Contact-Aided Invariant Extended Kalman Filtering for Legged Robot State Estimation

This paper derives a contact-aided inertial navigation observer for a 3D bipedal robot using the theory of invariant observer design. Aided inertial navigation is fundamentally a nonlinear observer design problem; thus, current solutions are based on approximations of the system dynamics, such as an Extended Kalman Filter (EKF), which uses a system's Jacobian linearization along the current best estimate of its trajectory. On the basis of the theory of invariant observer design by Barrau and Bonnabel, and in particular, the Invariant EKF (InEKF), we show that the error dynamics of the point contact-inertial system follows a log-linear autonomous differential equation; hence, the observable state variables can be rendered convergent with a domain of attraction that is independent of the system's trajectory. Due to the log-linear form of the error dynamics, it is not necessary to perform a nonlinear observability analysis to show that when using an Inertial Measurement Unit (IMU) and contact sensors, the absolute position of the robot and a rotation about the gravity vector (yaw) are unobservable. We further augment the state of the developed InEKF with IMU biases, as the online estimation of these parameters has a crucial impact on system performance. We evaluate the convergence of the proposed system with the commonly used quaternion-based EKF observer using a Monte-Carlo simulation. In addition, our experimental evaluation using a Cassie-series bipedal robot shows that the contact-aided InEKF provides better performance in comparison with the quaternion-based EKF as a result of exploiting symmetries present in the system dynamics.Comment: Published in the proceedings of Robotics: Science and Systems 201

State Estimation for the Individual and the Population in Mean Field Control with Application to Demand Dispatch

This paper concerns state estimation problems in a mean field control setting. In a finite population model, the goal is to estimate the joint distribution of the population state and the state of a typical individual. The observation equations are a noisy measurement of the population. The general results are applied to demand dispatch for regulation of the power grid, based on randomized local control algorithms. In prior work by the authors it has been shown that local control can be carefully designed so that the aggregate of loads behaves as a controllable resource with accuracy matching or exceeding traditional sources of frequency regulation. The operational cost is nearly zero in many cases. The information exchange between grid and load is minimal, but it is assumed in the overall control architecture that the aggregate power consumption of loads is available to the grid operator. It is shown that the Kalman filter can be constructed to reduce these communication requirements,Comment: To appear, IEEE Trans. Auto. Control. Preliminary version appeared in the 54rd IEEE Conference on Decision and Control, 201

Fuzzy H-infinity output feedback control of nonlinear systems under sampled measurements

This paper studies the problem of designing an H∞ fuzzy feedback control for a class of nonlinear systems described by a continuous-time fuzzy system model under sampled output measurements. The premise variables of the fuzzy system model are allowed to be unavailable. We develop a technique for designing an H∞ fuzzy feedback control that guarantees the L2 gain from an exogenous input to a controlled output is less than or equal to a prescribed value. A design algorithm for constructing the H∞ fuzzy feedback controller is given

Distributed Event-Based State Estimation for Networked Systems: An LMI-Approach

In this work, a dynamic system is controlled by multiple sensor-actuator agents, each of them commanding and observing parts of the system's input and output. The different agents sporadically exchange data with each other via a common bus network according to local event-triggering protocols. From these data, each agent estimates the complete dynamic state of the system and uses its estimate for feedback control. We propose a synthesis procedure for designing the agents' state estimators and the event triggering thresholds. The resulting distributed and event-based control system is guaranteed to be stable and to satisfy a predefined estimation performance criterion. The approach is applied to the control of a vehicle platoon, where the method's trade-off between performance and communication, and the scalability in the number of agents is demonstrated.Comment: This is an extended version of an article to appear in the IEEE Transactions on Automatic Control (additional parts in the Appendix

Observer-based fault-tolerant control for a class of networked control systems with transfer delays

Abstract not availableZehui Mao, Bin Jiang, Peng Sh

On IMU preintegration: A nonlinear observer viewpoint and its application

The inertial measurement unit (IMU) preintegration approach nowadays is widely used in various robotic applications. In this article, we revisit the preintegration theory and propose a novel interpretation to understand it from a nonlinear observer perspective, specifically the parameter estimation-based observer (PEBO). We demonstrate that the preintegration approach can be viewed as recursive implementation of PEBO in moving horizons, and that the two approaches are equivalent in the case of perfect measurements. We then discuss how these findings can be used to tackle practical challenges in estimation problems. As byproducts, our results lead to a novel hybrid sampled-data observer design and an approach to address statistical optimality for PEBO in presence of noise

DISTRIBUTED-DELAY MODELS OF THE GLUCOSE-INSULIN HOMEOSTASIS AND ASYMPTOTIC STATE OBSERVATION

Abstract In this paper the problem of the real-time reconstruction of plasma insulin concentration by using only blood glucose measurements is investigated. This is an interesting problem because the knowledge of the time course of the glucose and insulin concentrations in an individual provides precious informations concerning its health state, and may assume the role of a clinical instrument. For the purpose of the reconstruction of the insulinemia a dynamical model of the glucose-insuline homeostasis is required. The present work considers distributed delay models. Such models have been preferred in recent papers with respect to the standard Minimal Models, available in literature from 70's, because they allow to couple the glucose and insulin dynamics in a unique extended system, whose solutions have been proven to be positive, bounded, and globally asymptotically stable around the basal values of the equilibrium point. Data are acquired according to the Intra Venous Glucose Tolerance Test (IVGTT). Simulation results are reported in order to validate the developed theory

State observer with Round-Robin aperiodic sampled measurements with jitter

A sampled-data observer is proposed for linear continuous-time systems whose outputs are sequentially sampled via non-uniform sampling intervals repeating a prescribed Round-Robin sequence. With constant sampling intervals (jitter-free case) we provide constructive necessary and sufficient conditions for the design of an asymptotic continuous–discrete observer whose estimation error is input-to-state stable (ISS) from process disturbances and measurement noise. We use a time-varying gain depending on the elapsed time since the last measurement. With non-constant sampling intervals (jitter-tolerant case), our design conditions are only sufficient. A suspension system example shows the effectiveness of the proposed approach