Approximate Gaussian Conjugacy: Parametric Recursive Filtering Under Nonlinearity, Multimodal, Uncertainty, and Constraint, and Beyond

This is a post-peer-review, pre-copyedit version of an article published in Frontiers of Information Technology & Electronic Engineering. The final authenticated version is available online at: https://doi.org/10.1631/FITEE.1700379Since the landmark work of R. E. Kalman in the 1960s, considerable efforts have been devoted to time series state space models for a large variety of dynamic estimation problems. In particular, parametric filters that seek analytical estimates based on a closed-form Markov–Bayes recursion, e.g., recursion from a Gaussian or Gaussian mixture (GM) prior to a Gaussian/GM posterior (termed ‘Gaussian conjugacy’ in this paper), form the backbone for a general time series filter design. Due to challenges arising from nonlinearity, multimodality (including target maneuver), intractable uncertainties (such as unknown inputs and/or non-Gaussian noises) and constraints (including circular quantities), etc., new theories, algorithms, and technologies have been developed continuously to maintain such a conjugacy, or to approximate it as close as possible. They had contributed in large part to the prospective developments of time series parametric filters in the last six decades. In this paper, we review the state of the art in distinctive categories and highlight some insights that may otherwise be easily overlooked. In particular, specific attention is paid to nonlinear systems with an informative observation, multimodal systems including Gaussian mixture posterior and maneuvers, and intractable unknown inputs and constraints, to fill some gaps in existing reviews and surveys. In addition, we provide some new thoughts on alternatives to the first-order Markov transition model and on filter evaluation with regard to computing complexity

Robust state estimation for the control of flexible robotic manipulators

In this thesis, a novel robust estimation strategy for observing the system state variables of robotic manipulators with distributed flexibility is established. Motivation for the derived approach stems from the observation that lightweight, high speed, and large workspace robotic manipulators often suffer performance degradation because of inherent structural compliance. This flexibility often results in persistent residual vibration, which must be damped before useful work can resume. Inherent flexibility in robotic manipulators, then, increases cycle times and shortens the operational lives of the robots. Traditional compensation techniques, those which are commonly used for the control of rigid manipulators, can only approach a fraction of the open-loop system bandwidth without inducing significant excitation of the resonant dynamics. To improve the performance of these systems, the structural flexibility cannot simply be ignored, as it is when the links are significantly stiff and approximate rigid bodies. One thus needs a model to design a suitable compensator for the vibration, but any model developed to correct this problem will contain parametric error. And in the case of very lightly damped systems, like flexible robotic manipulators, this error can lead to instability of the control system for even small errors in system parameters. This work presents a systematic solution for the problem of robust state estimation for flexible manipulators in the presence of parametric modeling error. The solution includes: 1) a modeling strategy, 2) sensor selection and placement, and 3) a novel, multiple model estimator. Modeling of the FLASHMan flexible gantry manipulator is accomplished using a developed hybrid transfer matrix / assumed modes method (TMM/AMM) approach to determine an accurate low-order state space representation of the system dynamics. This model is utilized in a genetic algorithm optimization in determining the placement of MEMs accelerometers for robust estimation and observability of the system’s flexible state variables. The initial estimation method applied to the task of determining robust state estimates under conditions of parametric modeling error was of a sliding mode observer type. Evaluation of the method through analysis, simulations and experiments showed that the state estimates produced were inadequate. This led to the development of a novel, multiple model adaptive estimator. This estimator utilizes a bank of similarly designed sub-estimators and a selection algorithm to choose the true value from a given set of possible system parameter values as well as the correct state vector estimate. Simulation and experimental results are presented which demonstrate the applicability and effectiveness of the derived method for the task of state variable estimation for flexible robotic manipulators.Ph.D

Summary of Research 1994

The views expressed in this report are those of the authors and do not reflect the official policy or position of the Department of Defense or the U.S. Government.This report contains 359 summaries of research projects which were carried out under funding of the Naval Postgraduate School Research Program. A list of recent publications is also included which consists of conference presentations and publications, books, contributions to books, published journal papers, and technical reports. The research was conducted in the areas of Aeronautics and Astronautics, Computer Science, Electrical and Computer Engineering, Mathematics, Mechanical Engineering, Meteorology, National Security Affairs, Oceanography, Operations Research, Physics, and Systems Management. This also includes research by the Command, Control and Communications (C3) Academic Group, Electronic Warfare Academic Group, Space Systems Academic Group, and the Undersea Warfare Academic Group

Design and verification of Guidance, Navigation and Control systems for space applications

