Adaptive planar curve tracking control and robustness analysis under state constraints and unknown curvature

We provide adaptive controllers for curve tracking in the plane, under unknown curvatures and control uncertainty, which is a central problem in robotics. The system dynamics include a nonlinear dependence on the curvature, and are coupled with an estimator for the unknown curvature, to form the augmented error dynamics. We prove input-to-state stability of the augmented error dynamics with respect to an input that is represented by additive uncertainty on the control, under polygonal state constraints and under suitable known bounds on the curvature and on the control uncertainty. When the uncertainty is zero, this gives tracking of the curve and convergence of the curvature estimate to the unknown curvature. Our curvature identification result is a significant improvement over earlier results, which do not ensure parameter identification, or which identify the control gain but not the curvature

Curve Tracking Control Under State Constraints and Uncertainties

We study a class of steering control problems for free-moving particles tracking a curve in the plane and also in a three-dimensional environment, which are central problems in robotics. In the two-dimensional case, we provide adaptive controllers for curve tracking under unknown curvatures and control uncertainty. The system dynamics include a nonlinear dependence on the curvature, and are coupled with an estimator for the unknown curvature to form the augmented error dynamics. This nonlinear dependence puts our curvature identification objective outside the scope of existing adaptive tracking and parameter identification results that were limited to cases where the unknown parameters enter the system in an affine way. We prove input-to-state stability of the augmented error dynamics under polygonal state constraints and under suitable known bounds on the curvature and on the control uncertainty. When the uncertainty is zero, this ensures tracking of the curve and convergence of the curvature estimate to the unknown curvature. In the three-dimensional setting, we provide a new method to achieve curve tracking, identify unknown control gains, and maintain robust forward invariance of compact regions in the state space, under arbitrarily large perturbation bounds. Our new technique entails scaling certain control components

A general material removal strategy based on surface sampling and reconstruction on unknown objects

In most material removal processes, the size and shape of the stock material, the desired surface and the orientation of the part are known. If some or all of these factors are unknown, typical automatic systems will not be able to handle the situation. In reality, most of these cases are subsequently handled by human operators. This results in low productivity and inconsistency in the production and potential ergonomic problems for the human operators. Therefore, a new system needs to be designed to meet the requirements for material removal with unknown objects.;This dissertation presents a feasible and efficient automatic system for material removal with unknown processing factors. The characteristics of this type of processes were investigated. The corresponding inputs of the system were decided, while balancing the ease of use and the complexity of the system. A simple point sampling strategy was developed to sample the reference points, which are used to create the approximated surface for the unknown objects with a modified triangular based surface approximation method. A universal layer based path planning method was developed to guide the tool among the layers within the designated working area to remove the excess material effectively and efficiently without changing the programming codes.;This system was verified by simulations and a prototype of the grinding system

Line-of-Sight Path Following for Dubins Paths with Adaptive Sideslip Compensation of Drift Forces

This is the author’s final, accepted and refereed manuscript to the article.We present a nonlinear adaptive path-following controller that compensates for drift forces through vehicle sideslip. Vehicle sideslip arises during path following when the vehicle is subject to drift forces caused by ocean currents, wind and waves. The proposed algorithm is motivated by a lineof-sight (LOS) guidance principle used by ancient navigators, which is here extended to path following of Dubins paths. The unknown sideslip angle is treated as a constant parameter, which is estimated using an adaptation law. The equilibrium points of the cross-track and parameter estimation errors are proven to be uniformly semiglobally exponentially stable (USGES). This guarantees that the estimated sideslip angle converges to its true value exponentially. The adaptive control law is in fact an integral LOS controller for path following since the parameter adaptation law provides integral action. The proposed guidance law is intended for maneuvering in the horizontal-plane at given speeds and typical applications are marine craft, autonomous underwater vehicles (AUVs), unmanned aerial vehicles (UAVs) as well as other vehicles and craft where the goal is to follow a predefined parametrized curve without time constraints. Two vehicle cases studies are included to verify the theoretical results.http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=6868251 "(c) 2014 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.

