Chetan D. Pahlajani

Stochastic receding horizon control for robots with probabilistic state constraints

This paper presents a receding horizon control design for a robot subject to stochastic uncertainty, moving in a constrained environment. Instead of minimizing the expectation of a cost functional while ensuring satisfaction of probabilistic state constraints, we propose a two-stage solution where the path that minimizes the cost functional is planned deterministically, and a local stochastic optimal controller with exit constraints ensures satisfaction of probabilistic state constraints while following the planned path. This control design strategy ensures boundedness of errors around the reference path and collision-free convergence to the goal with probability one under the assumption of unbounded inputs. We show that explicit expressions for the control law are possible for certain cases. We provide simulation results for a point robot moving in a constrained two-dimensional environment under Brownian noise. The method can be extended to systems with bounded inputs, if a small nonzero probability of failure can be accepted.

Networked Decision Making for Poisson Processes With Applications to Nuclear Detection

This paper addresses a detection problem where a network of radiation sensors has to decide, at the end of a fixed time interval, if a moving target is a carrier of nuclear material. The problem entails determining whether or not a time-inhomogeneous Poisson process due to the moving target is buried in the recorded background radiation. In the proposed method, each of the sensors transmits once to a fusion center a locally processed summary of its information in the form of a likelihood ratio. The fusion center then combines these messages to arrive at an optimal decision in the Neyman-Pearson framework. The approach offers a pathway toward the development of novel fixed-interval detection algorithms that combine decentralized processing with optimal centralized decision making.

Probability of success in stochastic robot navigation with state feedback

The analysis in this paper applies to robots with dynamics described by a stochastic differential equation, which need to navigate in constrained environments. The approach offers a method to calculate the probability that a feedback control policy designed for the drift component of the dynamics, will succeed in allowing the robot to avoid collisions and converge to its navigation goal in the presence of stochastic (white) noise. The problem is formulated as an exit problem and known techniques in the field of stochastic processes are brought to bear to determine the probabilities that the stochastic process describing the motion of the robot will “exit” the workspace through a particular part of the boundary. We motivate the use of this analysis using a controller constructed using negative gradient of a navigation function and give the analytic solution for the case of a constrained but obstacle-free workspace.

Error probability bounds for nuclear detection

A collection of static and mobile radiation sensors is tasked with deciding, within a fixed time interval, whether a moving target carries radioactive material. Formally, this is a problem of detecting weak time-inhomogeneous Poisson signals (target radiation) concealed in another Poisson signal (naturally occurring background radiation). Each sensor locally processes its observations to form a likelihood ratio, which is transmitted once-at the end of the decision interval-to a fusion center. The latter combines the transmitted information to optimally (in the Neyman-Pearson sense) decide whether the measurements contain a radiation signal, or just noise. We provide a set of analytically derived upper bounds for the probabilities of false alarm and missed detection, which are used to design threshold tests without the need for computationally intensive Monte Carlo simulations. These analytical bounds couple the physical quantities of interest to facilitate planning the motion of the mobile sensors for minimizing the probability of missed detection. The network reconfigures itself in response to the target motion, to allow more accurate collective decisions within the given time interval. The approach is illustrated in numerical simulations, and its effectiveness demonstrated in experiments that emulate the statistics of nuclear emissions using a pulsed laser.

Decision making in sensor networks observing poisson processes

This paper addresses a detection problem where several spatially distributed sensors independently observe a time-inhomogeneous stochastic process. The task is to decide at the end of a fixed time interval between two hypotheses regarding the statistics of the observed process. In the proposed method, each of the sensors transmits once to a fusion center a locally processed summary of its information in the form of a likelihood ratio. The fusion center then combines these messages to arrive at an optimal decision in the Neyman-Pearson framework. The approach is motivated by applications arising in the detection of mobile radioactive sources, and it serves as a first step toward the development of novel fixed-interval detection algorithms that combine decentralized processing with optimal centralized decision making.

Optimal Navigation for Vehicles With Stochastic Dynamics

This brief presents a framework for input-optimal navigation under state constraints for vehicles exhibiting stochastic behavior. The resulting stochastic control law is implementable in real time on vehicles with limited computational power. When control actuation is unconstrained, then convergence with probability 1 can be theoretically guaranteed. When inputs are bounded, the probability of convergence is quantifiable. The experimental implementation on a 5.5 g, 720-MHz processor that controls a bioinspired crawling robot with stochastic dynamics, corroborates the design framework.

Error probabilities and threshold selection in networked nuclear detection

We consider the problem of computing analytical bounds on error probabilities in the setting of networked nuclear detection based on a likelihood ratio test. The detection scenario involves a mobile source of known trajectory passing within the sensing range of a spatially distributed sensor array, which has to decide on its nature (benign or radioactive) within a fixed time interval. Exploiting the particular modeling structure of remote nuclear measurement, and the form that the likelihood ratio takes in this setting, the paper presents analytical Chernoff bounds for the error probabilities, which in turn allow the selection of threshold constants for the likelihood ratio test in a computationally efficient manner compared to Monte Carlo simulations

Performance bounds for mismatched decision schemes with Poisson process observations

Abstract This paper develops a framework for analyzing the performance loss in fixed time interval decision algorithms that are based on observations of time-inhomogeneous Poisson processes, when some parameters characterizing the observation process are not known exactly. Key to the development is the formulation of an analytically computable performance metric which can be used in lieu of the true, but intractable, error probabilities. The proposed metric is obtained by identifying analytical upper bounds on the error probabilities in terms of the uncertain parameters. Using these tools, it is shown that performance degrades gracefully as long as the true values of the parameters remain within a neighborhood of the nominal values used in decision making. The results find direct application to problems of detecting illicit nuclear materials in transit.

Decision-Making Accuracy for Sensor Networks with Inhomogeneous Poisson Observations

The paper considers a network of sensors which observes a time-inhomogeneous Poisson signal and has to decide, within a fixed time interval, between two hypotheses concerning the intensity of the observed signal. The focus is on the impact of information sharing among individual sensors on the accuracy of a decision. Each sensor computes locally a likelihood ratio based on its own observations, and, at the end of the decision interval, shares this information with its neighbors according to a communication graph, transforming each sensor to a decision-making unit. Using analytically derived upper bounds on the decision error probabilities, the capacity of each sensor as a decision maker is evaluated, and consequences of ranking are explored. Example communication topologies are studied to highlight the interplay between a sensor’s location in the underlying communication graph (quantity of information) and the strength of the signal it observes (quality of information). The results are illustrated through application to the problem of deciding whether or not a moving target carries a radioactive source.

Information-sharing and decision-making in networks of radiation detectors

A network of sensors observes a time-inhomo-geneous Poisson signal and within a fixed time interval has to decide between two hypotheses regarding the signal’s intensity. The paper reveals an interplay between network topology, essentially determining the quantity of information available to different sensors, and the quality of individual sensor information as captured by the sensor’s likelihood ratio. Armed with analytic expressions of bounds on the error probabilities associated with the binary hypothesis test regarding the intensity of the observed signal, the insight into the interplay between sensor communication and data quality helps in deciding which sensor is better positioned to make a decision on behalf of the network, and links the analysis to network centrality concepts. The analysis is illustrated on networked radiation detection examples, first in simulation and then on cases utilizing field measurement data available through a U.S. Domestic Nuclear Detection Office (dndo) database.