Efficient descriptor state estimation with a case study in catalytic partial oxidation reforming

2014 Fall.Includes illustrations (some color).Includes bibliographical references (pages 170-179).The structure of many first principle engineering models is in the form of non-linear differential algebraic equations (DAE). Standard system theory, however, pre-assumes that the system model is described by ordinary differential equations (ODE) and hence can not accommodate DAE models unless if they can be transformed to an equivalent ODE form. However, such transformation, even if possible, can become cumbersome and the descriptive representation of the model will be lost. The size of these models is typically in the order of 1000's of equations for systems with multiple units or for systems described by discretized partial differential algebraic equations. This demands numerically robust and efficient methods to use these models for real time applications. The focus of this study is to develop estimation techniques that can be used with linear and non-linear differential algebraic equations that are robust and numerically efficient. Estimation of DAE systems can be used for monitoring and control applications and will exploit the modelling software capabilities that are becoming prevalent in the industry. The first part of this dissertation examines the problem of state estimation of linear discrete time descriptor systems from new perspectives. First, the available theory on differential algebraic equations has been used to examine the problem of stochastically modelling a linear differential algebraic equation to avoid non-causality of the solution. Second, the Baysian paradigm has been used to find the Maximum a Posteriori (MAP) estimate for index 1 and higher index descriptor systems with the utility of Kronecker canonical transformation of a matrix pencil. This analysis indicated that state estimation of high index descriptor systems can be conducted without the need of any model transformations provided that the high index model is causal. This also showed that the MAP estimate is identical to the Maximum Likelihood (ML) estimate in the usual sense. Third, MAP estimation of descriptor systems was utilized for addressing problems of practical interest; namely state estimation with truncated Gaussian distributions, state estimation with measurement outliers and state estimation of singularly perturbed systems using the quasi-steady state model approximation. The second part of this dissertation addresses the need to find stable and efficient algorithms to solve the minimization problems presented in the theory section of this dissertation. The first algorithm solves the MAP estimation problem when mixed deterministic and stochastic equations are involved. The second algorithm solves the MAP estimation problem when inequality constraints are involved using a new strategy called Multiple Window Moving Horizon Estimation (MW-MHE) that enhances the performance of conventional Moving Horizon Estimation (MHE). This is achieved by exploiting periods of constraint inactivity in sliding window minimization problems by adaptively changing the objective function in response to the activity of constraints. In other words, the 'sparsity' of active constraints is exploited to enable efficient long horizon estimation. Demonstration of the efficiency of the technique was made with problems involving unknown input estimation and filtering subject to outliers in measurements and impulsive process disturbances. The third part of this dissertation serves the dual objective of examining the effectiveness of descriptor state estimation and addressing the practical need for estimating gas mole fractions in catalytic partial oxidation in real time. This process is critical for producing H2 for portable fuel cell applications and accurate on-line estimation of mole fractions is important for system operability and reliability. The residence time of the reactor is in the order of 10 milliseconds, imposing stringent real time operational constraints. A detail analysis of this estimation problem in terms of process dynamics, model reduction and observability analysis has been conducted with the utility of descriptor system state estimation techniques. A descriptor MHE has been developed successfully with update rates faster than 0.02 seconds

Genetic agent approach for improving on-the-fly web map generalization

The utilization of web mapping becomes increasingly important in the domain of cartography. Users want access to spatial data on the web specific to their needs. For this reason, different approaches were appeared for generating on-the-fly the maps demanded by users, but those not suffice for guide a flexible and efficient process. Thus, new approach must be developed for improving this process according to the user needs. This work focuses on defining a new strategy which improves on-the-fly map generalization process and resolves the spatial conflicts. This approach uses the multiple representation and cartographic generalization. The map generalization process is based on the implementation of multi- agent system where each agent was equipped with a genetic patrimony.Comment: 10 pages, 07 figures, International Journal of Information Technology Convergence and Services (IJITCS) Vol.2, No.3, June 201

