We introduce a distributed finite element algorithm that allows swarms of mobile robots to persistently monitor environmental quantities such as temperature or salinity. The robots deploy themselves into the environment, covering the domain and dividing it into nonoverlapping regions. Each robot estimates the environment over its own region using local measurements and communication with nearby robots. The algorithm ensures that each robot's estimate constitutes a piece of a global estimate that spans the entire domain, fuses the whole swarm's measurements, and accounts for the spatial correlation between measurement and estimation locations. By incorporating spatial correlation without requiring the transmission of measurements or measurement locations, the algorithm decouples its communication requirements from the spatial statistics of the environment and enables robots with fixed capabilities to monitor environments with different spatial correlation lengths. Analysis and simulation demonstrate that, as the number of robots increases, the memory and communication requirements of each individual robot decrease until reaching a minimum, after which the resolution of the environmental model increases. Additional robots, therefore, add computational resources to the swarm rather than introducing extra computational burdens.

In wireless sensor networks, estimating a global parameter from locally obtained measurements via local interactions is known as the distributed parameter estimation problem. Solving these problems often require the deployment of distributed optimization algorithms that rely on a constant exchange of information among the sensor nodes. This makes such distributed algorithms vulnerable to attackers or malicious nodes that want to gain access to private information regarding the network. Based on the sliding mode control scheme, here we present a novel approach to infer sensitive information (e.g., gradient or private parameters of the local objective function) regarding a node of interest by intercepting the communication between the nodes. The effectiveness of the proposed approach is illustrated in a representative example of distributed event localization using an acoustic sensor network.

Average consensus estimators enable robots in a communication network to calculate the mean of their local inputs in a distributed manner. Many distributed control methods for robot swarms rely on these estimators. The performance of such estimators depends on their design and the network topology. For mobile sensor networks, this topology may be unknown, making it difficult to design average consensus estimators for optimal performance. We introduce a design method for proportional-integral (PI) average consensus estimators that decouples estimator synthesis from network topology. This method also applies to the more general internal model (IM) estimator, yielding extended PI estimators that improve convergence rates without increasing communication costs. In simulations over many geometric random graphs, the extended PI estimator consistently reduces the estimation error settling time by a factor of five.

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.

We consider the problem of multiple mobile sensor agents tracking the position of one or more moving targets. In our formulation, each agent maintains a target estimate, and each agent moves so as to maximize the expected information from its sensor, relative to the current uncertainty in the estimate. The novelty of our approach is that each agent need only communicate with one-hop neighbors in a communication network, resulting in a fully distributed and scalable algorithm, yet the performance of the system approximates that of a centralized optimal solution to the same problem. We provide two fully distributed algorithms based on one-time measurements and a Kalman filter approach, and we validate the algorithms with simulations.

This paper studies the effect of communication link weighting schemes and long-range connections in speeding convergence to consensus on the average of the inputs to agents in a sensor network. Linear programming and LMI solutions are provided for the problem of centralized optimization of communication weights considering the possibility of intermittent bounded communication delays. Heuristic weighting schemes that can be implemented in a distributed fashion are also studied. Consensus convergence time may also be reduced by introducing long-range interactions, creating a "small world" network

Passivity theory has been used for the past decade to derive stability conditions for human/machine interface applications. Demonstrating passivity of the haptic display implies stable and safe interaction for the human user. At the heart of the stability analysis is the physical dissipation provided by the haptic device, as it plays a key role in the design process for all components. This paper will derive the condition that the haptic device must satisfy in order to achieve passivity of the haptic display. These results will be used to investigate a general nonlinear device model.

Investigates the influence environment delay has on haptic systems. Work presented by the authors (1999) demonstrated that it is possible to account for environment delay (even though it is a non-passive behavior) and still achieve a stability result based on passivity concepts. The details were given for haptic systems with environments having impedance causality. This paper presents the companion results for haptic systems with environments having admittance causality, resulting in a slightly more complicated analysis. Although the main focus is on delay, the approach is valid for analysing any environment that exhibits non-passive behavior.

Design of haptic systems that guarantee stable interaction is a challenging task. Virtual environments are typically highly nonlinear-resulting in a nonpassive discrete-time model. This paper will investigate how nonlinear mass/spring/damper virtual environments can be designed to guarantee the absence of oscillations and other chaotic behavior in the signal presented to the human operator. In particular, delayed and nondelayed implementation of the mass/spring/damper virtual environment is considered, revealing a nonintuitive result with regard to the allowable local stiffness.

This paper derives conditions for the absence of oscillations for a parametrized class of nonlinear environments. This class includes discrete-time environments that can exhibit non-passive behavior. The motivation for considering non-passive discrete-time environments is based on the fact that an interesting class of passive continuous-time environments have non-passive discrete-time counterparts. A design methodology is introduced that provides relationships between the haptic device, virtual coupling and maximum negative stiffness exhibited by the environment.