University of Macau / Faculty of Science and Technology / Department of Electromechanical Engineering

University of Macau / Faculty of Science and Technology / Department of Electromechanical Engineering

This thesis is concerned with input-output stability theory. Within this framework, it is of interest how inputs map to outputs through an operator that represents a system to be controlled or the controller itself. The Small Gain, Passivity, and Conic Sector Stability Theorems can be used to assess the stability of a negative feedback interconnection involving two systems that each have specific input-output properties. Our first contribution concerns characterization of the input-output properties of linear time-varying (LTV) systems. We present various theorems that ensure that a LTV system has finite gain, is passive, or is conic. We also consider the stability of various negative feedback interconnections. Motivated by the robust nature of passivity-based control, we consider how to overcome passivity violations. This investigation leads to the hybrid conic systems framework whereby systems are described in terms of multiple conic bounds over different operating ranges. A special case relevant to systems that experience a passivity violation is the hybrid passive/finite gain framework. Sufficient conditions are derived that ensure the negative feedback interconnection of two hybrid conic systems is stable. The input-output properties of gain-scheduled systems are also investigated. We show that a gain-scheduled system composed of conic subsystems has conic bounds as well. Using the conic bounds of the subsystems along with the scheduling signal properties, the overall conic bounds of the gain-scheduled system can be calculated. We also show that when hybrid very strictly passive/finite gain (VSP/finite gain) subsystems are gain-scheduled, the overall map is also hybrid VSP/finite gain. Being concerned with the control of aerospace systems, we use the theory developed in this thesis to control two interesting plants. We consider passivity-based control of a spacecraft endowed with magnetic torque rods and reaction wheels. In particular, we synthesize a LTV input strictly passive controller. Using hybrid theory we control single- and two-link flexible manipulators. We present two controller synthesis schemes, each of which employs numerical optimization techniques and attempts to have the hybrid VSP/finite gain controllers mimic a H2 controller. One of our synthesis methods uses the Generalized Kalman-Yakubovich-Popov Lemma, thus realizing a convex optimization problem.

This thesis is concerned with input-output stability theory. Within this framework, it is of interest how inputs map to outputs through an operator that represents a system to be controlled or the controller itself. The Small Gain, Passivity, and Conic Sector Stability Theorems can be used to assess the stability of a negative feedback interconnection involving two systems that each have specific input-output properties. Our first contribution concerns characterization of the input-output properties of linear time-varying (LTV) systems. We present various theorems that ensure that a LTV system has finite gain, is passive, or is conic. We also consider the stability of various negative feedback interconnections. Motivated by the robust nature of passivity-based control, we consider how to overcome passivity violations. This investigation leads to the hybrid conic systems framework whereby systems are described in terms of multiple conic bounds over different operating ranges. A special case relevant to systems that experience a passivity violation is the hybrid passive/finite gain framework. Sufficient conditions are derived that ensure the negative feedback interconnection of two hybrid conic systems is stable. The input-output properties of gain-scheduled systems are also investigated. We show that a gain-scheduled system composed of conic subsystems has conic bounds as well. Using the conic bounds of the subsystems along with the scheduling signal properties, the overall conic bounds of the gain-scheduled system can be calculated. We also show that when hybrid very strictly passive/finite gain (VSP/finite gain) subsystems are gain-scheduled, the overall map is also hybrid VSP/finite gain. Being concerned with the control of aerospace systems, we use the theory developed in this thesis to control two interesting plants. We consider passivity-based control of a spacecraft endowed with magnetic torque rods and reaction wheels. In particular, we synthesize a LTV input strictly passive controller. Using hybrid theory we control single- and two-link flexible manipulators. We present two controller synthesis schemes, each of which employs numerical optimization techniques and attempts to have the hybrid VSP/finite gain controllers mimic a H2 controller. One of our synthesis methods uses the Generalized Kalman-Yakubovich-Popov Lemma, thus realizing a convex optimization problem.

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This thesis presents a novel bilateral teleoperation algorithm for n degree of freedom nonlinear manipulators connected through time delays. Teleoperation has many practical uses, as there are many benefits that come from being able to operate machines from a distance. For instance, the ability to send a remote controlled robotic vehicle into a hazardous environment can be a great asset in many industrial applications. As well, the field of remote medicine can benefit from these technologies. A highly skilled surgeon could perform surgery on a patient who is located in another city, or even country. Earth to space operations and deep sea exploration are other areas where teleoperation is quite useful. Central to the approach presented in this work is the use of second order sliding mode unknown input observers for estimating the external forces acting on the manipulators. The use of these observers removes the need for both velocity and force sensors, leading to a lower cost hardware setup that provides all of the advantages of a position-force teleoperation algorithm. Stability results for this new algorithm are presented for several cases. Stability of each of the master and slave sides of the teleoperation system is demonstrated, showing that the master and slave are both stabilized by their respective controllers when the unknown input observers are used for state and force estimation. Additionally, closed loop stability results for the teleoperation system connected to a variety of slave side environments are presented. Delay-independent stability results for a linear spring-damper environment as well as a general finite-gain stable nonlinear environment are given. Delay-dependent stability results for the case where the slave environment is a liner spring-damper and the delays are commensurate are also presented. As well, stability results for the closed loop under the assumption that the human operator is modeled as a finite-gain stable nonlinear environment are given. Following the theoretical presentation, numerical simulations illustrating the algorithm are presented, and experimental results verifying the practical application of the approach are given.

