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

Target Assignment in Robotic Networks: Distance Optimality Guarantees and Hierarchical Strategies

We study the problem of multi-robot target assignment to minimize the total distance traveled by the robots until they all reach an equal number of static targets. In the first half of the paper, we present a necessary and sufficient condition under which true distance optimality can be achieved for robots with limited communication and target-sensing ranges. Moreover, we provide an explicit, non-asymptotic formula for computing the number of robots needed to achieve distance optimality in terms of the robots' communication and target-sensing ranges with arbitrary guaranteed probabilities. The same bounds are also shown to be asymptotically tight. In the second half of the paper, we present suboptimal strategies for use when the number of robots cannot be chosen freely. Assuming first that all targets are known to all robots, we employ a hierarchical communication model in which robots communicate only with other robots in the same partitioned region. This hierarchical communication model leads to constant approximations of true distance-optimal solutions under mild assumptions. We then revisit the limited communication and sensing models. By combining simple rendezvous-based strategies with a hierarchical communication model, we obtain decentralized hierarchical strategies that achieve constant approximation ratios with respect to true distance optimality. Results of simulation show that the approximation ratio is as low as 1.4

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

Exponential Stability Region Estimates for the State-Dependent Riccati Equation Controllers

We investigate the nonlinear exponential stability of the State-Dependent Riccati Equation (SDRE)-based control. The SDRE technique is a nonlinear control method, which has emerged since the mid 1990's and has been applied to a wide range of nonlinear control problems. Despite the systematic method of SDRE, it is difficult to prove stability because the general analytic solution to the SDRE is not known. Some notable prior work has shown local asymptotic stability of SDRE by using numerical and analytical methods. In this paper, we introduce a new strategy, based on contraction analysis, to estimate the exponential stability region for SDRE controlled systems. Examples demonstrate the superiority of the proposed method

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

Bio-Inspired Adaptive Cooperative Control of Heterogeneous Robotic Networks

We introduce a new adaptive cooperative control strategy for robotic networks comprised of heterogeneous members. The proposed feedback synchronization exploits an active parameter adaptation strategy as opposed to adaptive parameter estimation of adaptive control theory. Multiple heterogeneous robots or vehicles can coordinate their motions by parameter adaptation analogous to bio-genetic mutation and adaptation. In contrast with fixed gains used by consensus theory, both the tracking control and diffusive coupling gains are automatically computed based on the adaptation law, the synchronization errors, and the tracking errors of heterogeneous robots. The optimality of the proposed adaptive cooperative control is studied via inverse optimal control theory. The proposed adaptive cooperative control can be applied to any network structure. The stability proof, by using a relatively new nonlinear stability tool, contraction theory, shows globally asymptotically synchronized motion of a heterogeneous robotic network. This adaptive cooperative control can be widely applied to cooperative control of unmanned aerial vehicles (UAVs), formation flying spacecraft, and multi-robot systems. Results of the simulation show the effectiveness of the proposed adaptive cooperative control laws especially for a network comprised of heterogeneous members

Switched systems with multiple invariant sets

This paper explores dwell time constraints on switched systems with multiple, possibly disparate invariant limit sets. We show that, under suitable conditions, trajectories globally converge to a superset of the limit sets and then remain in a second, larger superset. We show the effectiveness of the dwell-time conditions by using examples of switching limit cycles commonly found in robotic locomotion and flapping flight