Towards dynamic camera calibration for constrained flexible mirror imaging

Flexible mirror imaging systems consisting of a perspective camera viewing a scene reflected in a flexible mirror can provide direct control over image field-of-view and resolution. However, calibration of such systems is difficult due to the vast range of possible mirror shapes and the flexible nature of the system. This paper proposes the fundamentals of a dynamic calibration approach for flexible mirror imaging systems by examining the constrained case of single dimensional flexing. The calibration process consists of an initial primary calibration stage followed by in-service dynamic calibration. Dynamic calibration uses a linear approximation to initialise a non-linear minimisation step, the result of which is the estimate of the mirror surface shape. The method is easier to implement than existing calibration methods for flexible mirror imagers, requiring only two images of a calibration grid for each dynamic calibration update. Experimental results with both simulated and real data are presented that demonstrate the capabilities of the proposed approach

Flat systems, equivalence and trajectory generation

Flat systems, an important subclass of nonlinear control systems introduced via differential-algebraic methods, are defined in a differential geometric framework. We utilize the infinite dimensional geometry developed by Vinogradov and coworkers: a control system is a diffiety, or more precisely, an ordinary diffiety, i.e. a smooth infinite-dimensional manifold equipped with a privileged vector field. After recalling the definition of a Lie-Backlund mapping, we say that two systems are equivalent if they are related by a Lie-Backlund isomorphism. Flat systems are those systems which are equivalent to a controllable linear one. The interest of such an abstract setting relies mainly on the fact that the above system equivalence is interpreted in terms of endogenous dynamic feedback. The presentation is as elementary as possible and illustrated by the VTOL aircraft

Developing Intuitive, Closed-Loop, Teleoperative Control of Continuum Robotic Systems

This thesis presents a series of related new results in the area of continuum robot teleoperation and control. A new nonlinear control strategy for the teleoperation of extensible continuum robots is described. Previous attempts at controlling continuum robots have proven difficult due to the complexity of their system dynamics. Taking advantage of a previously developed dynamic model for a three-section, planar, continuum manipulator, we present an adaptation control-inspired law. Simulation and experimental results of a teleoperation scheme between a master device and an extensible continuum slave manipulator using the new controller are presented. Two novel user interface approaches to the teleoperation of continuum robots are also presented. In the first, mappings from a six Degree-of-Freedom (DoF) rigid-link robotic arm to a nine degree-of-freedom continuum robot are synthesized, analyzed, and implemented, focusing on their potential for creating an intuitive operational interface. Tests were conducted across a range of planar and spatial tasks, using fifteen participant operators. The results demonstrate the feasibility of the approach, and suggest that it can be effective independent of the prior robotics, gaming, or teleoperative experience of the operator. In the second teleoperation approach, a novel nine degree-of-freedom input device for the teleoperation of extensible continuum robots is introduced. As opposed to previous works limited by kinematically dissimilar master devices or restricted degrees-of-freedom, the device is capable of achieving configurations identical to a three section continuum robot, and simplifying the control of such manipulators. The thesis discusses the design of the control device and its construction. The implementation of the new master device is discussed and the effectiveness of the system is reported

Anatomical curve identification

Methods for capturing images in three dimensions are now widely available, with stereo-photogrammetry and laser scanning being two common approaches. In anatomical studies, a number of landmarks are usually identified manually from each of these images and these form the basis of subsequent statistical analysis. However, landmarks express only a very small proportion of the information available from the images. Anatomically defined curves have the advantage of providing a much richer expression of shape. This is explored in the context of identifying the boundary of breasts from an image of the female torso and the boundary of the lips from a facial image. The curves of interest are characterised by ridges or valleys. Key issues in estimation are the ability to navigate across the anatomical surface in three-dimensions, the ability to recognise the relevant boundary and the need to assess the evidence for the presence of the surface feature of interest. The first issue is addressed by the use of principal curves, as an extension of principal components, the second by suitable assessment of curvature and the third by change-point detection. P-spline smoothing is used as an integral part of the methods but adaptations are made to the specific anatomical features of interest. After estimation of the boundary curves, the intermediate surfaces of the anatomical feature of interest can be characterised by surface interpolation. This allows shape variation to be explored using standard methods such as principal components. These tools are applied to a collection of images of women where one breast has been reconstructed after mastectomy and where interest lies in shape differences between the reconstructed and unreconstructed breasts. They are also applied to a collection of lip images where possible differences in shape between males and females are of interest