arXiv subjects

Hashim A. Hashim

Publications and source records attributed to Hashim A. Hashim.

54 records · Page 3Linked to original sources

arXiv2021

Stochastic Observer for SLAM on the Lie Group

A robust nonlinear stochastic observer for simultaneous localization and mapping (SLAM) is proposed using the available uncertain measurements of angular velocity, translational velocity, and features. The proposed observer is posed on the Lie Group of $\mathbb{SLAM}_{n}\left(3\right)$ to mimic the true stochastic SLAM dynamics. The proposed approach considers the velocity measurements to be attached with an unknown bias and an unknown Gaussian noise. The proposed SLAM observer ensures that the closed loop error signals are semi-globally uniformly ultimately bounded. Simulation results demonstrates the efficiency and robustness of the proposed approach, revealing its ability to localize the unknown vehicle, as well as mapping the unknown environment given measurements obtained from low-cost units.

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arXiv2021

Nonlinear Attitude Filter on SO(3): Fast Adaptation and Robustness

Nonlinear attitude filters have been recognized to have simpler structure and better tracking performance when compared with Gaussian attitude filters and other methods of attitude determination. A key element of nonlinear attitude filter design is the selection of error criteria. The conventional design of nonlinear attitude filters has a trade-off between fast adaptation and robustness. In this work, a new functional approach based on fuzzy rules for on-line continuous tuning of the nonlinear attitude filter adaptation gain is proposed. The input and output membership functions are optimally tuned using artificial bee colony optimization algorithm taking into account both attitude error and rate of change of attitude error. The proposed approach results of high adaptation gain at large error and small adaptation gain at small error. Thereby, the proposed approach allows fast convergence properties with high measures of robustness. The simulation results demonstrate that the proposed approach offers robust and high convergence capabilities against large error in initialization and uncertain measurements.

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arXiv2021

Fast Adaptation Nonlinear Observer for SLAM

The process of simultaneously mapping the environment in three dimensional (3D) space and localizing a moving vehicle's pose (orientation and position) is termed Simultaneous Localization and Mapping (SLAM). SLAM is a core task in robotics applications. In the SLAM problem, each of the vehicle's pose and the environment are assumed to be completely unknown. This paper takes the conventional SLAM design as a basis and proposes a novel approach that ensures fast adaptation of the nonlinear observer for SLAM. Due to the fact that the true SLAM problem is nonlinear and is modeled on the Lie group of $\mathbb{SLAM}_{n}\left(3\right)$, the proposed observer for SLAM is nonlinear and modeled on $\mathbb{SLAM}_{n}\left(3\right)$. The proposed observer compensates for unknown bias attached to velocity measurements. The results of the simulation illustrate the robustness of the proposed approach.

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arXiv2021

Geometric Stochastic Filter with Guaranteed Performance for Autonomous Navigation based on IMU and Feature Sensor Fusion

This paper concerns the estimation problem of attitude, position, and linear velocity of a rigid-body autonomously navigating with six degrees of freedom (6 DoF). The navigation dynamics are highly nonlinear and are modeled on the matrix Lie group of the extended Special Euclidean Group $\mathbb{SE}_{2}(3)$. A computationally cheap geometric nonlinear stochastic navigation filter is proposed on $\mathbb{SE}_{2}(3)$ with guaranteed transient and steady-state performance. The proposed filter operates based on a fusion of sensor measurements collected by a low-cost inertial measurement unit (IMU) and features (obtained by a vision unit). The closed loop error signals are guaranteed to be almost semi-globally uniformly ultimately bounded in the mean square from almost any initial condition. The equivalent quaternion representation is included in the Appendix. The filter is proposed in continuous form, and its discrete form is tested on a real-world dataset of measurements collected by a quadrotor navigating in three dimensional (3D) space. Keywords: Localization, navigation, position and orientation estimation, stochastic systems, GPS-denied navigation observer, navigation estimator, vision-aided inertial navigation systems (VA-INSs), stochastic differential equation, Gaussian noise, sensor fusion.

