Robust State and Unknown Input Estimator and Its Application to Robot Localization

SummaryThe event‐triggered joint sensor fault estimation and mobile robot (MR) localization (MRL) problem (MRLP) subject to the potential fluctuations of the estimator gain are investigated. From the external sensor to the estimator, to decrease the consumption of sensor energy and cut down network bandwidth resources, an event‐triggered scheme is considered. For the sake of characterizing the phenomenon induced by the inaccurate calculation of estimator gain, an uncertainty with the bounded second moment is employed. The purpose of this study is theoretically to find a feasible and effective approach to the addressed joint estimation problem such that the estimation error (EE) covariance (EEC) meets the given performance index. First, a minimum upper bound (UB) of the EEC is derived. Subsequently, in terms of the proposed joint estimation approach and the corresponding results obtained, an algorithm to address the resilient joint sensor fault estimation and MRLP is summarized. At the end, the effectiveness of the proposed algorithm is validated through conducting a set of comparisive experiments.

In this paper, the localization problem of the mobile robot (MR) with an energy harvesting sensor (EHS) is studied. A specific situation is regarded, which is that the MR equips with an EHS who owns the capacity for absorbing the energy from the surroundings. When the sensor energy is sufficient, the sensor can send its measurement to the filter. Otherwise, the sensor energy‐induced measurement missing phenomenon will occur. For the sake of acquiring the measurement missing rate, the relationship between the amount of the sensor energy and its probability distribution is derived recursively at each time instant. The purpose of this paper is to seek out a feasible solution to the addressed MR localization (MRL) problem (MRLP) by devising the desired time‐varying filter. Firstly, in the presence of the sensor energy‐induced measurement missing phenomenon, an upper bound (UB) for the filtering error (FE) covariance (FEC) is acquired recursively. Then, the acquired UB is minimized by characterizing the desired filter gain adequately. Finally, a simulation is conducted to testify the availability of the proposed MRL algorithm (MRLA).

Localization problem of mobile robot in an environment of interest is one of research fields that are not still completely solved. Many methods to settle this problem are unceasingly being examined. Although a lot of researchers have dedicated themselves to this problem, it demands new but more accurate method by which mobile robot itself recognizes its own position while moving. It tries to find solution by making mention of various localization problems with estimation method in this chapter. Robot researchers had to recognize the current position information for movement control of mobile robot to last destination. It is being adopted from the conventional Kalman filter, which was proposed to reduce stochastic noise error, to complicated algorithms in the field of target tracking. The localization of the mobile robot occurred in various environments such as indoor, outdoor, warehouse, harbors, airports, and offices is based on estimation theories of target tracking field. The estimation method to be proposed in this chapter is mentioned with localization problem in the text. As the most widely used method for providing the current position of mobile robot, odometry is inexpensive method to implement in real time, but has vital demerit of accumulation of position error for long distance navigation. Various external sensors were used to supplement this problem, but the adopted sensors have also intrinsic errors. GPS, used as a global sensor in the outdoors, has a fatal weak point suffering from multi-path effects in the surrounding of buildings or trees. In this chapter, method for decreasing the above error occurred in localization problem are provided and embodied. This error is assumed as bias error. New nonlinear estimation method included in data integration method to reduce that error is derived and evaluated through experiment. The proposed integration method is provided to take full advantage of characteristics of mobile and outdoor environment sensors. 11

For autonomous navigation in workspace, a mobile robot has to be able to know its position in this space in a precise way that means that the robot must be able to self-localize to move and perform successfully the different entrusted tasks. At present, one of the most used systems in open spaces is the GPS navigation system; however, in indoor spaces (factories, buildings, hospitals, warehouses...) GPS signals are not operative because their intensity is too weak. The absence of GPS navigation systems in these environments has stimulated the development of new local positioning systems with their particular problems. Such systems have required in many cases the installation of beacons that operate like satellites (similar to GPS), the use of landmarks or even the use of other auxiliary systems to determine the robot’s position. The problem of mobile robot localization is a part of a more global problem because in autonomous navigation when a robot is exploring an unknown environment, it usually needs to obtain some important information: a map of the environment and the robot’s location in the map. Since mapping and localization are related to each other, these two problems are usually considered as a single problem called simultaneous localization and mapping (SLAM). The problem of Simultaneous Localization and Map Building is a significant open problem in mobile robotics which is difficult because of the following paradox: to localize itself the robot needs the map of the environment, and, for building a map the robot location must be known precisely. Mobile robots use different kinds of sensors to determine their position: for instance it is very common the use of odometric or inertial sensors, however it is remarkable to consider that in wheel slippage, sensor drifts a noise causing error accumulation, thus leading to erroneous estimates. Another kind of external sensors used in robotics in order to solve localization are for instance CCD cameras, infrared sensor, ultra sonic sensor, mechanical wave and laser. Other sensors recently applied are the instruments sensible to the magnetic field known as the electronic compass (Navarro & Benet, 2009). Mobile robotics are interested on those able to measure the Earths magnetic field and express it through an electrical signal. One type of electronic compass is based on magneto-resistive transducers, whose electrical resistance varies with the changes on the applied magnetic field. This type of sensors presents sensitivities below 0.1 milligauss, with response times below 1 sec, allowing its reliable use in vehicles moving at high speeds (Caruso, 2000). In SLAM some applications with electronic compass have been developed working simultaneously with other sensors such as artificial vision (Kim et al., 2006) and ultrasonic sensors (Kim et al., 2007).

