Modelling and experimental investigation of carangiform locomotion for control

We propose a model for planar carangiform swimming based on conservative equations for the interaction of a rigid body and an incompressible fluid. We account for the generation of thrust due to vortex shedding through controlled coupling terms. We investigate the correct form of this coupling experimentally with a robotic propulsor, comparing its observed behavior to that predicted by unsteady hydrodynamics. Our analysis of thrust generation by an oscillating hydrofoil allows us to characterize and evaluate certain families of gaits. Our final swimming model takes the form of a control-affine nonlinear system

Nonholonomic systems and exponential convergence: some analysis tools

In this paper the authors make a contribution to the analysis of nonholonomic systems with exponential rates of convergence. A key idea is the use of control laws which render the closed loop system homogeneous with respect to a dilation. The analysis is applied to nonholonomic systems in power form and consists of two steps. The first step is a reduction to an invariant set and then the application of an averaging result. The averaging theorem is a stability result for C^0 homogeneous order zero vector fields

Experiments in exponential stabilization of a mobile robot towing a trailer

Applies some previously developed control laws for stabilization of mechanical systems with non-holonomic constraints to an experimental system consisting of a mobile robot towing a trailer. The authors verify the applicability of various control laws which have appeared in the recent literature, and compare the performance of these controllers in an experimental setting. In particular, the authors show that time-periodic, non-smooth controllers can be used to achieve exponential stability of a desired equilibrium configuration, and that these controllers outperform smooth, time-varying control laws. The authors also point out several practical considerations which must be taken into account when implementing these controllers

Convergence Rates for Nonholonomic Systems in Power Form

This paper investigates the convergence rates of several controllers for low dimenional nonholonomic systems in power form. The method of multiple scales is found to be effective in determining the asymptotic form of the solutions. The general form of the perturbation solutions indicates how parameters in the control laws may be chosen to achieve a desired convergence rate. A detailed analysis of controllers exhibiting exponential convergence is included

Exponential stabilization of driftless nonlinear control systems via time-varying, homogeneous feedback

This paper brings together results from a number of different areas in control theory to provide an algorithm for the synthesis of locally exponentially stabilizing control laws for a large class of driftless nonlinear control systems. The stability is defined with respect to a nonstandard dilation and is termed "δ-exponential" stability. The δ-exponential stabilization relies on the use of feedbacks which render the closed loop vector field homogeneous with respect to a dilation. These feedbacks are generated from a modification of Pomet's algorithm (1992) for smooth feedbacks. Converse Lyapunov theorems for time-periodic homogeneous vector fields guarantee that local exponential stability is maintained in the presence of higher order (with respect to the dilation) perturbing terms

Convergence Rates for Nonholonomic Systems in Power Form

This paper investigates the convergence rates of several controllers for low dimenional nonholonomic systems in power form. The method of multiple scales is found to be effective in determining the asymptotic form of the solutions. The general form of the perturbation solutions indicates how parameters in the control laws may be chosen to achieve a desired convergence rate. A detailed analysis of controllers exhibiting exponential convergence is included

Exponential Stabilization of Driftless Nonlinear Control Systems using Homogeneous Feedback

This paper focuses on the problem of exponential stabilization of controllable, driftless systems using time-varying, homogeneous feedback. The analysis is performed with respect to a homogeneous norm in a non-standard dilation that is compatible with the algebraic structure of the control Lie algebra. Using this structure, we show that any continuous, time-varying controller that achieves exponential stabilization relative to the Euclidean norm is necessarily non-Lipschitz. Despite these restrictions, we provide a set of constructive, sufficient conditions for extending smooth, asymptotic stabilizers to homogeneous, exponential stabilizers. The modified feedbacks are everywhere continuous, smooth away from the origin, and can be extended to a large class of systems with torque inputs. The feedback laws are applied to an experimental mobile robot and show significant improvement in convergence rate over smooth stabilizers

Exponential stabilization of driftless nonlinear control systems via time-varying, homogeneous feedback

This paper brings together results from a number of different areas in control theory to provide an algorithm for the synthesis of locally exponentially stabilizing control laws for a large class of driftless nonlinear control systems. The stability is defined with respect to a nonstandard dilation and is termed "δ-exponential" stability. The δ-exponential stabilization relies on the use of feedbacks which render the closed loop vector field homogeneous with respect to a dilation. These feedbacks are generated from a modification of Pomet's algorithm (1992) for smooth feedbacks. Converse Lyapunov theorems for time-periodic homogeneous vector fields guarantee that local exponential stability is maintained in the presence of higher order (with respect to the dilation) perturbing terms

Nonholonomic systems and exponential convergence: some analysis tools

In this paper the authors make a contribution to the analysis of nonholonomic systems with exponential rates of convergence. A key idea is the use of control laws which render the closed loop system homogeneous with respect to a dilation. The analysis is applied to nonholonomic systems in power form and consists of two steps. The first step is a reduction to an invariant set and then the application of an averaging result. The averaging theorem is a stability result for C^0 homogeneous order zero vector fields