The Application of The Steepest Gradient Descent for Control Design of Dubins Car for Tracking a Desired Path

In this paper, we consider the control design of the Dubins car system to track a desired path. We design the control of the Dubins car system using optimal control approach. The control of the Dubins car system is designed for tracking the desired path. Instead of the usual quadratic cost function, a special type of cost functional which includes a tracking error term will be considered. By this special cost functional, the minimum tracking error of path of the Dubins car toward a desired path using Pontryagin Maximum Principle is obtained. The analytical solution of the Hamiltonian system is di±cult to obtain. So, a numerical solution with the steepest gradient descent method is proposed. The numerical results are given at the last section of this paper

Nilpotentization of the kinematics of the n-trailer system at singular points and motion planning through the singular locus

We propose in this paper a constructive procedure that transforms locally, even at singular configurations, the kinematics of a car towing trailers into Kumpera-Ruiz normal form. This construction converts the nonholonomic motion planning problem into an algebraic problem (the resolution of a system of polynomial equations), which we illustrate by steering the two-trailer system in a neighborhood of singular configurations. We show also that the n-trailer system is a universal local model for all Goursat structures and that all Goursat structures are locally nilpotentizable.Comment: LaTeX2e, 23 pages, 4 figures, submitted to International journal of contro

Adaptive multiple-surface sliding mode control of nonholonomic systems with matched and unmatched uncertainties

The problem of stabilizing a class of nonholonomic systems in chained form affected by both matched and unmatched uncertainties is addressed in this paper. The proposed design methodology is based on a discontinuous transformation of the perturbed nonholonomic system to which an adaptive multiple-surface sliding mode technique is applied. The generation of a sliding mode allows to eliminate the effect of matched uncertainties, while a suitable function approximation technique enables to deal with the residual uncertainties, which are unmatched. The control problem is solved by choosing a particular sliding manifold upon which a second order sliding mode is enforced via a continuous control with discontinuous derivative. A positive feature of the present proposal, apart from the fact of being capable of dealing with the presence of both matched and unmatched uncertainties, is that no knowledge of the bounds of the unmatched uncertainty terms is required. Moreover, the fact of producing a continuous control makes the proposed approach particularly appropriate in nonholonomic applications, such as those of mechanical nature

The Application of the Steepest Gradient Descent for Control Design of Dubins Car for Tracking a Desired Path

In this paper, we consider the control design of the Dubins car system to track a desired path. We design the control of the Dubins car system using optimal control approach. The control of the Dubins car system is designed for tracking the desired path. Instead of the usual quadratic cost function, a special type of cost functional which includes a tracking error term will be considered. By this special cost functional, the minimum tracking error of path of the Dubins car toward a desired path using Pontryagin Maximum Principle is obtained. The analytical solution of the Hamiltonian system is di±cult to obtain. So, a numerical solution with the steepest gradient descent method is proposed. The numerical results are given at the last section of this paper

On Observer-Based Control of Nonlinear Systems

Filtering and reconstruction of signals play a fundamental role in modern signal processing, telecommunications, and control theory and are used in numerous applications. The feedback principle is an important concept in control theory. Many different control strategies are based on the assumption that all internal states of the control object are available for feedback. In most cases, however, only a few of the states or some functions of the states can be measured. This circumstance raises the need for techniques, which makes it possible not only to estimate states, but also to derive control laws that guarantee stability when using the estimated states instead of the true ones. For linear systems, the separation principle assures stability for the use of converging state estimates in a stabilizing state feedback control law. In general, however, the combination of separately designed state observers and state feedback controllers does not preserve performance, robustness, or even stability of each of the separate designs. In this thesis, the problems of observer design and observer-based control for nonlinear systems are addressed. The deterministic continuous-time systems have been in focus. Stability analysis related to the Positive Real Lemma with relevance for output feedback control is presented. Separation results for a class of nonholonomic nonlinear systems, where the combination of independently designed observers and state-feedback controllers assures stability in the output tracking problem are shown. In addition, a generalization to the observer-backstepping method where the controller is designed with respect to estimated states, taking into account the effects of the estimation errors, is presented. Velocity observers with application to ship dynamics and mechanical manipulators are also presented

Adaptive control of uncertain nonholonomic systems in finite time

summary:In this paper, the finite-time stabilization problem of chained form systems with parametric uncertainties is investigated. A novel switching control strategy is proposed for adaptive finite-time control design with the help of Lyapunov-based method and time-rescaling technique. With the proposed control law, the uncertain closed-loop system under consideration is finite-time stable within a given settling time. An illustrative example is also given to show the effectiveness of the proposed controller