Navigating doorways is a fundamental capability for mobile manipulators operating in human environments, requiring coordinated motion between the mobile base and manipulator arm. This paper presents a motion planning framework that generates dynamically feasible and collision-free trajectories for autonomously opening and traversing both push and pull doors. The proposed method formulates the robot and door as a coupled dynamical system within a nonlinear Model Predictive Control (MPC) optimization framework. Manipulation feasibility is enforced through a penalty-based constraint, avoiding explicit arm kinematic modeling in the planner. Simulations and a hardware experiment demonstrate that the approach successfully plans feasible trajectories for door traversal.

In practice, sensor measurements can often be subject to environmental noise, which can degrade the accuracy of state estimators. Traditional Kalman filters typically assume that sensor noise is Gaussian, which can reduce their effectiveness and lead to poor performance when sensors are affected by unknown external noises that might be nonzero-mean and non-Gaussian. This letter proposes two adaptive Kalman filters (AKFs) that can compensate for unknown, potentially nonzero-mean external noise, an aspect often overlooked in the literature. Compared to variational Bayesian Kalman filters, our proposed AKFs achieve more accurate state estimates with lower computational complexity, without needing assumptions about the probability distribution of the noise.

Adaptive controllers offer powerful tools for controlling nonlinear systems with parametric uncertainties, yet ensuring safety, particularly during the initial learning phase, remains a significant challenge. Conventional safety approaches often rely on filtering the control output using Control Barrier Functions (CBFs), which may fail to prevent unsafe behavior when parameter estimates are poor and can lead to reckless or overly conservative actions. This paper introduces a novel framework that directly integrates safety constraints into the parameter adaptation process itself. We propose enforcing safety by modulating the parameter update law through a minimally invasive perturbation, calculated via a real-time Quadratic Program (QP). This QP incorporates constraints derived from both a Robust Adaptive Control Lyapunov Function (RaCLF), ensuring system stability, and a CBF, guaranteeing forward invariance of a safe set. Critically, the CBF constraint leverages a formally derived, time-varying upper bound on the parameter estimation error, mitigating conservativeness as the system learns. We provide formal proofs for the stability of the closed-loop system and the validity of the safety constraint. The efficacy and practicality of the proposed safe parameter update strategy are demonstrated across diverse platforms, including numerical simulations of a mass-damper system and a mobile robot, high-fidelity simulation of a UR10 manipulator, and hardware experiments on a quadrupedal robot navigating amidst obstacles.

The Extended Kalman Filter (EKF) and Un-scented Kalman Filter (UKF) are widely used for nonlinear state estimation. The EKF employs first-order linearizations, while the UKF uses the unscented transformation to more accurately capture higher-order moments. Despite their effectiveness, both filters can suffer from limitations such as linearization errors, biased estimates, and potential instability when subject to significant nonlinearities. This paper shows that the performance of the EKF can be improved by compensating for the effects of the higher-order terms that are typically neglected during the linearization of the measurement equation in the EKF derivation through an adaptive mechanism. Simulation results over several Monte Carlo runs across two nonlinear systems show that our proposed Adaptive Extended Kalman Filter (AEKF) can adaptively learn and compensate for these uncertainties, improving estimation accuracy and consistently outperforming both the traditional EKF and the UKF.

Mathematical models have provided a general framework for understanding the dynamics and control of infectious disease. Many compartmental models are limited in that they do not account for the range of behavioral feedbacks that have been observed in the response to emerging infections. Here we expand on the SIR compartmental model framework by introducing a general class of behavioral feedbacks that encompasses both individual responses and nonpharmaceutical interventions. By linking transmission dynamics and behavior, this class of models can capture the interplay of disease incidence, behavioral response, and controls such as vaccination. We prove mathematically the existence of two endemic equilibria depending on the vaccination rate: one in the presence of low vaccination but with reduced societal activity (the "new normal"), and one with return to normal activity but with vaccination rate below that required for disease elimination. Establishing the existence and stability of these equilibria is a precursor to designing control strategies that may exploit them.