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arXiv2021

Nonlinear Pose Filters on the Special Euclidean Group SE(3) with Guaranteed Transient and Steady-state Performance

Two novel nonlinear pose (i.e, attitude and position) filters developed directly on the Special Euclidean Group SE(3)able to guarantee prescribed characteristics of transient and steady-state performance are proposed. The position error and normalized Euclidean distance of attitude error are trapped to arbitrarily start within a given large set and converge systematically and asymptotically to the origin from almost any initial condition. The transient error is guaranteed not to exceed a prescribed value while the steady-state error is bounded by a predefined small value. The first pose filter operates based on a set of vectorial measurements coupled with a group of velocity vectors and requires preliminary pose reconstruction. The second filter, on the contrary, is able to perform its function using a set of vectorial measurements and a group of velocity vectors directly. Both proposed filters provide reasonable pose estimates with superior convergence properties while being able to use measurements obtained from low-cost inertial measurement, landmark measurement, and velocity measurement units. Simulation results demonstrate effectiveness and robustness of the proposed filters considering large error in initialization and high level of uncertainties in velocity vectors as well as in the set of vector measurements. Attitude, position, pose estimation, nonlinear observer, estimate, special orthogonal group, special Euclidean group, SO(3), SE(3), prescribed performance function, transient, steady-state error, transformed error, Landmark, feature measurement, PPF, IMU, Lie algebra, Lie group, projection, Gyroscope, Inertial measurement units, rigid body, micro electromechanical systems, sensor, IMUs, MEMS, Roll, Pitch, Yaw, UAVs, QUAV, SVD, Fixed, Moving, Vehicles, Robot, Robotic System, Spacecraft, submarine, Underwater vehicle.

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arXiv2021

A Geometric Nonlinear Stochastic Filter for Simultaneous Localization and Mapping

Simultaneous Localization and Mapping (SLAM) is one of the key robotics tasks as it tackles simultaneous mapping of the unknown environment defined by multiple landmark positions and localization of the unknown pose (i.e., attitude and position) of the robot in three-dimensional (3D) space. The true SLAM problem is modeled on the Lie group of $\mathbb{SLAM}_{n}\left(3\right)$, and its true dynamics rely on angular and translational velocities. This paper proposes a novel geometric nonlinear stochastic estimator algorithm for SLAM on $\mathbb{SLAM}_{n}\left(3\right)$ that precisely mimics the nonlinear motion dynamics of the true SLAM problem. Unlike existing solutions, the proposed stochastic filter takes into account unknown constant bias and noise attached to the velocity measurements. The proposed nonlinear stochastic estimator on manifold is guaranteed to produce good results provided with the measurements of angular velocities, translational velocities, landmarks, and inertial measurement unit (IMU). Simulation and experimental results reflect the ability of the proposed filter to successfully estimate the six-degrees-of-freedom (6 DoF) robot's pose and landmark positions. Keywords: Simultaneous Localization and Mapping, nonlinear stochastic observer for SLAM, stochastic differential equations, pose estimator, position, attitude, Brownian motion process, inertial measurement unit, landmarks, features, SDE, SO(3), SE(3), SLAM.

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arXiv2020

Guaranteed Performance Nonlinear Observer for Simultaneous Localization and Mapping

A geometric nonlinear observer algorithm for Simultaneous Localization and Mapping (SLAM) developed on the Lie group of \mathbb{SLAM}_{n}\left(3\right) is proposed. The presented novel solution estimates the vehicle's pose (i.e. attitude and position) with respect to landmarks simultaneously positioning the reference features in the global frame. The proposed estimator on manifold is characterized by predefined measures of transient and steady-state performance. Dynamically reducing boundaries guide the error function of the system to reduce asymptotically to the origin from its starting position within a large given set. The proposed observer has the ability to use the available velocity and feature measurements directly. Also, it compensates for unknown constant bias attached to velocity measurements. Unit-qauternion of the proposed observer is presented. Numerical results reveal effectiveness of the proposed observer. Keywords: Nonlinear filter algorithm, Nonlinear observer for Simultaneous Localization and Mapping, Nonlinear estimator, nonlinear SLAM observer on manifold, nonlinear SLAM filter on matrix Lie Group, observer design, asymptotic stability, systematic convergence, Prescribed performance function, pose estimation, attitude filter, position filter, feature filter, landmark filter, gradient based SLAM observer, gradient based observer for SLAM, adaptive estimate, SLAM observer, observer SLAM framework, equivariant observer, inertial vision unit, visual, SLAM filter, SE(3), SO(3).

