Christopher Nielsen

Path following for the PVTOL aircraft

This article presents a solution to the path following problem for the planar vertical take-off and landing aircraft (PVTOL) which is applicable to a class of smooth Jordan curves. Our path following methodology enjoys the two properties of output invariance of the path (i.e., if the PVTOLs centre of mass is initialized on the path and its initial velocity is tangent to the path, then the PVTOL remains on the path at all future times) and boundedness of the roll dynamics. Further, our controller guarantees that, after a finite time, the time average of the roll angle is zero, and the PVTOL does not perform multiple revolutions about its longitudinal axis.

Brief paper: Path following using transverse feedback linearization: Application to a maglev positioning system

This article presents an approach to path following control design based on transverse feedback linearization. A “transversal” controller is designed to drive the output of the plant to the path. A “tangential” controller meets application-specific requirements on the path, such as speed regulation and internal stability. This methodology is applied to a five degree-of-freedom (5-DOF) magnetically levitated positioning system. Experimental results demonstrate the effectiveness of our control design.

On Local Transverse Feedback Linearization

Given a control-affine system and a controlled invariant submanifold, we present necessary and sufficient conditions for local feedback equivalence to a system whose dynamics transversal to the submanifold are linear and controllable. A key ingredient used in the analysis is the new notion of transverse controllability indices of a control system with respect to a set.

Path following using transverse feedback linearization: Application to a maglev positioning system

This article presents an approach to path following control design based on transverse feedback linearization. A “transversal” controller is designed to drive the output of the plant to the path. A “tangential” controller meets application-specific requirements on the path, such as speed regulation and internal stability. This methodology is applied to a five degree-of-freedom (5-DOF) magnetically levitated positioning system. Experimental results demonstrate the effectiveness of our control design.

Output stabilization and maneuver regulation: A geometric approach

This paper investigates maneuver regulation for single-input control-affine systems from a geometric perspective. The maneuver regulation problem is converted to output stabilization and necessary and sufficient conditions are provided to solve the latter problem by feedback linearizing the dynamics transverse to a suitable embedded submanifold of the state space. When specialized to the linear time invariant setting, this work recovers well-known results on output stabilization.

Path Following for a Class of Mechanical Systems

Path following entails having the output of a control system approach a path and traverse it without a priori time parameterization of the motion along the path. We design path-following controllers for a class of mechanical control systems applicable to closed and nonclosed paths. Our approach uses transverse feedback linearization (TFL) to partially meet our objective by putting the system into a convenient normal form for control design. To meet the remaining control requirements, we present a method of refining the TFL normal form. Our approach is demonstrated experimentally on a five-bar robotic manipulator and in simulation on a nonminimum phase robotic manipulator with a flexible link.

Maneuver regulation via transverse feedback linearization: Theory and examples

Abstract This paper presents a methodology to solve maneuver regulation problems which is based on transverse feedback linearization. Necessary and sufficient conditions for the linearization of dynamics transverse to an embedded submanifold of the state space are presented. Various examples illustrate the main features of this framework.

Path Following Using Dynamic Transverse Feedback Linearization for Car-Like Robots

This paper presents an approach for designing path-following controllers for the kinematic model of car-like mobile robots using transverse feedback linearization with dynamic extension. This approach is applicable to a large class of paths and its effectiveness is experimentally demonstrated on a Chameleon R100 Ackermann steering robot. Transverse feedback linearization makes the desired path attractive and invariant, while the dynamic extension allows the closed-loop system to achieve the desired motion along the path.

Path following for the PVTOL: A set stabilization approach

This article proposes a path following controller that regulates the center of mass of the planar vertical take-off and landing aircraft (PVTOL) to the unit circle and makes the aircraft traverse the circle in a desired direction. A static feedback controller is designed using the ideas of transverse feedback linearization, finite time stabilization and virtual constraints. No time parameterization is given to the desired motion on the unit circle. Instead, our approach relies on the nested stabilization of two sets on which the dynamics of the PVTOL exhibit desirable behavior.

Path following for a car-like robot using transverse feedback linearization and tangential dynamic extension

This article proposes a path following controller for the two input kinematic model of a car-like robot. A smooth dynamic feedback control law is designed to make the cars position follow a large class of curves with the desired speed along the curve. The controller guarantees the property of path invariance. The controller is designed by characterizing the path following manifold when one input is fixed. Once the path following manifold is found we apply dynamic extension to increase its dimension. We refer to this process as tangential dynamic extension. We then find a physically meaningful differentially flat output for the extended system which allows us to easily solve the path following problem.