Global attitude and gyro bias estimation based on set-valued observers

The problem of attitude and rate gyro bias estimation is addressed by resorting to measurements acquired from rate gyros and vector observations. A Set-Valued Observer (SVO) is proposed that has no singularities and that, for any initial conditions, provides a bounding set with guarantees of containing the actual (unknown) rotation matrix. The sensor readings are assumed to be corrupted by bounded measurement noise and constant gyro bias. Conditions for the boundedness of the estimated sets are established and implementation details are discussed. The feasibility of the technique is demonstrated in simulation.     

Globally exponentially stable filters for source localization and navigation aided by direction measurements

This paper presents a set of filters with globally exponentially stable error dynamics for source localization and navigation, in 3-D, based on direction measurements from the agent (or vehicle) to the source, in addition to relative velocity readings of the agent. Both the source and the agent are allowed to have constant unknown drift velocities and the relative drift velocity is also explicitly estimated. The observability of the system is studied and realistic simulation results are presented, in the presence of measurement noise, that illustrate the performance of the achieved solutions. Comparison results with the Extended Kalman Filter are also provided and similar performances are achieved.     

Online stiffness estimation for robotic tasks with force observers

In this paper we propose an online stiffness estimation technique for robotic tasks based only on force data, therefore, not requiring contact position information. This allows estimations to be obtained in robotic tasks involving interactions with unstructured and unknown environments where geometrical data is unavailable or unreliable. Our technique – the Candidate Observer Based Algorithm (COBA) – uses two force observers, configured with different candidate stiffnesses, to estimate online the actual target object stiffness. COBA is embedded in a force control architecture with computed torque in the task space. The theoretical presentation of the algorithm, as well as simulation tests and experimental results with a lightweight robot arm are also presented.     

Globally exponentially stable attitude observer with Earth velocity estimation

This paper presents a novel observer for attitude estimation based on a triad of high‐grade rate gyros aided by a body‐fixed vector measurement of a constant inertial vector, departing from the majority of solutions that consider at least two of these vectors. A cascade approach is proposed, where the first block estimates a vector that is related to the angular velocity of the Earth and a second block estimates the attitude. While the topological characteristics are relaxed in the attitude observer so that global exponential stability is achieved, an additional stage is also devised that yields estimates directly on the special orthogonal group, preserving global convergence of the estimation error. Simulation results with realistic sensor noise were performed, including extensive Monte Carlo runs. These results illustrate the convergence of the proposed solution, as well as the achievable performance and robustness to sensor noise.     

Visual motion and structure estimation using sliding mode observers

The problem of estimating motion and structure from a sequence of images has been a major research theme in machine vision for many years and remains one of the most challenging ones. In this work, we use sliding mode observers to estimate the motion and the structure of a moving body with the aid of a change-coupled device (CCD) camera. We consider a variety of dynamical systems which arise in machine vision applications and develop a novel identification procedure for the estimation of both constant and time-varying parameters. The basic procedure introduced for parameter estimation is to recast image feature dynamics linearly in terms of unknown parameters and construct a sliding mode observer to produce asymptotically correct estimates of the observed image features, and then use the observer input to compute parameters. Much of our analysis has been substantiated by computer simulations and real experiments.     

Velocity observers for non-linear mechanical systems subject to non-smooth impacts

This paper is concerned with the estimation of the velocity variables (when the position variables are the measured outputs) for non-linear mechanical systems subject to non-smooth impacts, both elastic and inelastic (i.e., with coefficient of restitution e=1 and e(0,1), respectively). A reduced-order observer is proposed, which guarantees that the corresponding error system, despite the possible presence of an infinite sequence of non-smooth impacts, is locally exponentially stable. An estimate of the basin of attraction is also given.     

An adaptive strategy for Li-ion battery internal state estimation

Further developing a study presented in Di Domenico, Prada, and Creff (2011), this paper presents an extended Kalman filter (EKF) based on an electro-thermal model for the estimation of the internal state of a lithium-ion battery, i.e. state of charge and the cell overpotential. In order to compensate for uncertainties in the model parameters and in the measurements, it is first shown that the filter robustness strongly depends on the State of Charge (SOC) range. Then the filter weights are adapted according to the estimated SOC value. This estimation technique is tested using experimental data collected from a commercial A123 Systems lithium iron phosphate/graphite (LiFePO₄/graphite) cell. The filter shows good performance. The estimation of SOC exhibits an average error within 3% range and the overpotential is estimated with a precision higher than 5 mV.     

Terminal sliding mode observers for a class of nonlinear systems

This paper proposes a terminal sliding mode observer for a class of nonlinear systems to achieve finite time convergence for all error states. Compared to standard sliding mode observers which only enable finite time convergence of the output error, the observer in this paper makes use of fractional powers to reduce other non-output errors to zero in finite time. A 2-degree-of-freedom robotic manipulator is used to demonstrate the effectiveness of the proposed observer.     

Redesign of adaptive observers for improved parameter identification in nonlinear systems

We propose a method for redesigning adaptive observers for nonlinear systems. The redesign uses an adaptive law that is based on delayed observers. This increases the computational burden, but gives significantly better parameter identification and robustness properties. In particular, given that a special persistency of excitation condition is satisfied, we prove uniform global asymptotic stability and semi-global exponential stability of the origin of the state and parameter estimation error, and give explicit lower bounds on the convergence rate of both the state and parameter estimation error dynamics. For initial conditions with a known upper bound, we prove tunable exponential convergence rate. To illustrate the use of the proposed method, we apply it to estimate the unmeasured flow rate and the uncertain friction parameters in a model of a managed pressure drilling system. The simulation results clearly show the improved performance of the redesigned adaptive observer compared to a traditional design.     

