This paper introduces an advanced Quaternion-based Unscented Kalman Filter (QUKF) for real-time, robust estimation of system states and external wrenches in assistive aerial payload transportation systems that engage in direct physical interaction. Unlike conventional filtering techniques, the proposed approach employs a unit-quaternion representation to inherently avoid singularities and ensure globally consistent, drift-free estimation of the platform’s pose and interaction wrenches. A rigorous quaternion-based dynamic model is formulated to capture coupled translational and rotational dynamics under interaction forces. Building on this model, a comprehensive QUKF framework is established for state prediction, measurement updates, and external wrench estimation. The proposed formulation fully preserves the nonlinear characteristics of rotational motion, enabling more accurate and numerically stable estimation during physical interaction compared to linearized filtering schemes. Extensive simulations validate the effectiveness of the QUKF, showing significant improvements over the Extended Kalman Filter (EKF). Specifically, the QUKF achieved a 79.41% reduction in Root Mean Squared Error (RMSE) for torque estimation, with average RMSE improvements of 79% and 56%, for position and angular rates, respectively. These findings demonstrate enhanced robustness to measurement noise and modeling uncertainties, providing a reliable foundation for safe, stable, and responsive human-UAV physical interaction in cooperative payload transportation tasks.

This paper addresses the challenge of estimating the orientation, position, and velocity of a vehicle operating in three-dimensional (3D) space with six degrees of freedom (6-DoF). A Deep Learning-based Adaptation Mechanism (DLAM) is proposed to adaptively tune the noise covariance matrices of Kalman-type filters for the Visual-Inertial Navigation (VIN) problem, leveraging IMU-Vision-Net. Subsequently, an adaptively tuned Deep Learning Unscented Kalman Filter for 3D VIN (DeepUKF-VIN) is introduced to utilize the proposed DLAM, thereby robustly estimating key navigation components, including orientation, position, and linear velocity. The proposed DeepUKF-VIN integrates data from onboard sensors, specifically an inertial measurement unit (IMU) and visual feature points extracted from a camera, and is applicable for GPS-denied navigation. Its quaternion-based design effectively captures navigation nonlinearities and avoids the singularities commonly encountered with Euler-angle-based filters. Implemented in discrete space, the DeepUKF-VIN facilitates practical filter deployment. The filter’s performance is evaluated using real-world data collected from an IMU and a stereo camera at low sampling rates. The results demonstrate filter stability and rapid attenuation of estimation errors, highlighting its high estimation accuracy. Furthermore, comparative testing against the standard Unscented Kalman Filter (UKF) in two scenarios consistently shows superior performance across all navigation components, thereby validating the efficacy and robustness of the proposed DeepUKF-VIN. • Adaptively-tuned deep learning unscented Kalman filter. • Singularity-free navigation algorithm with deep learning. • IMU-Vision-Net-based adaptation for adaptive covariance estimation. • Superior performance at low sampling rates. • 3D visual-inertial navigation.

This paper proposes a nonlinear stochastic complementary filter design for inertial navigation that takes advantage of a fusion of Ultra-wideband (UWB) and Inertial Measurement Unit (IMU) technology ensuring semi-global uniform ultimate boundedness (SGUUB) of the closed loop error signals in mean square. The proposed filter estimates the vehicle’s orientation, position, linear velocity, and noise covariance. The filter is designed to mimic the nonlinear navigation motion kinematics and is posed on a matrix Lie Group, the extended form of the Special Euclidean Group$\mathbb {SE}_{2}\left ({3}\right)$. The Lie Group based structure of the proposed filter provides unique and global representation avoiding singularity (a common shortcoming of Euler angles) as well as non-uniqueness (a common limitation of unit-quaternion). Unlike Kalman-type filters, the proposed filter successfully addresses IMU measurement noise considering unknown upper-bounded covariance. Although the navigation estimator is proposed in a continuous form, the discrete version is also presented. Moreover, the unit-quaternion implementation has been provided in the Appendix. Experimental validation performed using a publicly available real-world six-degrees-of-freedom (6 DoF) flight dataset obtained from an unmanned Micro Aerial Vehicle (MAV) illustrating the robustness of the proposed navigation technique.