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arXiv2020

Systematic Convergence of Nonlinear Stochastic Estimators on the Special Orthogonal Group SO(3)

This paper introduces two novel nonlinear stochastic attitude estimators developed on the Special Orthogonal Group \mathbb{SO}\left(3\right) with the tracking error of the normalized Euclidean distance meeting predefined transient and steady-state characteristics. The tracking error is confined to initially start within a predetermined large set such that the transient performance is guaranteed to obey dynamically reducing boundaries and decrease smoothly and asymptotically to the origin in probability from almost any initial condition. The proposed estimators produce accurate attitude estimates with remarkable convergence properties using measurements obtained from low-cost inertial measurement units. Unit-quaternion representation of the proposed filters are presented. The estimators proposed in continuous form are complemented by their discrete versions for the implementation purposes. The simulation results illustrate the effectiveness and robustness of the proposed estimators against uncertain measurements and large initialization error, whether in continuous or discrete form. Keywods: Attitude estimates, transient, steady-state error, nonlinear filter, special orthogonal group, SO(3), stochastic system, stochastic differential equations, Ito, Stratonovich, asymptotic stability, Wong-Zakai, inertial measurment unit, IMU, prescribed performance function, Euler Angles, roll, bitch, yaw, color noise, white noise, Nonlinear attitude filter, Nonlinear attitude observer, Orientation, nonlinear stochastic attitude filter on SO(3), unit-quaternion based nonlinear stochastic attitude filter, discrete stochastic attitude filter.

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arXiv2020

Nonlinear Stochastic Attitude Filters on the Special Orthogonal Group 3: Ito and Stratonovich

Two nonlinear stochastic complimentary filters are developed on SO(3). They guarantee that errors in the Rodriguez vector and estimates are semi-globally uniformly ultimately bounded in mean square, and they converge to a small neighborhood of the origin. Simulation results are presented to illustrate the effectiveness of the proposed filters considering high level of uncertainties in angular velocity as well as body-frame vector measurements. Keywords: Attitude estimate, Attitude estimator, Attitude observer, Attitude filter, Nonlinear stochastic filter, stochastic differential equations, Brownian motion process, Ito, Stratonovich, Wong Zakai, Rodriguez vector, unit-quaternion, special orthogonal group 3, Euclidean, Euler angles, Angle-axis, Mapping, Parameterization, Representation, Robust, Invariant, Kalman Filter, Extended Kalman Filter, Multiplicative Extended Kalman Filter, Unscented Kalman Filter, Particle Filter, KF, EKF, MEKF, IEKF, first, second, Partial derivative, operator, probability, small, error, dynamics, kinematics, equilibrium, asymptotic, covariance, mean square, expected value, zero, unknown, time-varying, global, semi-global, stable, stability, uncertain, white noise, Gaussian noise, colored noise, bias, vectorial, vector measurement, angular velocity, singular value decomposition, bounded, rotational matrix, identity, deterministic, orientation, body frame, comparison, inertial frame, rigid body, three dimensional, 3D, space, Attitude Control, Lie algebra, Lie group, projection, Gyroscope, Inertial measurement units, micro electromechanical systems, sensor, IMUs, MEMS, Roll, Pitch, Yaw, UAVs, QUAV, SVD, Fixed, Moving, Vehicles, Robot, Robotic System, Spacecraft, submarine, Underwater vehicle, Problem, advantage, integral, integration, passive complementary filter, Disadvantage, autonomous, Review, Overview, Survey, comparative study, pose, SDEs, SE(3), SO(3).