Online Mapping and Motion Planning under Uncertainty for Safe Navigation in Unknown Environments

Safe autonomous navigation is an essential and challenging problem for robots operating in highly unstructured or completely unknown environments. Under these conditions, not only robotic systems must deal with limited localisation information, but also their manoeuvrability is constrained by their dynamics and often suffer from uncertainty. In order to cope with these constraints, this manuscript proposes an uncertainty-based framework for mapping and planning feasible motions online with probabilistic safety-guarantees. The proposed approach deals with the motion, probabilistic safety, and online computation constraints by: (i) incrementally mapping the surroundings to build an uncertainty-aware representation of the environment, and (ii) iteratively (re)planning trajectories to goal that are kinodynamically feasible and probabilistically safe through a multi-layered sampling-based planner in the belief space. In-depth empirical analyses illustrate some important properties of this approach, namely, (a) the multi-layered planning strategy enables rapid exploration of the high-dimensional belief space while preserving asymptotic optimality and completeness guarantees, and (b) the proposed routine for probabilistic collision checking results in tighter probability bounds in comparison to other uncertainty-aware planners in the literature. Furthermore, real-world in-water experimental evaluation on a non-holonomic torpedo-shaped autonomous underwater vehicle and simulated trials in the Stairwell scenario of the DARPA Subterranean Challenge 2019 on a quadrotor unmanned aerial vehicle demonstrate the efficacy of the method as well as its suitability for systems with limited on-board computational power.Comment: The International Journal of Robotics Research (under review

Discrete-time optimal attitude control of spacecraft with momentum and control constraints

This article solves an optimal control problem arising in attitude control of a spacecraft under state and control constraints. We first derive the discrete-time attitude dynamics by employing discrete mechanics. The orientation transfer, with initial and final values of the orientation and momentum and the time duration being specified, is posed as an energy optimal control problem in discrete-time subject to momentum and control constraints. Using variational analysis directly on the Lie group SO(3), we derive first order necessary conditions for optimality that leads to a constrained two point boundary value problem. This two point boundary value problem is solved via a novel multiple shooting technique that employs a root finding Newton algorithm. Robustness of the multiple shooting technique is demonstrated through a few representative numerical experiments

A Hybrid Systems Model for Simple Manipulation and Self-Manipulation Systems

Rigid bodies, plastic impact, persistent contact, Coulomb friction, and massless limbs are ubiquitous simplifications introduced to reduce the complexity of mechanics models despite the obvious physical inaccuracies that each incurs individually. In concert, it is well known that the interaction of such idealized approximations can lead to conflicting and even paradoxical results. As robotics modeling moves from the consideration of isolated behaviors to the analysis of tasks requiring their composition, a mathematically tractable framework for building models that combine these simple approximations yet achieve reliable results is overdue. In this paper we present a formal hybrid dynamical system model that introduces suitably restricted compositions of these familiar abstractions with the guarantee of consistency analogous to global existence and uniqueness in classical dynamical systems. The hybrid system developed here provides a discontinuous but self-consistent approximation to the continuous (though possibly very stiff and fast) dynamics of a physical robot undergoing intermittent impacts. The modeling choices sacrifice some quantitative numerical efficiencies while maintaining qualitatively correct and analytically tractable results with consistency guarantees promoting their use in formal reasoning about mechanism, feedback control, and behavior design in robots that make and break contact with their environment

A mosaic of eyes

Autonomous navigation is a traditional research topic in intelligent robotics and vehicles, which requires a robot to perceive its environment through onboard sensors such as cameras or laser scanners, to enable it to drive to its goal. Most research to date has focused on the development of a large and smart brain to gain autonomous capability for robots. There are three fundamental questions to be answered by an autonomous mobile robot: 1) Where am I going? 2) Where am I? and 3) How do I get there? To answer these basic questions, a robot requires a massive spatial memory and considerable computational resources to accomplish perception, localization, path planning, and control. It is not yet possible to deliver the centralized intelligence required for our real-life applications, such as autonomous ground vehicles and wheelchairs in care centers. In fact, most autonomous robots try to mimic how humans navigate, interpreting images taken by cameras and then taking decisions accordingly. They may encounter the following difficulties

