We provide a framework for the assignment of multiple robots to goal locations, when robot travel times are uncertain. Our premise is that time is the most valuable asset in the system. Hence, we make use of redundant robots to counter the effect of uncertainty and minimize the average waiting time at destinations. We apply our framework to transport networks represented as graphs, and consider uncertainty in the edge costs (i.e., travel time). Since solving the redundant assignment problem is strongly NP-hard, we exploit structural properties of our problem to propose a polynomial-time solution with provable sub-optimality bounds. Our method uses distributive aggregate functions, which allow us to efficiently (i.e., incrementally) compute the effective cost of assigning redundant robots. Experimental results on random graphs show that the deployment of redundant robots through our method reduces waiting times at goal locations, when edge traversals are uncertain.
Consider a setting where robots must visit sites represented as nodes in a graph, but each robot may fail when traversing an edge. The goal is to find a set of paths for a team of robots which maximizes the expected number of nodes collectively visited, while guaranteeing that the paths satisfy a notion of “independence” formalized by a matroid (e.g. limits on team size, number of visits to regions), and that the probabilities that each robot survives to its destination are above a given threshold. We call this problem the Matroid Team Surviving Orienteers (MTSO) problem, which has broad applications such as environmental monitoring in risky regions and search and rescue in dangerous conditions. We present the MTSO formally and detail numerous examples of matroids in a path planning context. We then propose an approximate greedy algorithm for selecting a feasible set of paths and prove that the value of the output is within a factor p s p s + λ of the optimum, where p s is the per-robot survival probability threshold and 1 λ ≤ 1 is the approximation factor of an oracle routine for the well known orienteering problem. We demonstrate the efficiency of our approach by applying it to a scenario where a team of robots must gather information while avoiding pirates in the Coral Triangle. We consider the problem of scheduling a set of sensors to observe the state of a discrete-time linear system subject to a limited energy budget. Our goal is to devise a sensor schedule that minimizes the mean squared error (MSE) of an optimal estimator (i.e., the Kalman Filter). Both the minimum-MSE and the minimum-cardinality optimal sensor scheduling problems are inherently combinatorial, and computationally intractable. We remedy the combinatorial complexity by using a greedy heuristic; the greedy heuristic is guaranteed to return near-optimal solutions when minimizing supermodular objectives. While it is known that the MSE is not supermodular (with counterexamples available in literature), we provide conditions on the prior information matrix and on the observation matrix under which supermodularity holds. More specifically, we require the prior information matrix to be a strictly-diagonally-dominant M-matrix (plus an extra technical requirement on its inverse). Empirical results confirm that random M-matrices lead to supermodular problems, while this is not the case for generic prior information matrices. M-matrices naturally arise in estimation problems over networks and we provide a practical application of our findings to an energy-constrained multi robot localization problem.  The need for efficient monitoring of spatio-temporal dynamics in large environmental applications, such as the water quality monitoring in rivers and lakes, motivates the use of robotic sensors in order to achieve sufficient spatial coverage. Typically, these robots have bounded resources, such as limited battery or limited amounts of time to obtain measurements. Thus, careful coordination of their paths is required in order to maximize the amount of information collected, while respecting the resource constraints. In this paper, we present an efficient approach for near-optimally solving the NP-hard optimization problem of planning such informative paths. In particular, we first develop eSIP (efficient Single-robot Informative Path planning), an approximation algorithm for optimizing the path of a single robot. Hereby, we use a Gaussian Process to model the underlying phenomenon, and use the mutual information between the visited locations and remainder of the space to quantify the amount of information collected. We prove that the mutual information collected using paths obtained by using eSIP is close to the information obtained by an optimal solution. We then provide a general technique, sequential allocation, which can be used to extend any single robot planning algorithm, such as eSIP, for the multi-robot problem. This procedure approximately generalizes any guarantees for the single-robot problem to the multi-robot case. We extensively evaluate the effectiveness of our approach on several experiments performed infield for two important environmental sensing applications, lake and river monitoring, and simulation experiments performed using several real world sensor network data sets.