In the last decades, systems have strongly increased their complexity in terms of number of functions that can be performed and quantity of relationships between functions and hardware as well as interactions of elements and disciplines concurring to the definition of the system. The growing complexity remarks the importance of defining methods and tools that improve the design, verification and validation of the system process: effectiveness and costs reduction without loss of confidence in the final product are the objectives that have to be pursued. Within the System Engineering context, the modern Model and Simulation based approach seems to be a promising strategy to meet the goals, because it reduces the wasted resources with respect to the traditional methods, saving money and tedious works. Model Based System Engineering (MBSE) starts from the idea that it is possible at any moment to verify, through simulation sessions and according to the phase of the life cycle, the feasibility, the capabilities and the performances of the system. Simulation is used during the engineering process and can be classified from fully numerical (i.e. all the equipment and conditions are reproduced as virtual model) to fully integrated hardware simulation (where the system is represented by real hardware and software modules in their operational environment). Within this range of simulations, a few important stages can be defined: algorithm in the loop (AIL), software in the loop (SIL), controller in the loop (CIL), hardware in the loop (HIL), and hybrid configurations among those. The research activity, in which this thesis is inserted, aims at defining and validating an iterative methodology (based on Model and Simulation approach) in support of engineering teams and devoted to improve the effectiveness of the design and verification of a space system with particular interest in Guidance Navigation and Control (GNC) subsystem. The choice of focusing on GNC derives from the common interest and background of the groups involved in this research program (ASSET at Politecnico di Torino and AvioSpace, an EADS company). Moreover, GNC system is sufficiently complex (demanding both specialist knowledge and system engineer skills) and vital for whatever spacecraft and, last but not least the verification of its behavior is difficult on ground because strong limitations on dynamics and environment reproduction arise. Considering that the verification should be performed along the entire product life cycle, a tool and a facility, a simulator, independent from the complexity level of the test and the stage of the project, is needed. This thesis deals with the design of the simulator, called StarSim, which is the real heart of the proposed methodology. It has been entirely designed and developed from the requirements definition to the software implementation and hardware construction, up to the assembly, integration and verification of the first simulator release. In addition, the development of this technology met the modern standards on software development and project management. StarSim is a unique and self-contained platform: this feature allows to mitigate the risk of incompatibility, misunderstandings and loss of information that may arise using different software, simulation tools and facilities along the various phases. Modularity, flexibility, speed, connectivity, real time operation, fidelity with real world, ease of data management, effectiveness and congruence of the outputs with respect to the inputs are the sought-after features in the StarSim design. For every iteration of the methodology, StarSim guarantees the possibility to verify the behavior of the system under test thanks to the permanent availability of virtual models, that substitute all those elements not yet available and all the non-reproducible dynamics and environmental conditions. StarSim provides a furnished and user friendly database of models and interfaces that cover different levels of detail and fidelity, and supports the updating of the database allowing the user to create custom models (following few, simple rules). Progressively, pieces of the on board software and hardware can be introduced without stopping the process of design and verification, avoiding delays and loss of resources. StarSim has been used for the first time with the CubeSats belonging to the e-st@r program. It is an educational project carried out by students and researchers of the “CubeSat Team Polito” in which StarSim has been mainly used for the payload development, an Active Attitude Determination and Control System, but StarSim’s capabilities have also been updated to evaluate functionalities, operations and performances of the entire satellite. AIL, SIL, CIL, HIL simulations have been performed along all the phases of the project, successfully verifying a great number of functional and operational requirements. In particular, attitude determination algorithms, control laws, modes of operation have been selected and verified; software has been developed step by step and the bugs-free executable files have been loaded on the micro-controller. All the interfaces and protocols as well as data and commands handling have been verified. Actuators, logic and electrical circuits have been designed, built and tested and sensors calibration has been performed. Problems such as real time and synchronization have been solved and a complete hardware in the loop simulation test campaign both for A-ADCS standalone and for the entire satellite has been performed, verifying the satisfaction of a great number of CubeSat functional and operational requirements. The case study represents the first validation of the methodology with the first release of StarSim. It has been proven that the methodology is effective in demonstrating that improving the design and verification activities is a key point to increase the confidence level in the success of a space mission

A Foot Placement Strategy for Robust Bipedal Gait Control

This thesis introduces a new measure of balance for bipedal robotics called the foot placement estimator (FPE). To develop this measure, stability first is defined for a simple biped. A proof of the stability of a simple biped in a controls sense is shown to exist using classical methods for nonlinear systems. With the addition of a contact model, an analytical solution is provided to define the bounds of the region of stability. This provides the basis for the FPE which estimates where the biped must step in order to be stable. By using the FPE in combination with a state machine, complete gait cycles are created without any precalculated trajectories. This includes gait initiation and termination. The bipedal model is then advanced to include more realistic mechanical and environmental models and the FPE approach is verified in a dynamic simulation. From these results, a 5-link, point-foot robot is designed and constructed to provide the final validation that the FPE can be used to provide closed-loop gait control. In addition, this approach is shown to demonstrate significant robustness to external disturbances. Finally, the FPE is shown in experimental results to be an unprecedented estimate of where humans place their feet for walking and jumping, and for stepping in response to an external disturbance

Six Decades of Flight Research: An Annotated Bibliography of Technical Publications of NASA Dryden Flight Research Center, 1946-2006

Titles, authors, report numbers, and abstracts are given for nearly 2900 unclassified and unrestricted technical reports and papers published from September 1946 to December 2006 by the NASA Dryden Flight Research Center and its predecessor organizations. These technical reports and papers describe and give the results of 60 years of flight research performed by the NACA and NASA, from the X-1 and other early X-airplanes, to the X-15, Space Shuttle, X-29 Forward Swept Wing, X-31, and X-43 aircraft. Some of the other research airplanes tested were the D-558, phase 1 and 2; M-2, HL-10 and X-24 lifting bodies; Digital Fly-By-Wire and Supercritical Wing F-8; XB-70; YF-12; AFTI F-111 TACT and MAW; F-15 HiDEC; F-18 High Alpha Research Vehicle, F-18 Systems Research Aircraft and the NASA Landing Systems Research aircraft. The citations of reports and papers are listed in chronological order, with author and aircraft indices. In addition, in the appendices, citations of 270 contractor reports, more than 200 UCLA Flight System Research Center reports, nearly 200 Tech Briefs, 30 Dryden Historical Publications, and over 30 videotapes are included