A Mathematical Theory of Co-Design

One of the challenges of modern engineering, and robotics in particular, is designing complex systems, composed of many subsystems, rigorously and with optimality guarantees. This paper introduces a theory of co-design that describes "design problems", defined as tuples of "functionality space", "implementation space", and "resources space", together with a feasibility relation that relates the three spaces. Design problems can be interconnected together to create "co-design problems", which describe possibly recursive co-design constraints among subsystems. A co-design problem induces a family of optimization problems of the type "find the minimal resources needed to implement a given functionality"; the solution is an antichain (Pareto front) of resources. A special class of co-design problems are Monotone Co-Design Problems (MCDPs), for which functionality and resources are complete partial orders and the feasibility relation is monotone and Scott continuous. The induced optimization problems are multi-objective, nonconvex, nondifferentiable, noncontinuous, and not even defined on continuous spaces; yet, there exists a complete solution. The antichain of minimal resources can be characterized as a least fixed point, and it can be computed using Kleene's algorithm. The computation needed to solve a co-design problem can be bounded by a function of a graph property that quantifies the interdependence of the subproblems. These results make us much more optimistic about the problem of designing complex systems in a rigorous way

Combining Homotopy Methods and Numerical Optimal Control to Solve Motion Planning Problems

This paper presents a systematic approach for computing local solutions to motion planning problems in non-convex environments using numerical optimal control techniques. It extends the range of use of state-of-the-art numerical optimal control tools to problem classes where these tools have previously not been applicable. Today these problems are typically solved using motion planners based on randomized or graph search. The general principle is to define a homotopy that perturbs, or preferably relaxes, the original problem to an easily solved problem. By combining a Sequential Quadratic Programming (SQP) method with a homotopy approach that gradually transforms the problem from a relaxed one to the original one, practically relevant locally optimal solutions to the motion planning problem can be computed. The approach is demonstrated in motion planning problems in challenging 2D and 3D environments, where the presented method significantly outperforms a state-of-the-art open-source optimizing sampled-based planner commonly used as benchmark

Routing Multiple Unmanned Vehicles in GPS-Denied Environments

This article aims to develop novel path planning algorithms required to deploy multiple unmanned vehicles in Global Positioning System (GPS) denied environments. Unmanned vehicles (ground or aerial) are ideal platforms for executing monitoring and data gathering tasks in civil infrastructure management, agriculture, public safety, law enforcement, disaster relief and transportation. Significant advancement in the area of path planning for unmanned vehicles over the last decade has resulted in a suite of algorithms that can handle heterogeneity, motion and other on-board resource constraints for these vehicles. However, most of these routing and path planning algorithms rely on the availability of the GPS information. Unintentional and intentional interference and design errors can cause GPS service outages, which in turn, can crucially affect all the systems that depend on GPS information. This article addresses a multiple vehicle path planning problem that arises while deploying a team of unmanned vehicles for monitoring applications in GPS-denied environments and presents a mathematical formulation and algorithms for solving the problem. Simulation results are also presented to corroborate the performance of the proposed algorithms.Comment: 10 pages. arXiv admin note: text overlap with arXiv:1708.0326

Fuel Minimisation for a Vehicle Equipped with a Flywheel and Battery on a Three-Dimensional Track

An optimal control based methodology is proposed for minimising the combustible fuel consumption of a hybrid vehicle equipped with an internal combustion engine, a high-speed flywheel and a battery. The three-dimensionality of the road is recognised by the optimal control calculations. Fuel efficiency is achieved by optimally exploiting the primary and secondary energy sources and controlling the vehicle so that the fuel consumption is minimised for a given, but arbitrary three-dimensional route. A time-of-arrival constraint rather than a driving cycle is used. The benefits of using multiple auxiliary storage systems are demonstrated and a lower-bound estimate of the fuel consumption is presented