Accounting for Parametric Model Uncertainty in Collision Avoidance for Unmanned Vehicles Using Sparse Grid Interpolation

2013 ◽  
Author(s):  
Sarah L. Noble ◽  
Joel M. Esposito ◽  
Jason Case
Keyword(s):  
Collision Avoidance ◽  
Ad Hoc ◽  
Initial Conditions ◽  
Interpolation Method ◽  
Unmanned Vehicles ◽  
Sparse Grid ◽  
Model Parameters ◽  
Ground Vehicles ◽  
Computationally Efficient ◽  
Grid Interpolation

In this paper we present an enhancement of model-based trajectory selection algorithms — a popular class of collision avoidance techniques for autonomous ground vehicles. Rather than dilate a set of individual candidate trajectories in an ad hoc way to account for uncertainty, we generate a set of trajectory clouds — sets of states that represent possible future poses over a product of intervals representing uncertainty in the model parameters, initial conditions and actuator commands. The clouds are generated using the sparse-grid interpolation method which is both error-controlled and computationally efficient. The approach is implemented on a differential drive vehicle.

Real-Time Path-Generation and Path-Following Using an Interoperable Multi-Agent Framework

2018 ◽  
Vol 06 (04) ◽  
pp. 231-250 ◽  
Author(s):  
Willson Amalraj Arokiasami ◽  
Prahlad Vadakkepat ◽  
Kay Chen Tan ◽  
Dipti Srinivasan
Keyword(s):  
Path Planning ◽  
Real Time ◽  
Collision Avoidance ◽  
Tracking Error ◽  
Unmanned Vehicles ◽  
Path Generation ◽  
Ground Vehicles ◽  
Agent Architectures ◽  
Time Path ◽  
Multi Agent

Autonomous unmanned vehicles are preferable in patrolling, surveillance and, search and rescue missions. Multi-agent architectures are commonly used for autonomous control of unmanned vehicles. Existing multi-robot architectures for unmanned aerial and ground robots are generally mission and platform oriented. Collision avoidance, path-planning and tracking are some of the fundamental requirements for autonomous operation of unmanned robots. Though aerial and ground vehicles operate differently, the algorithms for obstacle avoidance, path-planning and path-tracking can be generalized. Service Oriented Interoperable Framework for Robot Autonomy (SOIFRA) proposed in this work is an interoperable multi-agent framework focused on generalizing platform independent algorithms for unmanned aerial and ground vehicles. SOIFRA is behavior-based, modular and interoperable across unmanned aerial and ground vehicles. SOIFRA provides collision avoidance, and, path-planning and tracking behaviors for unmanned aerial and ground vehicles. Vector Directed Path-Generation and Tracking (VDPGT), a vector-based algorithm for real-time path-generation and tracking, is proposed in this work. VDPGT dynamically adopts the shortest path to the destination while minimizing the tracking error. Collision avoidance is performed utilizing Hough transform, Canny contour, Lucas–Kanade sparse optical flow algorithm and expansion of object-based time-to-contact estimation. Simulation and experimental results from Turtlebot and AR Drone show that VDPGT can dynamically generate and track paths, and SOIFRA is interoperable across multiple robotic platforms.

Adjoint- and Hybrid-Based Hessians for Optimization Problems in System Identification

2018 ◽  
Vol 140 (10) ◽  
Author(s):  
Souransu Nandi ◽  
Tarunraj Singh
Keyword(s):  
System Identification ◽  
Optimization Problems ◽  
Initial Conditions ◽  
Synthetic Data ◽  
Model Parameters ◽  
Computationally Efficient ◽  
Step Size ◽  
Adjoint Sensitivity ◽  
Gradient Based ◽  
Discrete Measurement

An adjoint sensitivity-based approach to determine the gradient and Hessian of cost functions for system identification of dynamical systems is presented. The motivation is the development of a computationally efficient approach relative to the direct differentiation (DD) technique and which overcomes the challenges of the step-size selection in finite difference (FD) approaches. An optimization framework is used to determine the parameters of a dynamical system which minimizes a summation of a scalar cost function evaluated at the discrete measurement instants. The discrete time measurements result in discontinuities in the Lagrange multipliers. Two approaches labeled as the Adjoint and the Hybrid are developed for the calculation of the gradient and Hessian for gradient-based optimization algorithms. The proposed approach is illustrated on the Lorenz 63 model where part of the initial conditions and model parameters are estimated using synthetic data. Examples of identifying model parameters of light curves of type 1a supernovae and a two-tank dynamic model using publicly available data are also included.