This letter deals with enforcing safety in position-controlled robotic systems. We propose a safety-critical position control framework that enables a robot to safely avoid unsafe reference input positions without compromising the overall tracking performance of the existing controller. Simulation results, as well as experimental results on a quadrupedal robot, validate the practicality of our proposed controller for position-controlled robots. Our proposed approach, which uses the well-known Control Barrier Functions (CBF) framework in a model-free fashion, can serve as a safety filter alongside any model-based or model-free controller.

The observations of linear and nonlinear physical processes are subject to random errors, which can be represented by a wide variety of probability distributions. In contrast, most estimation and inference techniques rely on a Gaussian assumption, which may limit our ability to make model-based predictions. There is a need for data assimilation methods that can capture and leverage the higher moments of these physical processes for state estimation and forecasting. In this paper, we develop the generalized unscented transform (GenUT), which uses a minimal number of sample points to accurately capture elements of the higher moments of most probability distributions. Constraints can be analytically enforced on the sample points while guaranteeing at least second-order accuracy. The GenUT is widely applicable to non-Gaussian distributions, which can substantially improve the assimilation of observations of nonlinear physics, such as the modeling of infectious diseases.

Regressor-based control of nonlinear systems uses a linear parameterization of the system dynamics. Most regressor-based controllers only consider uncertainties in the parameter vector, ignoring unmodeled dynamics and perturbations that might be present in the regressor matrix - factors that can significantly deteriorate the controller's performance. In this paper, we propose a novel robust control approach with safety guarantees that also accounts for uncertainties in both the regressor matrix and the parameter vector. We design a control law comprised of several signals that ensure uniform ultimate boundedness of the tracking error and forward invariance of a desired safe set via Control Barrier Functions. The controller's stability and safety are validated using numerical simulations, while Monte Carlo simulations demonstrate its robustness to random perturbations in the modeling uncertainties.

Existing research results on regressor-based control use the linear parameterization of the dynamic equation into a known regressor matrix and an uncertain parameter vector. In this note, we show that the well-known robust controller that assumes a known regressor matrix can yield undesirable performance and poor robustness capabilities if there is uncertainty in the regressor matrix, especially when dealing with larger robots. The novelty of our result lies in accounting for uncertainties in both the regressor matrix and parameter vector, while ensuring that the uncertainty bound of our controller depends on a tuning parameter, which reflects the confidence in the regressor matrix accuracy, and the upper bound on the inertia parameters. Our controller, when compared against the controller that assumes a known regressor matrix, facilitates improved robustness while maintaining a smaller uniform ultimate boundedness radius.

This letter introduces a Kalman Filter framework for systems with process noise and measurements characterized by state-dependent, nonlinear conditional means and covariances. Estimating such general nonlinear models is challenging because traditional methods, such as the Extended Kalman Filter, linearize only functions - not noise - and require state-independent covariances. These limitations often necessitate Bayesian approaches that rely on specific distribution assumptions. To address these challenges, we propose a framework that employs a recursive least squares method that relies solely on conditional means and covariances, eliminating the need for explicit probability distributions. By applying first-order linearizations and incorporating targeted modifications to manage state dependence, the filter simplifies implementation, reduces computational demands, and provides a practical solution for systems that deviate from the assumptions underlying traditional Kalman filters. Simulation results on a compartmental model demonstrate performance comparable to sequential Monte Carlo methods while significantly lowering computational costs, effectively addressing real-world challenges of scalability and precision.