This article proposes a real-time neural network (NN) stochastic filter-based controller on the Lie group of the special orthogonal group [Formula: see text] as a novel approach to the attitude tracking problem. The introduced solution consists of two parts: a filter and a controller. First, an adaptive NN-based stochastic filter is proposed, which estimates attitude components and dynamics using measurements supplied by onboard sensors directly. The filter design accounts for measurement uncertainties inherent to the attitude dynamics, namely, unknown bias and noise corrupting angular velocity measurements. The closed-loop signals of the proposed NN-based stochastic filter have been shown to be semiglobally uniformly ultimately bounded (SGUUB). Second, a novel control law on [Formula: see text] coupled with the proposed estimator is presented. The control law addresses unknown disturbances. In addition, the closed-loop signals of the proposed filter-based controller have been shown to be SGUUB. The proposed approach offers robust tracking performance by supplying the required control signal given data extracted from low-cost inertial measurement units. While the filter-based controller is presented in continuous form, the discrete implementation is also presented. In addition, the unit-quaternion form of the proposed approach is given. The effectiveness and robustness of the proposed filter-based controller are demonstrated using its discrete form and considering low sampling rate, high initialization error, high level of measurement uncertainties, and unknown disturbances.

Navigation in Global Positioning Systems (GPS)-denied environments requires robust estimators reliant on fusion of inertial sensors able to estimate rigid-body's orientation, position, and linear velocity. Ultra-wideband (UWB) and Inertial Measurement Unit (IMU) represent low-cost measurement technology that can be utilized for successful Inertial Navigation. This paper presents a nonlinear deterministic navigation observer in a continuous form that directly employs UWB and IMU measurements. The estimator is developed on the extended Special Euclidean Group$\mathbb{SE}_{2}$(3) and ensures exponential convergence of the closed loop error signals starting from almost any initial condition. The discrete version of the proposed observer is tested using a publicly available real-world dataset of a drone flight.

This paper outlines the essential components of developing an introductory course in Engineering Design for the first year, fi rst semester students at Thompson Rivers University (TRU). The course design accounts for the teaching context, stakeholder interests, and Canadian Engineering Accreditation Board (CEAB) criteria. The proposed course design scaffolds engineering design projects of three different levels. Through the described course, students become familiar with the engineering design process including translation of the design idea into virtual and physical prototypes. The course design is built around the concepts of engineering sustainability, ethics, and professionalism helping students understand the linkage between engineering design and social and human factors. The course is lecture and laboratory based with a focus on experiential hands-on learning where the Course Learning Outcomes (CLOs) are achieved by means of PowerPoint slides, presentations, lecture and laboratory notes, class discussions and activities, teamwork, lecture and lab video recordings, hand sketching, and virtual prototyping via Computer-Aided Design (CAD) software (Solidworks). Student performance was evaluated through quizzes, reports, homework assignments, laboratory assignments, projects, midterms and final exams. To ensure effective communication between students, anonymous team member peer review and evaluation were incorporated. Continual improvement of the course design was achieved by modifying the course structure based on student feedback.

This paper proposes a novel extended Kalman filter (EKF) along with its adaptive variant for effective magnetic, angular rate and gravity (MARG) sensor-only pose estimation of mobile robots operated longer periods in reference-denied environments. First, a gradient-descent orientation-based EKF framework is derived, which formulates the MARG-based pose propagation with both bandpass-filtered and bias compensated external acceleration signals. The proposed approach uses two correction signals beside the orientation update, namely, virtual observations and sparse reference signals are incorporated in the state correction. Next, the instantaneous dynamics is characterized by accelerometer/gyroscope signals-based measures and an adaptive strategy is derived for real-time tuning of EKF parameters. The algorithm is fine tuned in an optimization framework on an appropriate database. This database of ground truth and raw MARG measurements contains 16 robot motion scenarios, where both slow motions and agile maneuvers are performed on different terrains. The conducted analysis highlights that the proposed algorithms outperform the standard approaches, moreover, the adaptive strategy further improves the performance by 13%. The comprehensive performance evaluation demonstrates the efficacy of the new algorithms, thereby these robust approaches are proposed in environments characterized by sparse reference measurements.

Navigation solutions suitable for cases when both autonomous robot’s pose (i.e., attitude and position) and its environment are unknown are in great demand. Simultaneous Localization and Mapping (SLAM) fulfills this need by concurrently mapping the environment and observing robot’s pose with respect to the map. This work proposes a nonlinear observer for SLAM posed on the manifold of the Lie group of$\mathbb {SLAM}_{n}(3)$, characterized by systematic convergence, and designed to mimic the nonlinear motion dynamics of the true SLAM problem. The system error is constrained to start within a known large set and decay systematically to settle within a known small set. The proposed estimator is guaranteed to achieve predefined transient and steady-state performance and eliminate the unknown bias inevitably present in velocity measurements by directly using measurements of angular and translational velocity, landmarks, and information collected by an inertial measurement unit (IMU). Experimental results obtained by testing the proposed solution on a real-world dataset collected by a quadrotor demonstrate the observer’s ability to estimate the six-degrees-of-freedom (6 DoF) robot pose and to position unknown landmarks in three-dimensional (3D) space.