Maximal Distance Discounted and Weighted Revisit Period: A Utility Approach to Persistent Unmanned Surveillance

2019 ◽  
Vol 07 (04) ◽  
pp. 215-232 ◽  
Author(s):  
Christopher C. Olsen ◽  
Krishna Kalyanam ◽  
William P. Baker ◽  
Donald L. Kunz
Keyword(s):  
Utility Function ◽  
Ad Hoc ◽  
Initial Conditions ◽  
Order Approximation ◽  
Infinite Horizon ◽  
Unmanned Vehicles ◽  
Maximal Distance ◽  
Simulation Based ◽  
Single Vehicle ◽  
Long Endurance

Autonomous unmanned vehicles are well suited for long-endurance, persistent intelligence, surveillance and reconnaissance (PISR) missions. In order to conduct missions, vehicles must implement a method of task selection. We propose the Maximal Distance Discounted & Weighted Revisit Period ([Formula: see text]) utility function as a solution. We derive [Formula: see text] as a zeroth-order approximation to an infinite horizon solution of PISR when formulated as a dynamic programming (DP) problem. We then use the DP solution to develop a heuristic utility function for autonomous task selections, with the goal of minimizing the prioritized revisit time to each task. Our function adapts to different task maps and task priorities, is scalable in the number of tasks, and is robust to the ad-hoc addition or removal of tasks. We demonstrate how the [Formula: see text] parameters influence vehicle behavior. We also prove that the policy results in steady-state task selections that are periodic and that such periodicity occurs regardless of initial conditions. We then demonstrate periodicity via numerical simulations on a set of test scenarios. We present a two-step heuristic methodology for selecting utility function parameters that deliver empirically good performance, which we demonstrate through a simulation-based comparison to a single-vehicle Traveling Salesman Problem (TSP) solution. The comparisons are based on four sample task maps designed to resemble operational scenarios.

Variance-Based Global Sensitivity Analysis via Sparse-Grid Interpolation and Cubature

2011 ◽  
Vol 9 (3) ◽  
pp. 542-567 ◽  
Author(s):  
Gregery T. Buzzard ◽  
Dongbin Xiu
Keyword(s):  
Random Parameter ◽  
Sparse Grids ◽  
Sparse Grid ◽  
Test Cases ◽  
Computationally Efficient ◽  
Efficient Manner ◽  
Global Sensitivity ◽  
Grid Interpolation ◽  
Lagrange Basis ◽  
Single Set

AbstractThe stochastic collocation method using sparse grids has become a popular choice for performing stochastic computations in high dimensional (random) parameter space. In addition to providing highly accurate stochastic solutions, the sparse grid collocation results naturally contain sensitivity information with respect to the input random parameters. In this paper, we use the sparse grid interpolation and cubature methods of Smolyak together with combinatorial analysis to give a computationally efficient method for computing the global sensitivity values of Sobol’. This method allows for approximation of all main effect and total effect values from evaluation of f on a single set of sparse grids. We discuss convergence of this method, apply it to several test cases and compare to existing methods. As a result which may be of independent interest, we recover an explicit formula for evaluating a Lagrange basis interpolating polynomial associated with the Chebyshev extrema. This allows one to manipulate the sparse grid collocation results in a highly efficient manner.