Predicting the interplay between infectious disease and behavior has been an intractable problem because behavioral response is so varied. We introduce a general framework for feedback between incidence and behavior for an infectious disease. By identifying stable equilibria, we provide policy end-states that are self-managing and self-maintaining. We prove mathematically the existence of two new endemic equilibria depending on the vaccination rate: one in the presence of low vaccination but with reduced societal activity (the “new normal”), and one with return to normal activity but with vaccination rate below that required for disease elimination. This framework allows us to anticipate the long-term consequence of an emerging disease and design a vaccination response that optimizes public health and limits societal consequences. Significance Statement The experience of the COVID-19 pandemic has revealed that behavior can change dramatically in response to the spread of a disease. This behavioral response impacts disease transmission. Predicting future outcomes requires accounting for the feedback between behavior and transmission. We show that accounting for these feedbacks generates long-term predictions about disease burden and behavior that can guide policy.

It is known that the parameters in the deterministic and stochastic SEIR epidemic models are structurally identifiable. For example, from knowledge of the infected population time series I(t) during the entire epidemic, the parameters can be successfully estimated. In this article we observe that estimation will fail in practice if only infected case data during the early part of the epidemic (prepeak) is available. This fact can be explained using a well-known phenomenon called dynamical compensation. We use this concept to derive an unidentifiability manifold in the parameter space of SEIR that consists of parameters indistinguishable from I(t) early in the epidemic. Thus, identifiability depends on the extent of the system trajectory that is available for observation. Although the existence of the unidentifiability manifold obstructs the ability to exactly determine the parameters, we suggest that it may be useful for uncertainty quantification purposes. A variant of SEIR recently proposed for COVID-19 modeling is also analyzed, and an analogous unidentifiability surface is derived.

This paper develops a robust regressor-free controller for n -link robots with state constraints. We use the function approximation technique to represent the uncertain robot dynamics. Our controller, which uses a state-dependent barrier Lyapunov function, prevents the states from violating their constraints by guaranteeing uniform ultimate boundedness of the closed-loop dynamics via a fixed control structure and a continuous switching law. In contrast to the drawbacks of controllers developed via the widely used error-dependent barrier Lyapunov functions, our controller overcomes the need to impose constraints on the initial tracking errors and the reference trajectories. When the reference trajectories violate the state constraints, our controller is capable of maintaining states within their constraints. We show that it is easy to switch between the constrained and unconstrained versions of our controller. Our controller requires few tuning parameters and is robust to wide ranges of uncertainties. Simulation and real-time experimental tests validate the practicality of our proposed controller.

The unscented transform uses a weighted set of samples called sigma points to propagate the means and covariances of nonlinear transformations of random variables. However, unscented transforms developed using either the Gaussian assumption or a minimum set of sigma points typically fall short when the random variable is not Gaussian distributed and the nonlinearities are substantial. In this paper, we develop the generalized unscented transform (GenUT), which uses 2n+1 sigma points to accurately capture up to the diagonal components of the skewness and kurtosis tensors of most probability distributions. Constraints can be analytically enforced on the sigma points while guaranteeing at least second-order accuracy. The GenUT uses the same number of sigma points as the original unscented transform while also being applicable to non-Gaussian distributions, including the assimilation of observations in the modeling of infectious diseases such as coronavirus (SARS-CoV-2) causing COVID-19.

An optimal filter for Poisson observations is developed as a variant of the traditional Kalman filter. Poisson distributions are characteristic of infectious diseases, which model the number of patients recorded as presenting each day to a health care system. We develop both a linear and a nonlinear (extended) filter. The methods are applied to a case study of neonatal sepsis and postinfectious hydrocephalus in Africa, using parameters estimated from publicly available data. Our approach is applicable to a broad range of disease dynamics, including both noncommunicable and the inherent nonlinearities of communicable infectious diseases and epidemics such as from COVID-19.