The problem of mobile robot localization by using sensor information appeals to different communities since the need for accurate position has become crucial for many robot subtasks. The Kalman filter (KF) has been acknowledged as an appropriate tool for a suitable dynamic combination of the different measurements using the state and measurement models. However, when there are discrete uncertainties about the models, without additional restrictions, the performance of KF degrades drastically as the predicted estimate tends to be updated by a wrong measurement. This paper focuses on a suboptimal multiple model filter to deal with the associated measurement/model. Experimental and simulated results are achieved, which prove the feasibility of the proposal. The experimental setup consists of a structured environment constituted of elementary features such as walls and corners, while a possibly unmodeled obstacle may be encountered. The robot is equipped with odometry and a set of ultrasonic sensors.

In this paper, a novel methodology is proposed to solve the simultaneous localization and mapping (SLAM) problem of mobile robot with particle filter (PF) algorithm. Compared with Kalman filter (KF) and extended Kalman filter (EKF), PF has a better performance in non-linear non-Gaussian environments. A close-loop updating scheme is developed in which positions of the robot and landmarks are updated with particle filtering and a weighted averaging algorithm respectively, and are linked through an additional feedback and correction process. An adaptive re-sampling method is used to reduce the computational load. The results of the simulation indicate that the PF-SLAM algorithm can localize the robot and landmarks accurately, and the error of landmarks' estimation converges better than general SLAM algorithms.

The Simultaneous Localization and Mapping (SLAM) problem for mobile robots aims at consistently building a map of an unknown environment while simultaneously determining its position or location within this map. From a control-theory viewpoint, it is somehow analogous to simultaneously estimating the states and output map of the system. In the robotic based engineering applications, SLAM is arguably considered a solved problem on a theoretical and conceptual level, but still it requires considerable maturity on a practical level [16][22]. The state-of-the-art SLAM algorithms require computationally powerful processors, expensive sensors with dense feature extraction and multiple sensors for uncertainty reduction [21]. An approach to the SLAM problem using minimal sensing information is still lacking in both theoretical and practical aspects. This paper highlights the data acquisition & association issues with different sensors like odometric & infra red sensors used in SLAM application due to addition of random Gaussian noise leading to errors & uncertainty in mapping processes [17][22]. Simple filtering techniques using average filtering & Kalman filtering have been implemented on the acquired data to go for comparative analysis of sensor performance & its impact on SLAM process towards reduction in uncertainty or minimal shift in landmark extraction [19].

For the direct feedthrough system where unknown input affects both process equation and measurement equation, an unscented recursive three-step filter based unbiased minimum-variance (URTSF-UMV) estimation algorithm is proposed. The algorithm is based on the unbiased minimum-variance (UMV) method and uses statistical linearisation technology to approximate the nonlinear system and the nonlinear measurement function to linear regression form. The estimation of unknown input is obtained from innovation through weighted least-squares (WLS) estimation. The approximate linear regression form allows us to process the nonlinear system with unknown input direct feedthrough by using the UMV state estimation framework, and derive the filter by minimising the trace of the state error covariance of the measurement update under the unbiased condition. The URTSF-UMV requires that the unknown input distribution matrix is full column rank. We use the full rank decomposition method to deal with the nonlinear system containing the unknown input rank-deficient distribution matrix. The effectiveness of the URTSF-UMV algorithm is demonstrated through an illustrative simulation example.

In this paper, the localization problem of a mobile robot equipped with a Doppler–azimuth radar (D–AR) is investigated in the environment with multiple landmarks. For the type (2,0) robot kinematic model, the unknown modeling errors are generally aroused by the inaccurate odometer measurement. Meanwhile, the inaccurate odometer measurement can also give rise to a type of unknown bias for the D–AR measurement. For reducing the influence induced by modeling errors on the localization performance and enhancing the practicability of the developed robot localization algorithm, an adaptive fading extended Kalman filter (AFEKF)-based robot localization scheme is proposed. First, the robot kinematic model and the D–AR measurement model are modified by considering the impact caused by the inaccurate odometer measurement. Subsequently, in the frame of adaptive fading extended Kalman filtering, the way to the addressed robot localization problem with unknown biases is sought out and the stability of the developed AFEKF-based localization algorithm is also discussed. Finally, in order to testify the feasibility of the AFEKF-based localization scheme, three different kinds of modeling errors are considered and the comparative simulations are conducted with the conventional EKF. From the comparative simulation results, it can be seen that the average localization error under the developed AFEKF-based localization scheme is [0.0245 m0.0224 m0.0039 rad]T and the average localization errors using the conventional EKF are [1.0405 m2.2700 m0.1782 rad]T, [0.4963 m0.3482 m0.0254 rad]T and [0.2774 m0.3897 m0.0353 rad]T, respectively, under the three cases of the constant bias, the white Gaussian stochastic bias and the bounded uncertainty bias.