Nearly Exact Bayesian Estimation of Non-linear No-Arbitrage Term-Structure Models*

2021 ◽  
Author(s):  
Marcello Pericoli ◽  
Marco Taboga
Keyword(s):  
Bayesian Estimation ◽  
Term Structure ◽  
Broad Class ◽  
Model Parameters ◽  
State Variables ◽  
Computationally Efficient ◽  
Macroeconomic Factors ◽  
No Arbitrage ◽  
Term Structure Models ◽  
Non Linear

Abstract We propose a general method for the Bayesian estimation of a very broad class of non-linear no-arbitrage term-structure models. The main innovation we introduce is a computationally efficient method, based on deep learning techniques, for approximating no-arbitrage model-implied bond yields to any desired degree of accuracy. Once the pricing function is approximated, the posterior distribution of model parameters and unobservable state variables can be estimated by standard Markov Chain Monte Carlo methods. As an illustrative example, we apply the proposed techniques to the estimation of a shadow-rate model with a time-varying lower bound and unspanned macroeconomic factors.

scholarly journals Genetic Improvement of Routing Protocols for Delay Tolerant Networks

2021 ◽  
Vol 1 (1) ◽  
pp. 1-37
Author(s):  
Michela Lorandi ◽  
Leonardo Lucio Custode ◽  
Giovanni Iacca
Keyword(s):  
Routing Protocols ◽  
Genetic Improvement ◽  
Ad Hoc ◽  
Delay Tolerant Networks ◽  
Unmanned Vehicles ◽  
Test Cases ◽  
Urban Networks ◽  
Delivery Probability ◽  
Apply Genetic ◽  
Delay Tolerant

Routing plays a fundamental role in network applications, but it is especially challenging in Delay Tolerant Networks (DTNs). These are a kind of mobile ad hoc networks made of, e.g., (possibly, unmanned) vehicles and humans where, despite a lack of continuous connectivity, data must be transmitted while the network conditions change due to the nodes’ mobility. In these contexts, routing is NP-hard and is usually solved by heuristic “store and forward” replication-based approaches, where multiple copies of the same message are moved and stored across nodes in the hope that at least one will reach its destination. Still, the existing routing protocols produce relatively low delivery probabilities. Here, we genetically improve two routing protocols widely adopted in DTNs, namely, Epidemic and PRoPHET, in the attempt to optimize their delivery probability. First, we dissect them into their fundamental components, i.e., functionalities such as checking if a node can transfer data, or sending messages to all connections. Then, we apply Genetic Improvement (GI) to manipulate these components as terminal nodes of evolving trees. We apply this methodology, in silico, to six test cases of urban networks made of hundreds of nodes and find that GI produces consistent gains in delivery probability in four cases. We then verify if this improvement entails a worsening of other relevant network metrics, such as latency and buffer time. Finally, we compare the logics of the best evolved protocols with those of the baseline protocols, and we discuss the generalizability of the results across test cases.

scholarly journals Bayesian Inference of Species Trees using Diffusion Models

2020 ◽  
Vol 70 (1) ◽  
pp. 145-161 ◽  
Author(s):  
Marnus Stoltz ◽  
Boris Baeumer ◽  
Remco Bouckaert ◽  
Colin Fox ◽  
Gordon Hiscott ◽  
...  
Keyword(s):  
Bayesian Inference ◽  
Numerical Algorithms ◽  
Diffusion Models ◽  
Model Parameters ◽  
Data Sets ◽  
Species Trees ◽  
Computationally Efficient ◽  
Data Set ◽  
Snp Data ◽  
Binary Markers

Abstract We describe a new and computationally efficient Bayesian methodology for inferring species trees and demographics from unlinked binary markers. Likelihood calculations are carried out using diffusion models of allele frequency dynamics combined with novel numerical algorithms. The diffusion approach allows for analysis of data sets containing hundreds or thousands of individuals. The method, which we call Snapper, has been implemented as part of the BEAST2 package. We conducted simulation experiments to assess numerical error, computational requirements, and accuracy recovering known model parameters. A reanalysis of soybean SNP data demonstrates that the models implemented in Snapp and Snapper can be difficult to distinguish in practice, a characteristic which we tested with further simulations. We demonstrate the scale of analysis possible using a SNP data set sampled from 399 fresh water turtles in 41 populations. [Bayesian inference; diffusion models; multi-species coalescent; SNP data; species trees; spectral methods.]

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