Simultaneous localization and mapping (SLAM) is a process of concurrent estimation of the vehicle’s pose and feature locations with respect to a frame of reference. This article proposes a computationally cheap geometric nonlinear SLAM filter algorithm structured to mimic the nonlinear motion dynamics of the true SLAM problem posed on the matrix Lie group of$\mathbb {SLAM}_{n}(3)$. The nonlinear filter on manifold is proposed in continuous form and it utilizes available measurements obtained from group velocity vectors, feature measurements, and an inertial measurement unit (IMU). The unknown bias attached to velocity measurements is successfully handled by the proposed estimator. Simulation results illustrate the robustness of the proposed filter in discrete form, demonstrating its utility for the six-degrees-of-freedom (6 DoF) pose estimation as well as feature estimation in three-dimensional (3-D) space. In addition, the quaternion representation of the nonlinear filter for SLAM is provided.

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. The simulation results demonstrate the 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.

Two novel robust nonlinear stochastic full pose (i.e., attitude and position) estimators on the Special Euclidean Group$\mathbb {SE}(3)$are proposed using the available uncertain measurements. The resulting estimators utilize the basic structure of the deterministic pose estimators adopting it to the stochastic sense. The proposed estimators for six degrees of freedom (DOF) pose estimations consider the group velocity vectors to be contaminated with constant bias and Gaussian random noise, unlike nonlinear deterministic pose estimators which disregard the noise component in the estimator derivations. The proposed estimators ensure that the closed-loop error signals are semi-globally uniformly ultimately bounded in mean square. The efficiency and robustness of the proposed estimators are demonstrated by the numerical results which test the estimators against high levels of noise and bias associated with the group velocity and body-frame measurements and large initialization error.

Nonlinear pose (i.e, attitude and position) filters are characterized with simpler structure and better tracking performance in comparison with other methods of pose estimation. A critical factor when designing a nonlinear pose filter is the selection of the error function. Conventional design of nonlinear pose filter design trade-off between fast adaptation and robustness. This paper introduces a new practical approach based on fuzzy rules for on-line continuous tuning of the nonlinear pose filter. Each of input and output membership functions are optimally tuned using graphical search algorithm optimization considering both pose error and its rate of change. The proposed approach is characterized with high adaptation features and strong level of robustness. Therefore, the proposed approach results of robust and fast convergence properties. The simulation results show the effectiveness of the proposed approach considering uncertain measurements and large error in initialization.

This paper formulates the attitude filtering problem as a nonlinear stochastic filter problem evolved directly on the Special Orthogonal Group 3 (SO(3)). One of the traditional potential functions for nonlinear deterministic complimentary filters is studied and examined against angular velocity measurements corrupted with noise. This paper demonstrates that the careful selection of the attitude potential function allows to attenuate the noise associated with the angular velocity measurements and results into superior convergence properties of estimator and correction factor. The problem is formulated as a stochastic problem through mapping SO(3) to Rodriguez vector parameterization. Two nonlinear stochastic complimentary filters are developed on SO(3). The first stochastic filter is driven in the sense of Ito and the second one considers Stratonovich. The two proposed filters guarantee that errors in the Rodriguez vector and estimates are semi-globally uniformly ultimately bounded in mean square. 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.

This paper proposes a neuro-adaptive distributive cooperative tracking control with prescribed performance function (PPF) for highly nonlinear multiagent systems. PPF allows error tracking from a predefined large set to be trapped into a predefined small set. The key idea is to transform the constrained system into unconstrained one through transformation of the output error. Agents' dynamics are assumed to be completely unknown, and the controller is developed for strongly connected structured network. The proposed controller allows all agents to follow the trajectory of the leader node, while satisfying necessary dynamic requirements. The proposed approach guarantees uniform ultimate boundedness of the transformed error and the adaptive neural network weights. Simulations include two examples to validate the robustness and smoothness of the proposed controller against highly nonlinear heterogeneous networked system with time varying uncertain parameters and external disturbances.