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1. Stable nullspace adaptive parameter identification of 6 degree-of-freedom plant and actuator models for underactuated vehicles: Theory and experimental evaluation

   https://doi.org/10.1177/02783649231191184  

   Harris, Zachary J.; Mao, Annie M.; Paine, Tyler M.; Whitcomb, Louis L. (November 2023, The International Journal of Robotics Research)

   Model-based approaches to navigation, control, and fault detection that utilize precise nonlinear models of vehicle plant dynamics will enable more accurate control and navigation, assured autonomy, and more complex missions for such vehicles. This paper reports novel theoretical and experimental results addressing the problem of parameter estimation of plant and actuator models for underactuated underwater vehicles operating in 6 degrees-of-freedom (DOF) whose dynamics are modeled by finite-dimensional Newton-Euler equations. This paper reports the first theoretical approach and experimental validation to identify simultaneously plant-model parameters (parameters such as mass, added mass, hydrodynamic drag, and buoyancy) and control-actuator parameters (control-surface models and thruster models) in 6-DOF. Most previously reported studies on parameter identification assume that the control-actuator parameters are known a priori. Moreover, this paper reports the first proof of convergence of the parameter estimates to the true set of parameters for this class of vehicles under a persistence of excitation condition. The reported adaptive identification (AID) algorithm does not require instrumentation of 6-DOF vehicle acceleration, which is required by conventional approaches to parameter estimation such as least squares. Additionally, the reported AID algorithm is applicable under any arbitrary open-loop or closed-loop control law. We report simulation and experimental results for identifying the plant-model and control-actuator parameters for an L3 OceanServer Iver3 autonomous underwater vehicle. We believe this general approach to AID could be extended to apply to other classes of machines and other classes of marine, land, aerial, and space vehicles. 

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2. A Fixed-Time Stable Adaptation Law for Safety-Critical Control under Parametric Uncertainty

   Black, Mitchell; Arabi, Ehsan; Panagou, Dimitra (January 2021, 2021 European Control Conference)

   We present a novel technique for solving the problem of safe control for a general class of nonlinear, control-affine systems subject to parametric model uncertainty. Invoking Lyapunov analysis and the notion of fixed-time stability (FxTS), we introduce a parameter adaptation law which guarantees convergence of the estimates of unknown parameters in the system dynamics to their true values within a fixed-time independent of the initial parameter estimation error. We then synthesize the adaptation law with a robust, adaptive control barrier function (RaCBF) based quadratic program to compute safe control inputs despite the considered model uncertainty. To corroborate our results, we undertake a comparative case study on the efficacy of this result versus other recent approaches in the literature to safe control under uncertainty, and close by highlighting the value of our method in the context of an automobile overtake scenario. 

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3. Online Three-Axis Magnetometer Hard-Iron and Soft-Iron Bias and Angular Velocity Sensor Bias Estimation Using Angular Velocity Sensors for Improved Dynamic Heading Accuracy

   https://doi.org/10.55417/fr.2022033  

   Spielvogel, Andrew; Shah, Abhimanyu; Whitcomb, Louis (March 2022, Field Robotics)

   This article addresses the problem of dynamic online estimation and compensation of hard-iron and soft-iron biases of three-axis magnetometers under dynamic motion in field robotics, utilizing only biased measurements from a three-axis magnetometer and a three-axis angular rate sensor. The proposed magnetometer and angular velocity bias estimator (MAVBE) utilizes a 15-state process model encoding the nonlinear process dynamics for the magnetometer signal subject to angular velocity excursions, while simultaneously estimating nine magnetometer bias parameters and three angular rate sensor bias parameters, within an extended Kalman filter framework. Bias parameter local observability is numerically evaluated. The bias-compensated signals, together with three-axis accelerometer signals, are utilized to estimate bias-compensated magnetic geodetic heading. Performance of the proposed MAVBE method is evaluated in comparison to the widely cited magnetometer-only TWOSTEP method in numerical simulations, laboratory experiments, and full-scale field trials of an instrumented autonomous underwater vehicle in the Chesapeake Bay, Maryland, USA. For the proposed MAVBE, (i) instrument attitude is not required to estimate biases, and the results show that (ii) the biases are locally observable, (iii) the bias estimates converge rapidly to true bias parameters, (iv) only modest instrument excitation is required for bias estimate convergence, and (v) compensation for magnetometer hard-iron and soft-iron biases dramatically improves dynamic heading estimation accuracy. 

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4. Facial Input Decompositions for Robust Peak Estimation under Polyhedral Uncertainty

   https://doi.org/10.1016/j.ifacol.2022.09.323  

   Miller, Jared; Sznaier, Mario (January 2022, IFAC-PapersOnLine)

   This work bounds extreme values of state functions for a class of input-affine continuous-time systems that are affected by polyhedral-bounded uncertainty. Instances of these systems may arise in data-driven peak estimation, in which the state function must be bounded for all systems that are consistent with a set of state-derivative data records corrupted under L-infinity bounded noise. Existing occupation measure-based methods form a convergent sequence of outer approximations to the true peak value, given an initial set, by solving a hierarchy of semidefinite programs in increasing size. These techniques scale combinatorially in the number of state variables and uncertain parameters. We present tractable algorithms for peak estimation that scale linearly in the number of faces of the uncertainty-bounding polytope rather than combinatorially in the number of uncertain parameters by leveraging convex duality and a theorem of alternatives (facial decomposition). The sequence of decomposed semidefinite programs will converge to the true peak value under mild assumptions (convergence and smoothness of dynamics). 

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5. Functional estimation of perturbed positive real infinite dimensional systems using adaptive compensators

   https://doi.org/10.23919/ACC45564.2020.9147702  

   Demetriou, Michael A. (July 2020, 2020 American Control Conference (ACC))

   This paper extends earlier results on the adaptive estimation of nonlinear terms in finite dimensional systems utilizing a reproducing kernel Hilbert space to a class of positive real infinite dimensional systems. The simplest class of strictly positive real infinite dimensional systems has collocated input and output operators with the state operator being the generator of an exponentially stable C 0 semigroup on the state space X . The parametrization of the nonlinear term is considered in a reproducing kernel Hilbert space Q and together with the adaptive observer, results in an evolution system considered in X × Q. Using Lyapunov-redesign methods, the adaptive laws for the parameter estimates are derived and the well-posedness of the resulting evolution error system is summarized. The adaptive estimate of the unknown nonlinearity is subsequently used to compensate for the nonlinearity. A special case of finite dimensional systems with an embedded reproducing kernel Hilbert space to handle the nonlinear term is also considered and the convergence results are summarized. A numerical example on a one-dimensional diffusion equation is considered. 

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