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arXiv2020

Guaranteed Performance of Nonlinear Pose Filter on SE(3)

This paper presents a novel nonlinear pose filter evolved directly on the Special Euclidean Group SE(3) with guaranteed characteristics of transient and steady-state performance. The above-mention characteristics can be achieved by trapping the position error and the error of the normalized Euclidean distance of the attitude in a given large set and guiding them to converge systematically to a small given set. The error vector is proven to approach the origin asymptotically from almost any initial condition. The proposed filter is able to provide a reliable pose estimate with remarkable convergence properties such that it can be fitted with measurements obtained from low-cost measurement units. Simulation results demonstrate high convergence capabilities and robustness considering large error in initialization and high level of uncertainties in measurements. Keywords: Pose, estimator, observer, attitude, position, estimate, special orthogonal group, special Euclidean group, prescribed performance, steady-state, transient response, homogeneous transformation matrix, complimentary filter, mapping, Parameterization, Representation, Robust, stability, uncertain, Gaussian, noise, vectorial measurement, vector measurement, translational velocity, angular velocity, singular value decomposition, rotational matrix, identity, deterministic, comparison, inertial frame, rigid body, three dimensional, 3D, space, Lie group, projection, landmark, feature, gyroscope, micro electromechanical systems, Inertial measurement units, sensor, IMUs, Fixed, moving, orientation, Roll, Pitch, Yaw, SVD, UAVs, QUAV, unmanned, underwater vehicle, robot, robotic System, spacecraft, quadrotor, quadcopter, overview, autonomous, xyz, axis, SO(3), SE(3).

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arXiv2019

Nonlinear Stochastic Position and Attitude Filter on the Special Euclidean Group 3

This paper formulates the pose estimation problem as nonlinear stochastic filter kinematics evolved directly on the Special Euclidean Group SE(3). Proposed filter guarantees that the errors present in position and Rodriguez vector estimates are semi-globally uniformly ultimately bounded (SGUUB) in mean square, and that they converge to small neighborhood of the origin in probability. Simulation results show the robustness and effectiveness of the proposed filter in presence of high levels of noise and bias associated with the velocity vector as well as body-frame measurements. Keywords: Pose estimator, pose observer, attitude estimate, control, estimator, observer, Nonlinear stochastic pose filter, stochastic differential equations, Brownian motion process, Ito, Stratonovich, Wong Zakai, unit-quaternion, special orthogonal group, homogeneous transformation matrix, complimentary filter, Euler angles, Angle-axis, mapping, Parameterization, Representation, Robust, Multiplicative Extended Kalman Filter, Unscented Kalman Filter, Particle filter, KF, EKF, IEKF, UKF, MEKF, partial derivative, small, dynamics, equilibrium, asymptotic, covariance, expected value, zero, unknown, time-varying, global, semi-global, stable, stability, uncertain, Gaussian, colored, white, noise, vectorial measurement, vector measurement, translational velocity, angular velocity, singular value decomposition, rotational matrix, identity, deterministic, comparison, inertial frame, rigid body, three dimensional, 3D, space, adjoint, Lie group, projection, landmark, feature, Gyroscope, micro electromechanical systems, Inertial measurement units, sensor, IMUs, Fixed, moving, orientation, Roll, Pitch, Yaw, SVD, UAVs, QUAV, unmanned, underwater vehicle, robot, Robotic System, Spacecraft, quadrotor, quadcopter, integral, advantage, disadvantage, Comparative study, Review, Overview, Survey, autonomous, xyz, axis, SO(3), SE(3).

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arXiv2019

Guaranteed Performance of Nonlinear Attitude Filters on the Special Orthogonal Group SO(3)

This paper proposes two novel nonlinear attitude filters evolved directly on the Special Orthogonal Group SO(3) able to ensure prescribed measures of transient and steady-state performance. The tracking performance of the normalized Euclidean distance of attitude error is trapped to initially start within a large set and converge systematically and asymptotically to the origin from almost any initial condition. The convergence rate is guaranteed to be less than the prescribed value and the steady-state error does not exceed a predefined small value. The first filter uses a set of vectorial measurements with the need for attitude reconstruction. The second filter instead uses only a rate gyroscope measurement and two or more vectorial measurements. These filters provide good attitude estimates with superior convergence properties and can be applied to measurements obtained from low cost inertial measurement units (IMUs). Simulation results illustrate the robustness and effectiveness of the proposed attitude filters with guaranteed performance considering high level of uncertainty in angular velocity along with body-frame vector measurements. Keywords: Attitude, estimate, estimator, observer, filter, nonlinear deterministic attitude filter, special orthogonal group, Euler angles, angle-axis, Rodrigues vector, mapping, parameterization, prescribed performance, representation, robust, Multiplicative Extended Kalman Filter, KF, EKF, MEKF, asymptotic stability, almost global asymptotic, noise, rotational matrix, identity, origin, orientation, body frame, inertial frame, rigid body, three dimensional, 3D, space, micro electromechanical systems, sensor, MEMS, roll, pitch, yaw, UAVs, QUAV, SVD, fixed, moving, vehicles, robot, robotic system, spacecraft, submarine, underwater vehicle, passive complementary filter, explicit complementary filter, autonomous, comparative study, SO(3).

