We study the effects of loop quantum gravity motivated corrections in classical systems. Computational methods are used to simulate black hole formation from the gravitational collapse of a massless scalar field in Painleve-Gullstrand coordinates. Singularities present in the classical case are resolved by a radiation-like phase in the quantum collapse. The evaporation is not complete but leaves behind an outward moving shell of mass that disperses to infinity. We reproduce Choptuik scaling showing the usual behaviour for the curvature scaling, while observing previously unseen behaviour in the mass scaling. The quantum corrections are found to impose a lower limit on black hole mass and generate a new universal power law scaling relationship. In a parallel study, we quantize the Hamiltonian for a particle in the singular $1/r^2$ potential, a form that appears frequently in black hole physics. In addition to conventional Schrodinger methods, the quantization is performed using full and semiclassical polymerization. The various quantization schemes are in excellent agreement for the highly excited states but differ for the low-lying states, and the polymer spectrum is bounded below even when the Schrodinger spectrum is not. / May 2009

We study the effects of loop quantum gravity motivated corrections in classical systems. Computational methods are used to simulate black hole formation from the gravitational collapse of a massless scalar field in Painleve-Gullstrand coordinates. Singularities present in the classical case are resolved by a radiation-like phase in the quantum collapse. The evaporation is not complete but leaves behind an outward moving shell of mass that disperses to infinity. We reproduce Choptuik scaling showing the usual behaviour for the curvature scaling, while observing previously unseen behaviour in the mass scaling. The quantum corrections are found to impose a lower limit on black hole mass and generate a new universal power law scaling relationship. In a parallel study, we quantize the Hamiltonian for a particle in the singular $1/r^2$ potential, a form that appears frequently in black hole physics. In addition to conventional Schrodinger methods, the quantization is performed using full and semiclassical polymerization. The various quantization schemes are in excellent agreement for the highly excited states but differ for the low-lying states, and the polymer spectrum is bounded below even when the Schrodinger spectrum is not.

We study the effects of loop quantum gravity motivated corrections in classical systems. Computational methods are used to simulate black hole formation from the gravitational collapse of a massless scalar field in Painleve-Gullstrand coordinates. Singularities present in the classical case are resolved by a radiation-like phase in the quantum collapse. The evaporation is not complete but leaves behind an outward moving shell of mass that disperses to infinity. We reproduce Choptuik scaling showing the usual behaviour for the curvature scaling, while observing previously unseen behaviour in the mass scaling. The quantum corrections are found to impose a lower limit on black hole mass and generate a new universal power law scaling relationship. In a parallel study, we quantize the Hamiltonian for a particle in the singular $1/r^2$ potential, a form that appears frequently in black hole physics. In addition to conventional Schrodinger methods, the quantization is performed using full and semiclassical polymerization. The various quantization schemes are in excellent agreement for the highly excited states but differ for the low-lying states, and the polymer spectrum is bounded below even when the Schrodinger spectrum is not.

No / In this paper, we investigate trajectory tracking in a multi-input nonlinear system, where there is little knowledge of the system parameters and the form of the nonlinear function. An identification-based iterative learning control (ILC) scheme to repetitively estimate the linearity in a neighborhood of a desired trajectory is presented. Based on this estimation, the original nonlinear system can track the desired trajectory perfectly by the aid of a regional training scheme. Just like in adaptive control, a singularity exists in ILC when the input coupling matrix is estimated. Singularity avoidance is discussed. A new parameter modification procedure for ILC is presented such that the determinant of the estimate of the input coupling matrix is uniformly bounded from below. Compared with the scheme used for adaptive control of a MIMO system, the proposed scheme reduces the computation load greatly. It is used in a robotic visual system for manipulator trajectory tracking without any information about the camera-robot relationship. The estimated image Jacobian is updated repetitively and then its inverse is used to calculate the manipulator velocity without any singularity.

This study develops a discrete search-based optimization method for path planning in a highly nonlinear dynamical system. The method enables real-time trajectory improvement and singular configuration avoidance in satellite rotation using Control Moment Gyroscopes. By streamlining a legacy optimization method and combining it with a local singularity management scheme, this optimization method reduces the computational burden and advances the capability of satellites to make autonomous look-ahead decisions in real-time. Current optimization methods plan offline before uploading to the satellite and experience high sensitivity to disturbances. Local methods confer autonomy to the satellite but use only blind decision-making to avoid singularities. This thesis' method seeks near-optimal trajectories which balance between the optimal trajectories found using computationally intensive offline solvers and the minimal computational burden of non-optimal local solvers. The new method enables autonomous guidance capability for satellites using discretization and stage division to minimize the computational burden of real-time optimization.

A haptic interface is a robotic force feedback device that provides a sense of touch to users of virtual reality simulations. This thesis presents a general method for the design optimization of parallel planar haptic devices based on maximizing the manipulability of the interface over its workspace. Manipulability is selected as the key design objective to ensure avoidance of singular configurations within the workspace and to maximize the interface's ability to generate feedback forces and torques in each direction in each handle location and orientation. The optimization approach developed in this thesis results in a set of candidate designs that are found by stepping the design parameters through the range of possible values, and testing the manipulability and other measures (including workspace area and space) at each location and orientation of the interface handle. To find the optimal design, a multi-objective approach is taken to generate a set of Pareto optimal designs. A smart Pareto filter is employed to yield a smaller set of designs representative of the full Pareto frontier. The most desirable design is chosen from this reduced set. The result is a general optimization method applicable to parallel haptic interfaces. The method is demonstrated on the design of a 3-RPR parallel planar interface.

