Distributed Bayesian Filtering using Logarithmic Opinion Pool for Dynamic Sensor Networks

The discrete-time Distributed Bayesian Filtering (DBF) algorithm is presented for the problem of tracking a target dynamic model using a time-varying network of heterogeneous sensing agents. In the DBF algorithm, the sensing agents combine their normalized likelihood functions in a distributed manner using the logarithmic opinion pool and the dynamic average consensus algorithm. We show that each agent's estimated likelihood function globally exponentially converges to an error ball centered on the joint likelihood function of the centralized multi-sensor Bayesian filtering algorithm. We rigorously characterize the convergence, stability, and robustness properties of the DBF algorithm. Moreover, we provide an explicit bound on the time step size of the DBF algorithm that depends on the time-scale of the target dynamics, the desired convergence error bound, and the modeling and communication error bounds. Furthermore, the DBF algorithm for linear-Gaussian models is cast into a modified form of the Kalman information filter. The performance and robust properties of the DBF algorithm are validated using numerical simulations

Probabilistic and Distributed Control of a Large-Scale Swarm of Autonomous Agents

We present a novel method for guiding a large-scale swarm of autonomous agents into a desired formation shape in a distributed and scalable manner. Our Probabilistic Swarm Guidance using Inhomogeneous Markov Chains (PSG-IMC) algorithm adopts an Eulerian framework, where the physical space is partitioned into bins and the swarm's density distribution over each bin is controlled. Each agent determines its bin transition probabilities using a time-inhomogeneous Markov chain. These time-varying Markov matrices are constructed by each agent in real-time using the feedback from the current swarm distribution, which is estimated in a distributed manner. The PSG-IMC algorithm minimizes the expected cost of the transitions per time instant, required to achieve and maintain the desired formation shape, even when agents are added to or removed from the swarm. The algorithm scales well with a large number of agents and complex formation shapes, and can also be adapted for area exploration applications. We demonstrate the effectiveness of this proposed swarm guidance algorithm by using results of numerical simulations and hardware experiments with multiple quadrotors.Comment: Submitted to IEEE Transactions on Robotic

Distributed Estimation using Bayesian Consensus Filtering

We present the Bayesian consensus filter (BCF) for tracking a moving target using a networked group of sensing agents and achieving consensus on the best estimate of the probability distributions of the target’s states. Our BCF framework can incorporate nonlinear target dynamic models, heterogeneous nonlinear measurement models, non-Gaussian uncertainties, and higher-order moments of the locally estimated posterior probability distribution of the target’s states obtained using Bayesian filters. If the agents combine their estimated posterior probability distributions using a logarithmic opinion pool, then the sum of Kullback–Leibler divergences between the consensual probability distribution and the local posterior probability distributions is minimized. Rigorous stability and convergence results for the proposed BCF algorithm with single or multiple consensus loops are presented. Communication of probability distributions and computational methods for implementing the BCF algorithm are discussed along with a numerical example

Nonlinear Attitude Control of Spacecraft with a captured asteroid

One of the main control challenges of National Aeronautics and Space Administration’s proposed Asteroid Redirect Mission (ARM) is to stabilize and control the attitude of the spacecraft-asteroid combination in the presence of large uncertainty in the physical model of a captured asteroid. We present a new robust nonlinear tracking control law that guarantees global exponential convergence of the system’s attitude trajectory to the desired attitude trajectory. In the presence of modeling errors and disturbances, this control law is finite-gain L_p stable and input-to-state stable. We also present a few extensions of this control law, such as exponential tracking control on SO(3) and integral control, and show its relation to the well-known tracking control law for Euler-Lagrangian systems. We show that the resultant disturbance torques for control laws that use feed-forward cancellation is comparable to the maximum control torque of the conceptual ARM spacecraft and such control laws are therefore not suitable. We then numerically compare the performance of multiple viable attitude control laws, including the robust nonlinear tracking control law, nonlinear adaptive control, and derivative plus proportional-derivative linear control. We conclude that under very small modeling uncertainties, which can be achieved using online system identification, the robust nonlinear tracking control law that guarantees globally exponential convergence to the fuel-optimal reference trajectory is the best strategy as it consumes the least amount of fuel. On the other hand, in the presence of large modeling uncertainties and actuator saturations, a simple derivative plus proportional-derivative (D+PD) control law is effective, and the performance can be further improved by using the proposed nonlinear tracking control law that tracks a (D+PD)-control-based desired attitude trajectory. We conclude this paper with specific design guidelines for the ARM spacecraft for efficiently stabilizing a tumbling asteroid and spacecraft combination

Novel probabilistic and distributed algorithms for guidance, control, and nonlinear estimation of large-scale multi-agent systems

