In this paper, we present controllers that enable mobile robots to persistently monitor or sweep a changing environment. The environment is modeled as a field that is defined over a finite set of locations. The field grows linearly at locations that are not within the range of a robot and decreases linearly at locations that are within range of a robot. We assume that the robots travel on given closed paths. The speed of each robot along its path is controlled to prevent the field from growing unbounded at any location. We consider the space of speed controllers that are parametrized by a finite set of basis functions. For a single robot, we develop a linear program that computes a speed controller in this space to keep the field bounded, if such a controller exists. Another linear program is derived to compute the speed controller that minimizes the maximum field value over the environment. We extend our linear program formulation to develop a multirobot controller that keeps the field bounded. We characterize, both theoretically and in simulation, the robustness of the controllers to modeling errors and to stochasticity in the environment.
Autonomous mobile sensor networks are employed to measure large-scale environmental fields. Yet an optimal strategy for mission design addressing both the cooperative motion control and the cooperative sensing is still an open problem. We develop strategies for multiple sensor platforms to explore a noisy scalar field in the plane. Our method consists of three parts. First, we design provably convergent cooperative Kalman filters that apply to general cooperative exploration missions. Second, we present a novel method to determine the shape of the platform formation to minimize error in the estimates and design a cooperative formation control law to asymptotically achieve the optimal formation shape. Third, we use the cooperative filter estimates in a provably convergent motion control law that drives the center of the platform formation to move along level curves of the field. This control law can be replaced by control laws enabling other cooperative exploration motion, such as gradient climbing, without changing the cooperative filters and the cooperative formation control laws. Performance is demonstrated on simulated underwater platforms in simulated ocean fields.  This work deals with trajectory optimization for a robotic sensor network sampling a spatio-temporal random field. We examine the optimal sampling problem of minimizing the maximum predictive variance of the estimator over the space of network trajectories. This is a high-dimensional, multi-modal, nonsmooth optimization problem, known to be NP-hard even for static fields and discrete design spaces. Under an asymptotic regime of near-independence between distinct sample locations, we show that the solutions to a novel generalized disk-covering problem are solutions to the optimal sampling problem. This result effectively transforms the search for the optimal trajectories into a geometric optimization problem. Constrained versions of the latter are also of interest as they can accommodate trajectories that satisfy a maximum velocity restriction on the robots. We characterize the solution for the unconstrained and constrained versions of the geometric optimization problem as generalized multicircumcenter trajectories, and provide algorithms which enable the network to find them in a distributed fashion. Several simulations illustrate our results. We describe a framework for the design of collective behaviors for groups of identical mobile agents. The approach is based on decentralized simultaneous estimation and control, where each agent communicates with neighbors and estimates the global performance properties of the swarm needed to make a local control decision. Challenges of the approach include designing a control law with desired convergence properties, assuming each agent has perfect global knowledge; designing an estimator that allows each agent to make correct estimates of the global properties needed to implement the controller; and possibly modifying the controller to recover desired convergence properties when using the estimates of global performance. We apply this framework to the problem of controlling the moment statistics describing the location and shape of a swarm. We derive conditions which guarantee that the formation statistics are driven to desired values, even in the presence of a changing network topology. Exploration involving mapping and concurrent localization in an unknown environment is a pervasive task in mobile robotics. In general, the accuracy of the mapping process depends directly on the accuracy of the localization process. This paper address the problem of maximizing the accuracy of the map building process during exploration by adaptively selecting control actions that maximize localisation accuracy. The map building and exploration task is modeled using an Occupancy Grid (OG) with concurrent localisation performed using a feature-based Simultaneous Localisation And Mapping (SLAM) algorithm. Adaptive sensing aims at maximizing the map information by simultaneously maximizing the expected Shannon information gain (Mutual Information) on the OG map and minimizing the uncertainty of the vehicle pose and map feature uncertainty in the SLAM process. The resulting map building system is demonstrated in an indoor environment using data from a laser scanner mounted on a mobile platform. We consider the problem of optimizing the trajectory of a mobile sensor with perfect localization whose task is to estimate a stochastic, perhaps multidimensional field modeling the environment. When the estimator is the Kalman filter, and for certain classes of objective functions capturing the informativeness of the sensor paths, the sensor trajectory optimization problem is a deterministic optimal control problem. This estimation problem arises in many applications besides the field estimation problem, such as active mapping with mobile robots. The main difficulties in solving this problem are computational, since the Gaussian process of interest is usually high dimensional. We review some recent work on this problem and propose a suboptimal non-greedy trajectory optimization scheme with a manageable computational cost, at least in static field models based on sparse graphical models. This paper considers robotic sensor networks performing spatially-distributed estimation tasks. A robotic sensor network is deployed in an environment of interest, and takes successive point measurements of a dynamic physical process modeled as a spatio-temporal random field. Taking a Bayesian perspective on the Kriging interpolation technique from geostatistics, we design the distributed Kriged Kalman filter for predictive inference of the random field and of its gradient. The proposed algorithm makes use of a novel distributed strategy to compute weighted least squares estimates when measurements are spatially correlated. This strategy results from the combination of the Jacobi overrelaxation method with dynamic average consensus algorithms. As an application of the proposed algorithm, we design a gradient ascent cooperative strategy and analyze its convergence properties in the absence of measurement errors via stochastic Lyapunov functions. We illustrate our results in simulation. Cooperating mobile sensors can be used to model environmental functions such as the temperature or salinity of a region of ocean. In this paper, we adopt an optimal filtering approach to fusing local sensor data into a global model of the environment. Our approach is based on the use of proportional-integral (PI) average consensus estimators, whereby information from each mobile sensor diffuses through the communication network. As a result, this approach is scalable and fully decentralized, and allows changing network topologies and anonymous agents to be added and subtracted at any time. We also derive control laws for mobile sensors to move to maximize their sensory information relative to current uncertainties in the model. The approach is demonstrated by simulations including modeling ocean temperature.