A Variable Speed Control Moment Gyro (VSCMG) is a recently introduced actuator for spacecraft attitude control. As its name implies, a VSCMG is essentially a single-gimbal control moment gyro (CMG) with a flywheel allowed to have variable spin speed. Thanks to its extra degrees of freedom, a VSCMGs cluster can be used to achieve additional objectives, such as power tracking and/or singularity avoidance, as well as attitude control. In this thesis, control laws for an integrated power/attitude control system (IPACS) for a satellite using VSCMGs are introduced. The power tracking objective is achieved by storing or releasing the kinetic energy in the wheels. The proposed control algorithms perform both the attitude and power tracking goals simultaneously. This thesis also provides a singularity analysis and avoidance method using CMGs/VSCMGs. This issue is studied for both the cases of attitude tracking with and without a power tracking requirement. A null motion method to avoid singularities is presented, and a criterion is developed to determine the momentum region over which this method will successfully avoid singularities. The spacecraft angular velocity and attitude control problem using a single VSCMG is also addressed. A body-fixed axis is chosen to be perpendicular to the gimbal axis, and it is controlled to aim at an arbitrarily given inertial direction, while the spacecraft angular velocity is stabilized. Finally, an adaptive control algorithm for the spacecraft attitude tracking in case when the actuator parameters, for instance the spin axis directions, are uncertain is developed. The equations of motion in this case are fully nonlinear and represent a Multi-Input-Multi-Output (MIMO) system. The smooth projection algorithm is applied to keep the parameter estimates inside a singularity-free region. The design procedure can also be easily applied to general MIMO dynamical systems.

In recent years, there has been a significant increase in the interest for snake like modular robots due to their superior locomotion capabilities in terms of versatility, adaptability and scalability. Passive wheeled planar snake like robots are a major category and they are being actively researched. Due to the nonholonomic constraints imposed on them, certain configurations lead to the singularity which must be avoided at all costs. Furthermore, it is vital to generate a locomotion pattern such that they can track a wide range of trajectories. All of these objectives must be accomplished smoothly and in an energy efficient manner. Studies indicate that meeting all of these requirements is a challenging problem. In this study, a novel form of the serpenoid curve is proposed in order to make the robot track arbitrary paths. A controller has been designed using the feedback linearization method. Afterwards, a new performance measure, considering both the efficiency and sustainability of the locomotion, has been proposed to evaluate the locomotion. Optimal parameters for the proposed serpenoid curve and the linear controller have been determined for efficient locomotion by running series of simulations. Relations between the locomotion performance, locomotion speed and eigenvalues of the linear controller have been demonstrated. Simulation results show striking differences between the locomotion by using the proposed serpenoid curve with optimal parameters and the locomotion by purely tracking a given path. Obtained results also indicate that the aforementioned requirements are met successfully and confirm the validity and consistency of the proposed performance measure.

The objective of this thesis is to analyze the kinematics of a mobile parallel robot with contribution that pertain to the singularity analysis, the optimization of geometric parameters and the optimal control to avoid singularities when navigating across singular geometric configurations. The analysis of the workspace and singularities is performed in a prescribed reference workspace regions using discretization method. Serial and parallel singularities are analytically analyzed and all possible singular configurations are presented. Kinematic conditioning index is used to determine the robot’s proximity to a singular configuration. A method for the determination of a continuous and singularity-free workspace is detailed. The geometric parameters of the system are optimized in various types of pipe-like structures with respect to a suitable singularity index, in order to avoid singularities during the navigation across elbows. The optimization problem is formulated with an objective to maximize the reachable workspace and minimize the singularities. The objective function is also subjected to constraints such as collision avoidance, singularity avoidance, workspace continuity and contact constraints imposed between the boundaries and the wheels of the robot. A parametric variation method is used as a technique to optimize the design parameters. The optimal design parameters found are normalized with respect to the width of the pipe-like structures and therefore the results are generalized to be used in the development phase of the robot. An optimal control to generate singularity-free trajectories when the robotic device has to cross a geometric singularity in a sharp 90◦ elbow is proposed. Such geometric singularity inherently leads to singularities in the Jacobian of the system, and therefore a modified device with augmented number of degrees of freedom is introduced to be able to generate non-singular trajectories.

The objective of this thesis is to analyze the kinematics of a mobile parallel robot with contribution that pertain to the singularity analysis, the optimization of geometric parameters and the optimal control to avoid singularities when navigating across singular geometric configurations. The analysis of the workspace and singularities is performed in a prescribed reference workspace regions using discretization method. Serial and parallel singularities are analytically analyzed and all possible singular configurations are presented. Kinematic conditioning index is used to determine the robot’s proximity to a singular configuration. A method for the determination of a continuous and singularity-free workspace is detailed. The geometric parameters of the system are optimized in various types of pipe-like structures with respect to a suitable singularity index, in order to avoid singularities during the navigation across elbows. The optimization problem is formulated with an objective to maximize the reachable workspace and minimize the singularities. The objective function is also subjected to constraints such as collision avoidance, singularity avoidance, workspace continuity and contact constraints imposed between the boundaries and the wheels of the robot. A parametric variation method is used as a technique to optimize the design parameters. The optimal design parameters found are normalized with respect to the width of the pipe-like structures and therefore the results are generalized to be used in the development phase of the robot. An optimal control to generate singularity-free trajectories when the robotic device has to cross a geometric singularity in a sharp 90◦ elbow is proposed. Such geometric singularity inherently leads to singularities in the Jacobian of the system, and therefore a modified device with augmented number of degrees of freedom is introduced to be able to generate non-singular trajectories.