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arXiv2019

Nonlinear Explicit Stochastic Attitude Filter on SO(3)

This work proposes a nonlinear stochastic filter evolved on the Special Orthogonal Group SO(3) as a solution to the attitude filtering problem. One of the most common potential functions for nonlinear deterministic attitude observers is studied and reformulated to address the noise attached to the attitude dynamics. The resultant estimator and correction factor demonstrate convergence properties and remarkable ability to attenuate the noise. The stochastic dynamics of the attitude problem are mapped from SO(3) to Rodriguez vector. The proposed stochastic filter evolved on SO(3) guarantees that errors in the Rodriguez vector and estimates steer very close to the neighborhood of the origin and that the errors are semi-globally uniformly ultimately bounded in mean square. Simulation results illustrate the robustness of the proposed filter in the presence of high uncertainties in measurements. Keywords: Attitude, estimate, estimator, observer, filter, stochastic differential equations, SDEs, Ito, Rodriguez vector, special orthogonal group, Euler angles, Brownian motion process, Angle-axis, Mapping, Parameterization, Representation, Partial derivative, asymptotic, unknown, time-varying, global, stable, stability, uncertain, white noise, Gaussian, colored, bias, vectorial, vector measurement, angular velocity, rotational matrix, identity, orientation, body frame, inertial frame, rigid body, three dimensional, micro electromechanical systems, Gyroscope, sensor, Inertial measurement units, IMUs, MEMS, Roll, Pitch, Yaw, autonomous, Robotic System, Spacecraft, submarine, Vehicles, Robot, Underwater vehicle, derivative, explicit complementary filter.

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arXiv2018

Adaptive synchronisation of unknown nonlinear networked systems with prescribed performance

This paper proposes an adaptive tracking control with prescribed performance function for distributive cooperative control of highly nonlinear multi-agent systems. The use of such approach confines the tracking error within a large predefined set to a predefined smaller set. The key idea is to transform the constrained system into unconstrained one through the transformation of the output error. Agents' dynamics are assumed unknown, and the controller is developed for a strongly connected structured network. The proposed controller allows all agents to follow the trajectory of the leader node, while satisfying the necessary dynamic requirements. The proposed approach guarantees uniform ultimate boundedness for the transformed error as well as a bounded adaptive estimate of the unknown parameters and dynamics. Simulations include two examples to validate the robustness and smoothness of the proposed controller against highly nonlinear heterogeneous multi-agent system with uncertain time-variant parameters and external disturbances. Keywords: Prescribed performance, Transformed error, Multi-agents, Distributed adaptive control, Adaptive Consensus, Transient, Steady-state error, Semi-global asymptotic stability, uniformly ultimately bounded, Nonlinear Networked Systems, Distributed Control, Robustness.

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arXiv2018

A fuzzy logic feedback filter design tuned with PSO for L1 adaptive controller

L1 adaptive controller has been recognized for having a structure that allows decoupling between robustness and adaption owing to the introduction of a low pass filter with adjustable gain in the feedback loop. The trade-off between performance, fast adaptation and robustness, is the main criteria when selecting the structure or the coefficients of the filter. Several off-line methods with varying levels of complexity exist to help finding bounds or initial values for these coefficients. Such values may require further refinement using trial-and-error procedures upon implementation. Subsequently, these approaches suggest that once implemented these values are kept fixed leading to sub-optimal performance in both speed of adaptation and robustness. In this paper, a new practical approach based on fuzzy rules for online continuous tuning of these coefficients is proposed. The fuzzy controller is optimally tuned using Particle Swarm Optimization (PSO) taking into accounts both the tracking error and the controller output signal range. The simulation of several examples of systems with moderate to severe nonlinearities demonstrate that the proposed approach offers improved control performance. Keywords: Fuzzy logic control, single-objective, multi-objective particle swarm optimization, L1 Adaptive control, fuzzy L1 adaptive controller, L1 fuzzy adaptive control, L1 fuzzy adaptive controller, fuzzy L1 adaptive control, Filter tuning, Fuzzy membership function tuning, optimal, optimal tuning, Fuzzy membership function optimization, Robustness, Adaptation, multi-input multi-output, single-input single-output, estimate, PSO, FLC, nonlinear, adaptive, online, off-line, Fuzzy adaptive controller, Fuzzy adaptive control, single input single output, multi input multi output, SISO, MIMO, robust, uncertain, uncertain nonlinear system, disturbance, unknown, Adaptive Fuzzy Control Design, stable.