This paper proposes an unknown input root mean square cubature Kalman filter algorithm, which is applied to the fault diagnosis of nonlinear systems with unknown input. Firstly, a standard linear regression equation with unknown input is constructed, and orthogonal trigonometric decomposition is combined to solve the equation to improve the estimation accuracy of unknown input. In addition, in order to improve the numerical stability of algorithm, the root mean square algorithm is introduced into the error covariance matrix calculated from the unknown input estimation and state estimation results. Secondly, the root mean square value of the sliding window of residual obtained from the difference between the measured value and the estimated value is computed to judge whether the actuator has a fault. The generalized regression neural network is used for fault identification. Finally, a single link manipulator system is taken for simulation verification.

In this study, the control design problem of double-pinion-type electric power assist steering (EPAS) is carefully examined. Based on a Lagrangian-based dynamical model, an optimal control approach with unknown input is formulated thereby eliminating the need for torque sensor. A new controller is developed using combination of non-linear assist curve, unknown-input estimator (UIE) and linear quadratic integral theory. It has been established that the estimation of the state, and unknown input using UIE yields a good estimate with performance compared with the well-known Kalman estimator. It is further shown that the resulting closed-loop response is able to track non-linear assist curve for different velocity. This reveals a salient feature, that is, controlling an EPAS system can be done using only single constant gain.

For nonlinear discrete systems with dual unknown inputs, there are many limitations regarding previous nonlinear filters. This paper proposes two new, improved square-root cubature Kalman filtering (ISRCKF) algorithms to estimate system states and dual unknown inputs. Improved square-root cubature Kalman filtering 1 (ISRCKF1) introduces an innovation that first obtains the unknown input estimates from the measurement equation, then updates the innovation to derive the unknown input estimates from the state equation, then uses the already obtained estimates of the dual unknown inputs to correct the one-step estimate of the state, and finally the minimum variance unbiased estimate of the state is obtained. Improved square-root cubature Kalman filtering 2 (ISRCKF2) builds a unified innovation feedback model, then applies the minimum variance unbiased estimation (MVUE) criterion to obtain the estimates of system states and dual unknown inputs, refining a more concise recursive filter but requiring stronger assumptions. Finally, simulation results demonstrate that the above two algorithms can achieve the optimal estimates of system states and dual unknown inputs simultaneously, and ISRCKF2 further enhances the accuracy of both state and dual unknown inputs estimation, which verifies the validity of the proposed algorithms.

Estimating unknown inputs in indoor heating, ventilation, and air conditioning (HVAC) systems, particularly under the influence of diverse environmental constraints and time-varying relative humidity, presents a significant challenge. A viable solution is to employ a weighted least squares approach for estimating unknown inputs, which utilizes an unbiased minimum variance (UMV) estimator in conjunction with an unscented Kalman filter (UKF)-based nonlinear filtering technique. This allows for the simultaneous estimation of the system’s state and the unknown inputs. To accurately represent the real-life nonlinear thermal profile influenced by these uncertain inputs, it is essential to adopt an RC network-based mathematical modeling approach that captures the system’s dynamic behavior over time. The integration of the UMV-based optimal estimator with the UKF culminates in the proposed unscented Kalman filter with unbiased minimum variance for unknown inputs (UKF-UMV-UI) estimation algorithm. Extensive experimentation with the proposed UKF-UMV-UI algorithm has been conducted in a laboratory-scale realistic environment, dealing with uncertain and challenging unknown inputs. The results of the investigation indicate that the proposed method outperform the unscented Kalman filter with unknown input (UKF-UI) by 41.64% and 35.85% in Cumulative Mean Squared Error (CuMSE) for two distinct measurement conditions, respectively.

Input and state estimation for linear systems with a rank-deficient direct feedthrough matrix

In this paper a new unknown input estimation method is proposed for a class of nonlinear stochastic systems in the presence of time dependent unknown inputs, when the system states and process noises are unknown but bounded. In this study, a new augmented state vector is constructed by augmenting unknown inputs as a new state to the original state vector. Then a recursive algorithm based on unknown but bounded (UBB) uncertainty is developed, that unlike the Bayesian models which consider the state estimate as a single vector, produces a time-varying set of state estimates that contains the system's true state. The particular sets to be discussed, are ellipsoids. The proposed method doesn't need any unknown input detection stage procedure and covariance resetting that are necessary in previous works. At last, efficiency of the proposed method is shown in a numerical simulation for a nonlinear system.