Despite the popularity of drones and their relatively simple operation, the underlying control algorithms can be difficult to design due to the drones' underactuation and highly nonlinear properties. This paper focuses on position and orientation control of drones to address challenges such as path and edge tracking, and disturbance rejection. The adaptive function approximation technique control method is used to control an underactuated and nonlinear drone. The controller utilizes reference attitude signals, that are derived from a proportional derivative (PD) linear feedback control methodology. To avoid analytic expressions for the reference attitude velocities, we employ a continuoustime Kalman filter based on a model of the measurement signal - which is derived by passing the reference attitude position through a low-pass signal differentiator - as a second-order New-tonian system. Stability of the closed loop system is proven using a Lyapunov function. Our design methodology simplifies the control process by requiring only a few tuning variables, while being robust to time-varying and time-invariant uncertainties with unknown variation bounds, and avoids the requirement for the knowledge of the dynamic equation that governs the attitude of the drone. Three different scenarios are simulated and our control method shows better accuracy than the proportional-derivative controller in terms of edge tracking and disturbance rejection.

This paper develops a novel regressor-free robust controller for rigid robots whose dynamics can be described using the Euler-Lagrange equations of motion. The function approximation technique (FAT) is used to represent the robot's inertia matrix, the Coriolis matrix, and the gravity vector as finite linear combinations of orthonormal basis functions. The proposed controller establishes a robust FAT control framework that uses a fixed control structure. The control objectives are to track reference trajectories in worst case scenarios where the robot dynamics are too costly to develop or otherwise unavailable. Detailed stability analysis via Lyapunov functions, the passivity property, and continuous switching laws shows uniform ultimate boundedness of the closed-loop dynamics. The simulation results of a three-degree-of-freedom (DOF) robot when the robot parameters are perturbed from their nominal values show good robustness of the proposed controller when compared with some well-established control methods. We also demonstrate success in the real-time experimental implementation of the proposed controller, which validates practicality for real-world robotic applications.

This paper develops a new function approximation technique (FAT)-based adaptive controller for the control of rigid robots called the adaptive passivity function approximation technique (APFAT) controller. This controller utilizes the passivity based approach and simplifies the FAT controller design by eliminating the need for simultaneous estimation of the robot's inertia matrix, Coriolis matrix, and gravity vector. The controller achieves its simplicity by treating the product of the regressor matrix and parameter vector as an unknown time-varying function to be approximated. The controller can be implemented in robots where the dynamic equations of motion are unknown. The stability of the controller is verified with Lyapunov functions by taking advantage of the passivity property of the robot dynamics. Simulation results on a three degree-of-freedom (DOF) PUMA500 robot demonstrate the ability to track reference trajectories using reasonable control signals when the inertia matrix, Coriolis matrix, and gravity vector are unavailable.

This chapter concentrates on the correlation between research-based education, government priorities and research funding. Special attention is paid to an analysis of the role of modern information and communication technology (ICT) in the education of engineering students. Successful cases with specific description of computer modeling methods for the implementation of prosthesis and robotics research projects are presented based on experiences in the Embedded Control Systems Research Laboratory of Cleveland State University.

We develop a hybrid controller for an n-degree of freedom robot where one control approach is used for some joints while another control approach is used for the remaining joints. We combine Slotine and Li's regressor based control, and function approximation technique (FAT) based regressorfree control, to obtain a coupled controller. We verify the closed loop stability of the hybrid controller via Lyapunov functions and update laws to show that the tracking errors approach zero as time approaches infinity. We then apply the controller to an uncertain model of a robotic system comprised of a prosthesis which emulates the angular knee motion of a human leg, and a prosthesis test robot which emulates the vertical hip motion and the angular thigh motion of a human. Simulation results show good reference trajectory tracking in the presence of ground reaction forces while keeping the control signal magnitudes reasonably small. The minimum tracking errors were 1.57% for the hip vertical hip motion, 0.29% for the thigh angle, and 0.34% for the knee angle (relative to their respective ranges of motion). The maximum steady-state control signal magnitudes were 840 N, 456 Nm, and 253 Nm for the hip vertical hip motion, thigh angle, and knee angle respectively.