Control Of Rigid Robots With Large Uncertainties Using The Function Approximation Technique

This dissertation focuses on the control of rigid robots that cannot easily be modeled due to complexity and large uncertainties. The function approximation technique (FAT), which represents uncertainties as finite linear combinations of orthonormal basis functions, provides an alternate form of robot control - in situations where the dynamic equation cannot easily be modeled - with no dependency on the use of model information or training data. This dissertation has four aims - using the FAT - to improve controller efficiency and robustness in scenarios where reliable mathematical models cannot easily be derived or are otherwise unavailable. The first aim is to analyze the uncertain combination of a test robot and prosthesis in a scenario where the test robot and prosthesis are adequately controlled by different controllers - this is tied to efficiency. We develop a hybrid FAT controller, theoretically prove stability, and verify its performance using computer simulations. We show that systematically combining controllers can improve controller analysis and yield desired performance. In the second aim addressed in this dissertation, we investigate the simplification of the adaptive FAT controller complexity for ease of implementation - this is tied to efficiency. We achieve this by applying the passivity property and prove controller stability. We conduct computer simulations on a rigid robot under good and poor initial conditions to demonstrate the effectiveness of the controller. For an n degrees of freedom (DOFs) robot, we see a reduction of controller tuning parameters by 2n. The third aim addressed in this dissertation is the extension of the adaptive FAT controller to the robust control framework - this is tied to robustness. We invent a novel robust controller based on the FAT that uses continuous switching laws and eliminates the dependency on update laws. The controller, when compared against three state-of-the-art controllers via computer simulations and experimental tests on a rigid robot, shows good performance and robustness to fast time-varying uncertainties and random parameter perturbations. This introduces the first purely robust FAT-based controller. The fourth and final aim addressed in this dissertation is the development of a more compact form of the robust FAT controller developed in aim~3 - this is tied to efficiency and robustness. We investigate the simplification of the control structure and its applicability to a broader class of systems that can be modeled via the state-space approach. Computer simulations and experimental tests on a rigid robot demonstrate good controller performance and robustness to fast time-varying uncertainties and random parameter perturbations when compared to the robust FAT controller developed in aim 3. For an n-DOF robot, we see a reduction in the number of switching laws from 3 to 1

A Poisson Kalman filter for disease surveillance

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 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.Comment: 19 Pages, 8 Figure

CONTROL OF RIGID ROBOTS WITH LARGE UNCERTAINTIES USING THE FUNCTION APPROXIMATION TECHNIQUE

This dissertation focuses on the control of rigid robots that cannot easily be modeled due to complexity and large uncertainties. The function approximation technique (FAT), which represents uncertainties as finite linear combinations of orthonormal basis functions, provides an alternate form of robot control - in situations where the dynamic equation cannot easily be modeled - with no dependency on the use of model information or training data. This dissertation has four aims - using the FAT - to improve controller efficiency and robustness in scenarios where reliable mathematical models cannot easily be derived or are otherwise unavailable. The first aim is to analyze the uncertain combination of a test robot and prosthesis in a scenario where the test robot and prosthesis are adequately controlled by different controllers - this is tied to efficiency. We develop a hybrid FAT controller, theoretically prove stability, and verify its performance using computer simulations. We show that systematically combining controllers can improve controller analysis and yield desired performance. In the second aim addressed in this dissertation, we investigate the simplification of the adaptive FAT controller complexity for ease of implementation - this is tied to efficiency. We achieve this by applying the passivity property and prove controller stability. We conduct computer simulations on a rigid robot under good and poor initial conditions to demonstrate the effectiveness of the controller. For an n degrees of freedom (DOFs) robot, we see a reduction of controller tuning parameters by 2n. The third aim addressed in this dissertation is the extension of the adaptive FAT controller to the robust control framework - this is tied to robustness. We invent a novel robust controller based on the FAT that uses continuous switching laws and eliminates the dependency on update laws. The controller, when compared against three state-of-the-art controllers via computer simulations and experimental tests on a rigid robot, shows good performance and robustness to fast time-varying uncertainties and random parameter perturbations. This introduces the first purely robust FAT-based controller. The fourth and final aim addressed in this dissertation is the development of a more compact form of the robust FAT controller developed in aim~3 - this is tied to efficiency and robustness. We investigate the simplification of the control structure and its applicability to a broader class of systems that can be modeled via the state-space approach. Computer simulations and experimental tests on a rigid robot demonstrate good controller performance and robustness to fast time-varying uncertainties and random parameter perturbations when compared to the robust FAT controller developed in aim 3. For an n-DOF robot, we see a reduction in the number of switching laws from 3 to 1

A Passivity-Based Regressor-Free Adaptive Controller for Robot Manipulators With Combined Regressor/Parameter Estimation

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

Disclosure of errors in optometric practice in Nigeria

Background: Human beings are prone to making mistakes, whether in their personal or professional lives. Errors in health care are not uncommon. However, it is not certain if public and professional expectations of disclosure of these errors are met in everyday practice by practitioners. Objective: The purpose of this study was to investigate patients’ and optometrists’ attitudes towards disclosure of errors in eye care. Method: This was a qualitative study conducted in Benin City, Edo State, Nigeria, using focus group discussions (FGDs) and in-depth interviews (IDIs). The study population comprised 24 patients aged 18–42 years, with a mean age (±s.d.) of 38 ± 2.2 years, and 16 eye-care practitioners (ECPs), with a minimum of 5 years’ work experience. The optometrists were aged between 32 and 50 years with a mean age (±s.d.) of 42 ± 2.1 years. Three FGDs were conducted with the adult participants, while 16 IDIs were conducted with ECPs. Results: All participants agreed that errors do occur in eye care. Poor communication between doctors and patients, patients lying to doctors and negligence on the doctor’s part were some of the reasons given for the occurrence of errors in optometric practice. Most of the practitioners (14) agreed that major errors should be disclosed when they occur. While many of the patients (20) would want detailed information about the error, a few (4) would prefer the doctor to rectify the error rather than explaining it to them. Practitioners reported fear of litigation as a factor that could discourage them from disclosing errors. Eighteen patients reported litigation as a last resort, in the event of an error. Both parties agreed that errors caused emotional distress to them and also added that additional charges incurred should be borne by whichever party was the cause of the error. Conclusion: Errors are an unfortunate part of clinical practice. However, if patients were truthful and open in communication with their doctors and if doctors practiced within the ambit of ethical principles, the occurrence of serious errors should be few and far between

Hybrid Function Approximation Based Control with Application to Prosthetic Legs

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\u27s 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

Hybrid Function Approximation Based Control with Application to Prosthetic Legs

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\u27s 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