric form. Specically, we use Gaussian Process (GP) regression to learn a map of velocity vectors for the targets, similar to Joseph et al. [49]. Additionally, we show how to model the appearance and disappearance of targets within the environment. Next, we present a control policy to assign trajectories for all robots in order to maximize the objective function over a receding horizon. We study two objective functions using the PHD lter: mutual information and the expected number of detections by the robots. We show that both objective functions are submodular, and use a result based on [99] to prove that our greedy control policy is a 2-approximation.

In addition to the theoretical analysis we oer, we evaluate our algorithm using simu- lated experiments. While our framework may be applied to a number of robot and sensor models, for the purposes of testing we restrict our attention to xed winged aerial robots with downward facing cameras. We use a real-world taxi motion dataset from [80] for the targets and to verify our models. The simulation results reveal that robot teams using the information-based control objective track a smaller number of targets with higher precision compared to teams that maximize the expected number of detections.