We study two new informative path planning problems that are motivated by the use of aerial and ground robots in precision agriculture. The first problem, termed sampling traveling salesperson problem with neighborhoods (SAMPLINGTSPN), is motivated by scenarios in which unmanned ground vehicles (UGVs) are used to obtain time-consuming soil measurements. The input in SAMPLINGTSPN is a set of possibly overlapping disks. The objective is to choose a sampling location in each disk and a tour to visit the set of sampling locations so as to minimize the sum of the travel and measurement times. The second problem concerns obtaining the maximum number of aerial measurements using an unmanned aerial vehicle (UAV) with limited energy. We study the scenario in which the two types of robots form a symbiotic system-the UAV lands on the UGV, and the UGV transports the UAV between deployment locations. This paper makes the following contributions. First, we present an O((r _max )/(r _min )) approximation algorithm for SAMPLINGTSPN, where r _min and r _max are the minimum and maximum radii of input disks. Second, we show how to model the UAV planning problem using a metric graph and formulate an orienteering instance to which a known approximation algorithm can be applied. Third, we apply the two algorithms to the problem of obtaining ground and aerial measurements in order to accurately estimate a nitrogen map of a plot. Along with theoretical results, we present results from simulations conducted using real soil data and preliminary field experiments with the UAV.

The problem of target tracking with multiple robots consists of actively planning the motion of the robots to track the targets. A major challenge for practical deployments is to make the robots resilient to failures. In particular, robots may be attacked in adversarial scenarios, or their sensors may fail or get occluded. In this paper, we introduce planning algorithms for multi-target tracking that are resilient to such failures. In general, resilient target tracking is computationally hard. Contrary to the case where there are no failures, no scalable approximation algorithms are known for resilient target tracking when the targets are indistinguishable, or unknown in number, or with unknown motion model. In this paper we provide the first such algorithm, that also has the following properties: First, it achieves maximal resiliency, since the algorithm is valid for any number of failures. Second, it is scalable, as our algorithm terminates with the same running time as state-of-the-art algorithms for (non- resilient) target tracking. Third, it provides provable approximation bounds on the tracking performance, since our algorithm guarantees a solution that is guaranteed to be close to the optimal. We quantify our algorithm's approximation performance using a novel notion of curvature for monotone set functions subject to matroid constraints. Finally, we demonstrate the efficacy of our algorithm through MATLAB and Gazebo simulations, and a sensitivity analysis; we focus on scenarios that involve a known number of distinguishable targets.

In this paper, we study two sensor assignment problems for multitarget tracking with the goal of improving the observability of the underlying estimator. We consider various measures of the observability matrix as the assignment value function. We first study the general version where the sensors must form teams to track individual targets. If the value function is monotonically increasing and submodular, then a greedy algorithm yields a $1/2$ –approximation. We then study a restricted version where exactly two sensors must be assigned to each target. We present a $1/3$ –approximation algorithm for this problem, which holds for arbitrary value functions (not necessarily submodular or monotone). In addition to approximation algorithms, we also present various properties of observability measures. We show that the inverse of the condition number of the observability matrix is neither monotone nor submodular, but present other measures that are. Specifically, we show that the trace and rank of the symmetric observability matrix are monotone and submodular and the log determinant of the symmetric observability matrix is monotone and submodular when the matrix is nonsingular. If the target’s motion model is not known, the inverse cannot be computed exactly. Instead, we present a lower bound for distance sensors. In addition to theoretical results, we evaluate our results empirically through simulations.

We study the problem of reducing the amount of communication in decentralized target tracking. We focus on the scenario, where a team of robots is allowed to move on the boundary of the environment. Their goal is to seek a formation so as to best track a target moving in the interior of the environment. The robots are capable of measuring distances to the target. Decentralized control strategies have been proposed in the past, which guarantees that the robots asymptotically converge to the optimal formation. However, existing methods require that the robots exchange information with their neighbors at all time steps. Instead, we focus on decentralized strategies to reduce the amount of communication among robots. We propose a self-triggered communication strategy that decides when a particular robot should seek up-to-date information from its neighbors and when it is safe to operate with possibly outdated information. We prove that this strategy converges asymptotically to the desired formation when the target is stationary. For the case of a mobile target, we use a decentralized Kalman filter with covariance intersection to share the beliefs of neighboring robots. We evaluate all the approaches through simulations and a proof-of-concept experiment.