Drift-free attitude estimation for accelerated rigid bodies

In this paper we study the attitude estimation problem for an accelerated rigid body using gyros and accelerometers. The application in mind is that of a walking robot and particular attention is paid to the large and abrupt changes in accelerations that can be expected in such an environment. We propose a state estimation algorithm that fuses data from rate gyros and accelerometers to give long-term drift free attitude estimates. The algorithm does not use any local parameterization of the rigid body kinematics and can thus be used for a rigid body performing any kind of rotations. The algorithm is a combination of two non-standard, but in a sense linear, Kalman filters between which a trigger based switching takes place. The kinematics representation used makes it possible to construct a linear algorithm that can be shown to give convergent estimates for this nonlinear problem. The state estimator is evaluated in simulations demonstrating how the estimates are long-term stable even in the presence of gyro drift.     

An explicit finite difference method for finite-time observers

In this paper we present a numerical method for estimating the current state of a nonlinear control system. We use finite differences to discretize a modified version of the finite-time observer equations in James. The discretized equations are simple and easily programmed. The convergence and accuracy of the scheme is proved, and the scheme enjoys a number of important properties: availability of rate of convergence estimates, good robustness characteristics, and the ability to handle certain types of discontinuities in the observations. The major disadvantage is that the number of grid points required increases exponentially with the number of state dimensions.     

Decentralized observers with consensus filters for distributed discrete-time linear systems

This paper presents a decentralized observer with a consensus filter for the state observation of discrete-time linear distributed systems. Each agent in the distributed system has an observer with a model of the plant that utilizes the set of locally available measurements, which may not make the full plant state detectable. This lack of detectability is overcome by utilizing a consensus filter that blends the state estimate of each agent with its neighbors’ estimates. It is proven that the state estimates of the proposed observer exponentially converge to the actual plant states under arbitrarily changing, but connected, communication and pseudo-connected sensing graph topologies. Except these connectivity properties, full knowledge of the sensing and communication graphs is not needed at the design time. As a byproduct, we obtained a result on the location of eigenvalues, i.e., the spectrum, of the Laplacian for a family of graphs with self-loops.     

Nonlinear tension observers for web machines

Precise regulation of span tension in web-handling machines is critical to ensure product quality. Elevated tension causes web fracture during operation; depressed or highly variable tension leads to irregular and unacceptable spool. Web-handling machines typically employ costly load cell sensors to measure span tension. This work investigates the use of nonlinear estimators or observers to provide cost-effective span tension estimates from system measurements. After presenting the dynamic equations of a web-handling machine, their structure is exploited to design a reduced-order, nonlinear observer with linear time-varying error dynamics. Exponential stability of the error dynamics is demonstrated. Performance of the estimator is experimentally compared with two competing designs on a real web-handling machine.     

Semi-global finite-time observers for nonlinear systems

It is well known that high gain observers exist for single output nonlinear systems that are uniformly observable and globally Lipschitzian. Under the same conditions, we show that these systems admit semi-global and finite-time converging observers. This is achieved with a derivation of a new sufficient condition for local finite-time stability, in conjunction with applications of geometric homogeneity and Lyapunov theories.     

Jump modes analysis and observer design for discrete singular systems

This paper is concerned with the reconstructability and detectability of the jump modes of discrete singular systems. The notion of jump modes can be considered as the discrete counterpart of the impulsive modes of continuous singular systems which has been extensively studied. The effect of jump modes on the existence of reduced order normal Luenberger observers for discrete singular systems is investigated. Necessary and sufficient conditions for the existence of normal Luenberger observers and the corresponding observer design procedure are obtained.     

Dynamic observers for linear time-invariant systems

An alternative state estimator structure for linear time-invariant systems named for dynamic observer is presented, which can be considered as an extension of the usual observer in its configuration. As a possible design method for the dynamic observer, an efficient and plausible design algorithm is also provided. The mechanism of the proposed dynamic observer design is the dual of the output feedback controller design. The essential characteristics of the dynamic observer to be qualified as an effective observer are addressed.     

Dead beat observer synthesis

In the paper the observer design problem is investigated in the context of linear left shift invariant discrete behaviors, whose trajectories have support on the positive axis. Observability and reconstructibility properties of certain manifest variables from certain others, in the presence of latent variables, are defined and fully characterized. Necessary and sufficient conditions for the existence of either a dead-beat or an exact observer are introduced, and a complete parametrization of all dead-beat observers is given.     

State and input simultaneous estimation for a class of nonlinear systems

This paper addresses the problem of estimating simultaneously the state and input of a class of nonlinear systems. Here, the systems nonlinear part comprises a Lipschitz nonlinear function with respect to the state and input, and a state-dependent unknown function including additive disturbance as well as uncertain/nonlinear/time-varying terms. Upon satisfying some conditions, the observer design problem can be solved via a Riccati inequality or a LMI-based technique with asymptotic estimation guaranteed. A numerical example is included for illustration.     

Estimation of states and parameters for linear systems with nonlinearly parameterized perturbations

We consider systems that can be described by a linear part with a nonlinear perturbation, where the perturbation is parameterized by a vector of unknown, constant parameters. Under a set of technical assumptions about the perturbation and its relationship to the outputs, we present a modular design technique for estimating the system states and the unknown parameters. The design consists of a high-gain observer that estimates the states of the system together with the full perturbation, and a parameter estimator constructed by the designer to invert a nonlinear equation. We illustrate the technique on a simulated dc motor with friction.