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arXiv2018

Optimal Placement of Relay Nodes in Wireless Sensor Network Using Artificial Bee Colony Algorithm

Deploying sensor nodes randomly most of the time generates initial communication hole even in highly dense networks. These communication holes cannot be totally eliminated even when the deployment is done in a structured manner. In either case, the resulting inter-node distances may degrade the performance of the network. This paper proposes an enhanced deployment algorithm based on Artificial Bees Colony (ABC). The ABC-based deployment is guaranteed to extend the lifetime by optimizing the network parameters and constraining the total number of deployed relays. Simulations validate the effectiveness of the proposed strategy under different cases of problem complexity. Results show that the proposed approach improves the network lifetime considerably when compared to solutions reported in the literature such as Shortest Path 3-D grid Deployment (SP3D) algorithm. Keywords: Artificial Bee Colony, Wiener index, optimization, relay nodes, Laplacian matrix, connected graph, vertex, edge, average distance, Laplacian matrix, Shortest Path 3-D grid Deployment, ABC, SP3D, RNs/CHs, ILDCC, SPRN, O3DwLC, algorithm, approach, single objective, multi objective, eigenvalue, First Phase Relay Nodes, NP-Hard, Deployment, proposed, second phase relay nodes, Ideal Media Access Control, cluster head, Minimum Spanning Tree, non-deterministic polynomial-time hard, two-layer hierarchical structure, Optimized 3-D deployment with Lifetime Constraints, flux, Wireless Sensor Network, size, Lifetime, Network load, number of nodes using packets, Connectivity, two layered, protocols, collision and interference.

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arXiv2018

Optimal Tuning of Fuzzy Feedback filter for L1 Adaptive Controller Using Multi-Objective Particle Swarm Optimization for Uncertain Nonlinear MIMO Systems

This paper proposes an efficient approach for tuning L1 feedback filter of adaptive controller for multi-input multi-output (MIMO) systems. The feedback filter provides performance that trades off fast closed loop dynamics, robustness margin, and control signal range. Thus appropriate tuning of the filter's parameters is crucial to achieve optimal performance. For MIMO systems, the parameters tuning is challenging and requires a multi-objective performance indices to avoid instability. This paper proposes a fuzzy-based L1 feedback filter design tuned with multi-objective particle swarm optimization (MOPSO) to remove these bottlenecks. MOPSO guarantees the appropriate selection of the fuzzy membership functions. The proposed approach is validated using twin rotor MIMO system and simulation results demonstrate the efficacy of here proposed while preserving the system stabilizability.

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arXiv2018

Energy-efficient Deployment of Relay Nodes in Wireless Sensor Networks using Evolutionary Techniques

Random deployment of sensor nodes is susceptible to initial communication hole, even when the network is densely populated. However, eliminating holes using structural deployment poses its difficulties. In either case, the resulting coverage holes can degrade overall network performance and lifetime. Many solutions utilizing Relay Nodes (RNs) have been proposed to alleviate this problem. In this regard, one of the recent solutions proposed using Artificial Bee Colony (ABC) to deploy RNs. This paper proposes RN deployment using two other evolutionary techniques - Gravitational Search Algorithm (GSA) and Differential Evolution (DE) and compares them with existing solution that uses ABC. These popular optimization tools are deployed to optimize the positions of relay nodes for lifetime maximization. Proposed algorithms guarantee satisfactory RNs utilization while maintaining desired connectivity level. It is shown that DE-based deployment improves the network lifetime better than other optimization heuristics considered.

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