Nicholas R. Fischer

LaSalle-Yoshizawa Corollaries for Nonsmooth Systems

In this note, two generalized corollaries to the LaSalle-Yoshizawa Theorem are presented for nonautonomous systems described by nonlinear differential equations with discontinuous right-hand sides. Lyapunov-based analysis methods are developed using differential inclusions to achieve asymptotic convergence when the candidate Lyapunov derivative is upper bounded by a negative semi-definite function.In this technical note, two generalized corollaries to the LaSalle-Yoshizawa Theorem are presented for nonautonomous systems described by nonlinear differential equations with discontinuous right-hand sides. Lyapunov-based analysis methods that achieve asymptotic convergence when the candidate Lyapunov derivative is upper bounded by a negative semi-definite function in the presence of differential inclusions are presented. A design example illustrates the utility of the corollaries.

Nonlinear RISE-Based Control of an Autonomous Underwater Vehicle

This study focuses on the development of a nonlinear control design for a fully-actuated autonomous underwater vehicle (AUV) using a continuous robust integral of the sign of the error control structure to compensate for system uncertainties and sufficiently smooth bounded exogenous disturbances. A Lyapunov stability analysis is included to prove semiglobal asymptotic tracking. The resulting controller is experimentally validated on an AUV developed at the University of Florida in both controlled and open-water environments.

Single Camera Structure and Motion

A reduced order nonlinear observer is proposed for the problem of “structure and motion (SaM)” estimation of a stationary object observed by a moving calibrated camera. In comparison to existing work which requires some knowledge of the Euclidean geometry of an observed object or full knowledge of the camera motion, the developed reduced order observer only requires one camera linear velocity and corresponding acceleration to asymptotically identify the Euclidean coordinates of the feature points attached to an object (with proper scale reconstruction) and the remaining camera velocities. The unknown linear velocities are assumed to be generated using a model with unknown parameters. The unknown angular velocities are determined from a robust estimator which uses a standard Homography decomposition algorithm applied to tracked feature points. A Lyapunov analysis is provided to prove the observer asymptotically estimates the unknown states under a persistency of excitation condition.

Saturated RISE Feedback Control for a Class of Second-Order Nonlinear Systems

A saturated controller is developed for a class of uncertain, second-order, nonlinear systems which includes time-varying and nonlinearly parameterized functions with bounded disturbances using a continuous control law with smooth saturation functions. Based on the robust integral of the sign of the error (RISE) control methodology, the developed controller is able to utilize the benefits of high gain control strategies while guaranteeing saturation limits are not surpassed. The bounds on the control are known a priori and can be adjusted by changing the feedback gains. The saturated controller yields asymptotic tracking despite model uncertainty and added disturbances in the dynamics. Experimental results using a two-link robot manipulator demonstrate the performance of the developed controller.

Saturated control of an uncertain nonlinear system with input delay

This paper examines saturated control of a general class of uncertain nonlinear systems with time-delayed actuation and additive bounded disturbances. The bound on the control is known a priori and can be adjusted by changing the feedback gains. A Lyapunov-based stability analysis utilizing Lyapunov-Krasovskii (LK) functionals is provided to prove uniformly ultimately bounded tracking despite uncertainties in the dynamics. A numerical example is presented to demonstrate the performance of the controller.

Nonlinear control of an autonomous underwater vehicle: A RISE-based approach

Autonomous and remotely operated marine vehicles such as ships and submarines are becoming a key component in several aspects of maritime industry and defense. This paper explores the development of a nonlinear controller for a fully actuated autonomous underwater vehicle (AUV) using a robust integral of the sign of the error (RISE) feedback term with a neural network (NN) based feedforward term to achieve semi-global asymptotic tracking results in the presence of complete model uncertainty and unknown disturbances. A simulation is provided to demonstrate the proposed controller on an experimentally validated AUV model.

Lyapunov-based control of an uncertain Euler-Lagrange system with time-varying input delay

This paper examines control of a general class of uncertain nonlinear Euler-Lagrange systems with time-varying input delay and additive bounded disturbances. A Lyapunov-based stability analysis utilizing Lyapunov-Krasovskii functionals is provided to prove semi-global uniformly ultimately bounded tracking. Simulation results demonstrate the robustness of the control design with respect to the delay.

Structure and motion estimation of a moving object using a moving camera

A solution is presented to the problem of estimating the structure and motion of a moving object seen from a moving camera. A nonlinear observer is proposed, which asymptotically identifies the structure and motion of the moving object, when the camera motion is persistently exciting. The object is assumed to be moving with constant velocities. The proposed method makes no assumptions on the minimum number of views or point correspondences as required by the existing approaches.

Structure estimation of a moving object using a moving camera: An unknown input observer approach

A state observer is designed for estimating the structure of a moving object with time-varying velocities seen by a moving camera. A nonlinear unknown input observer strategy is used where the objects velocity is considered as an unknown input to the perspective dynamical system. The object is assumed to be moving on a ground plane. The downward-looking camera observing the moving object is also moving (e.g., attached to an air vehicle) with known velocities. The developed method provides the first causal, observer-based structure estimation algorithm for a moving camera viewing a moving object with unknown time-varying object velocities.

Saturated control of an uncertain Euler-Lagrange system with input delay

This paper examines saturated control of a general class of uncertain nonlinear Euler-Lagrange systems with time-delayed actuation and additive bounded disturbances. The bound on the control is known a priori and can be adjusted by changing the feedback gains. A Lyapunov-based stability analysis utilizing Lyapunov-Krasovskii functionals is provided to prove uniformly ultimately bounded tracking despite uncertainties in the dynamics.