This thesis presents a novel bilateral teleoperation algorithm for n degree of freedom nonlinear manipulators connected through time delays. Teleoperation has many practical uses, as there are many benefits that come from being able to operate machines from a distance. For instance, the ability to send a remote controlled robotic vehicle into a hazardous environment can be a great asset in many industrial applications. As well, the field of remote medicine can benefit from these technologies. A highly skilled surgeon could perform surgery on a patient who is located in another city, or even country. Earth to space operations and deep sea exploration are other areas where teleoperation is quite useful. Central to the approach presented in this work is the use of second order sliding mode unknown input observers for estimating the external forces acting on the manipulators. The use of these observers removes the need for both velocity and force sensors, leading to a lower cost hardware setup that provides all of the advantages of a position-force teleoperation algorithm. Stability results for this new algorithm are presented for several cases. Stability of each of the master and slave sides of the teleoperation system is demonstrated, showing that the master and slave are both stabilized by their respective controllers when the unknown input observers are used for state and force estimation. Additionally, closed loop stability results for the teleoperation system connected to a variety of slave side environments are presented. Delay-independent stability results for a linear spring-damper environment as well as a general finite-gain stable nonlinear environment are given. Delay-dependent stability results for the case where the slave environment is a liner spring-damper and the delays are commensurate are also presented. As well, stability results for the closed loop under the assumption that the human operator is modeled as a finite-gain stable nonlinear environment are given. Following the theoretical presentation, numerical simulations illustrating the algorithm are presented, and experimental results verifying the practical application of the approach are given.

Model-based control strategies for robot manipulators can present numerous performance advantages when an accurate model of the system dynamics is available. In practice, obtaining such a model is a challenging task which involves modeling such physical processes as friction, which may not be well understood and difficult to model. Furthermore, uncertainties in the physical parameters of a system may be introduced from significant discrepancies between the manufacturer data and the actual system. Traditionally, adaptive and robust control strategies have been developed to deal with parametric uncertainty in the dynamic model, but often require knowledge of the structure of the dynamics. Recent approaches to model-based manipulator control involve data-driven learning of the inverse dynamics relationship, eliminating the need for any a-priori knowledge of the system model. Locally Weighted Projection Regression (LWPR) has been proposed for learning the inverse dynamics function of a manipulator. Due to its use of simple local, linear models, LWPR is suitable for online and incremental learning. Although global regression techniques such as Gaussian Process Regression (GPR) have been shown to outperform LWPR in terms of accuracy, due to its heavy computational requirements, GPR has been applied mainly to offline learning of inverse dynamics. More recent efforts in making GPR computationally tractable for real-time control have resulted in several approximations which operate on a select subset, or sparse representation of the entire training data set. Despite the significant advancements that have been made in the area of learning control, there has not been much work in recent years to evaluate these newer regression techniques against traditional model-based control strategies such as adaptive control. Hence, the first portion of this thesis provides a comparison between a fixed model-based control strategy, an adaptive controller and the LWPR-based learning controller. Simulations are carried out in order to evaluate the position and orientation tracking performance of each controller under varied end effector loading, velocities and inaccuracies in the known dynamic parameters. Both the adaptive controller and LWPR controller are shown to have comparable performance in the presence of parametric uncertainty. However, it is shown that the learning controller is unable to generalize well outside of the regions in which it has been trained. Hence, achieving good performance requires significant amounts of training in the anticipated region of operation. In addition to poor generalization performance, most learning controllers commence learning entirely from `scratch,' making no use of any a-priori knowledge which may be available from the well-known rigid body dynamics (RBD) formulation. The second portion of this thesis develops two techniques for online, incremental learning algorithms which incorporate prior knowledge to improve generalization performance. First, prior knowledge is incorporated into the LWPR framework by initializing the local linear models with a first order approximation of the prior information. Second, prior knowledge is incorporated into the mean function of Sparse Online Gaussian Processes (SOGP) and Sparse Pseudo-input Gaussian Processes (SPGP), and a modified version of the algorithm is proposed to allow for online, incremental updates. It is shown that the proposed approaches allow the system to operate well even without any initial training data, and further performance improvement can be achieved with additional online training. Furthermore, it is also shown that even partial knowledge of the system dynamics, for example, only the gravity loading vector, can be used effectively to initialize the learning.

This work follows the design, prototyping and implementation of an automatic part loading and unloading system for use in thread rolling of aerospace fasteners. The thread rolling automation system is designed to function as part of a multi-process workcell, which emphasizes adaptability and ease of implementation. Design of the thread rolling automation facilitates the development of a universal gripping system, which is designed to grasp a large variety of fastener styles and sizes with a minimum of tooling changeover. A novel grasping model is developed to predict the error tolerance of the proposed gripping system design, which is validated experimentally. The proposed gripper and automation system are prototyped and tested, and shown to perform reliably with a wide range of fastener types.

published_or_final_version / Electrical and Electronic Engineering / Master / Master of Philosophy