Multi-agent systems are widely used for constructing a desired formation shape, exploring an area, surveillance, coverage, and other cooperative tasks. This dissertation introduces novel algorithms in the three main areas of shape formation, distributed estimation, and attitude control of large-scale multi-agent systems. In the first part of this dissertation, we address the problem of shape formation for thousands to millions of agents. Here, we present two novel algorithms for guiding a large-scale swarm of robotic systems into a desired formation shape in a distributed and scalable manner. These probabilistic swarm guidance algorithms adopt an Eulerian framework, where the physical space is partitioned into bins and the swarm's density distribution over each bin is controlled using tunable Markov chains. In the first algorithm - Probabilistic Swarm Guidance using Inhomogeneous Markov Chains (PSG-IMC) - each agent determines its bin transition probabilities using a time-inhomogeneous Markov chain that is constructed in real-time using feedback from the current swarm distribution. This PSG-IMC algorithm minimizes the expected cost of the transitions required to achieve and maintain the desired formation shape, even when agents are added to or removed from the swarm. The algorithm scales well with a large number of agents and complex formation shapes, and can also be adapted for area exploration applications. In the second algorithm - Probabilistic Swarm Guidance using Optimal Transport (PSG-OT) - each agent determines its bin transition probabilities by solving an optimal transport problem, which is recast as a linear program. In the presence of perfect feedback of the current swarm distribution, this algorithm minimizes the given cost function, guarantees faster convergence, reduces the number of transitions for achieving the desired formation, and is robust to disturbances or damages to the formation. We demonstrate the effectiveness of these two proposed swarm guidance algorithms using results from numerical simulations and closed-loop hardware experiments on multiple quadrotors. In the second part of this dissertation, we present two novel discrete-time algorithms for distributed estimation, which track a single target using a network of heterogeneous sensing agents. The Distributed Bayesian Filtering (DBF) algorithm, the sensing agents combine their normalized likelihood functions using the logarithmic opinion pool and the discrete-time dynamic average consensus algorithm. Each agent's estimated likelihood function converges to an error ball centered on the joint likelihood function of the centralized multi-sensor Bayesian filtering algorithm. Using a new proof technique, the convergence, stability, and robustness properties of the DBF algorithm are rigorously characterized. The explicit bounds on the time step of the robust DBF algorithm are shown to depend on the time-scale of the target dynamics. Furthermore, the DBF algorithm for linear-Gaussian models can be cast into a modified form of the Kalman information filter. In the Bayesian Consensus Filtering (BCF) algorithm, the agents combine their estimated posterior pdfs multiple times within each time step using the logarithmic opinion pool scheme. Thus, each agent's consensual pdf minimizes the sum of Kullback-Leibler divergences with the local posterior pdfs. The performance and robust properties of these algorithms are validated using numerical simulations. In the third part of this dissertation, we present an attitude control strategy and a new nonlinear tracking controller for a spacecraft carrying a large object, such as an asteroid or a boulder. If the captured object is larger or comparable in size to the spacecraft and has significant modeling uncertainties, conventional nonlinear control laws that use exact feed-forward cancellation are not suitable because they exhibit a large resultant disturbance torque. The proposed nonlinear tracking control law guarantees global exponential convergence of tracking errors with finite-gain Lp stability in the presence of modeling uncertainties and disturbances, and reduces the resultant disturbance torque. Further, this control law permits the use of any attitude representation and its integral control formulation eliminates any constant disturbance. Under small uncertainties, the best strategy for stabilizing the combined system is to track a fuel-optimal reference trajectory using this nonlinear control law, because it consumes the least amount of fuel. In the presence of large uncertainties, the most effective strategy is to track the derivative plus proportional-derivative based reference trajectory, because it reduces the resultant disturbance torque. The effectiveness of the proposed attitude control law is demonstrated by using results of numerical simulation based on an Asteroid Redirect Mission concept. The new algorithms proposed in this dissertation will facilitate the development of versatile autonomous multi-agent systems that are capable of performing a variety of complex tasks in a robust and scalable manner

Effect of iron oxide and gold nanoparticles on bacterial growth leading towards biological application

<p>Abstract</p> <p>Background</p> <p>Nanoparticle-metal oxide and gold represents a new class of important materials that are increasingly being developed for use in research and health related activities. The biological system being extremely critical requires the fundamental understanding on the influence of inorganic nanoparticles on cellular growth and functions. Our study was aimed to find out the effect of iron oxide (Fe₃O₄), gold (Au) nanoparticles on cellular growth of <it>Escherichia coli </it>(<it>E. coli</it>) and also try to channelize the obtained result by functionalizing the Au nanoparticle for further biological applications.</p> <p>Result</p> <p>Fe₃O₄and Au nanoparticles were prepared and characterized using Transmission electron microscopy (TEM) and Dynamic Light Scattering (DLS). Preliminary growth analysis data suggest that the nanoparticles of iron oxide have an inhibitory effect on E. coli in a concentration dependant manner, whereas the gold nanoparticle directly showed no such activity. However the phase contrast microscopic study clearly demonstrated that the effect of both Fe₃O₄and Au nanoparticle extended up to the level of cell division which was evident as the abrupt increase in bacterial cell length. The incorporation of gold nanoparticle by bacterial cell was also observed during microscopic analysis based on which glutathione functionalized gold nanoparticle was prepared and used as a vector for plasmid DNA transport within bacterial cell.</p> <p>Conclusion</p> <p>Altogether the study suggests that there is metal nanoparticle-bacteria interaction at the cellular level that can be utilized for beneficial biological application but significantly it also posses potential to produce ecotoxicity, challenging the ecofriendly nature of nanoparticles.</p

Feedback-Based Inhomogeneous Markov Chain Approach To Probabilistic Swarm Guidance

This paper presents a novel and generic distributed swarm guidance algorithm using inhomogeneous Markov chains that guarantees superior performance over existing homogeneous Markov chain based algorithms, when the feedback of the current swarm distribution is available. The probabilistic swarm guidance using inhomogeneous Markov chain (PSG–IMC) algorithm guarantees sharper and faster convergence to the desired formation or unknown target distribution, minimizes the number of transitions for achieving and maintaining the formation even if the swarm is damaged or agents are added/removed from the swarm, and ensures that the agents settle down after the swarm’s objective is achieved. This PSG–IMC algorithm relies on a novel technique for constructing Markov matrices for a given stationary distribution. This technique incorporates the feedback of the current swarm distribution, minimizes the coefficient of ergodicity and the resulting Markov matrix satisfies motion constraints. This approach is validated using Monte Carlo simulations of the PSG–IMC algorithm for pattern formation and goal searching application