1,513 research outputs found
Stabilization of trajectories for systems with nonholonomic constraints
A technique for stabilizing nonholonomic systems to trajectories is presented. It is well known that such systems cannot be stabilized to a point using smooth static-state feedback. The authors suggest the use of control laws for stabilizing a system about a trajectory, instead of a point. Given a nonlinear system and a desired nominal feasible trajectory, an explicit control law which will locally exponentially stabilize the system to the desired trajectory is given. The theory is applied to several examples, including a car-like robot
Stabilization of trajectories for systems with nonholonomic constraints
A technique for stabilizing nonholonomic systems to trajectories is presented. It is well known that such systems cannot be stabilized to a point using smooth static-state feedback. The authors suggest the use of control laws for stabilizing a system about a trajectory, instead of a point. Given a nonlinear system and a desired nominal feasible trajectory, an explicit control law which will locally exponentially stabilize the system to the desired trajectory is given. The theory is applied to several examples, including a car-like robot
Exponential ε-tracking and ε-stabilization of second-order nonholonomic SE(2) vehicles using dynamic state feedback
In this paper, we address the problem of ε-tracking and ε-stabilization for a class of SE(2) vehicles with second-order nonholonomic constraints. We introduce a class of transformations called near-identity diffeomorphism that allow dynamic partial feedback linearization of the translational dynamics of this class of SE(2) vehicles. This allows us to achieve global exponential ε-stabilization and ε-tracking (in position) for the aforementioned classes of autonomous vehicles using a coordinate-independent dynamic state feedback. This feedback is only discontinuous w.r.t. the augmented state. We apply our results to ε-stabilization and ε-tracking for an underactuated surface vessel
Discrete second order constrained Lagrangian systems: first results
We briefly review the notion of second order constrained (continuous) system
(SOCS) and then propose a discrete time counterpart of it, which we naturally
call discrete second order constrained system (DSOCS). To illustrate and test
numerically our model, we construct certain integrators that simulate the
evolution of two mechanical systems: a particle moving in the plane with
prescribed signed curvature, and the inertia wheel pendulum with a Lyapunov
constraint. In addition, we prove a local existence and uniqueness result for
trajectories of DSOCSs. As a first comparison of the underlying geometric
structures, we study the symplectic behavior of both SOCSs and DSOCSs.Comment: 17 pages, 6 figure
Nonholonomic motion planning: steering using sinusoids
Methods for steering systems with nonholonomic constraints between arbitrary configurations are investigated. Suboptimal trajectories are derived for systems that are not in canonical form. Systems in which it takes more than one level of bracketing to achieve controllability are considered. The trajectories use sinusoids at integrally related frequencies to achieve motion at a given bracketing level. A class of systems that can be steered using sinusoids (claimed systems) is defined. Conditions under which a class of two-input systems can be converted into this form are given
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 nonstandard dilation that is compatible with the algebraic structure of the control Lie algebra. It can be shown that any continuous, time-varying controller that achieves exponential stability 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
Stabilization of non-admissible curves for a class of nonholonomic systems
The problem of tracking an arbitrary curve in the state space is considered
for underactuated driftless control-affine systems. This problem is formulated
as the stabilization of a time-varying family of sets associated with a
neighborhood of the reference curve. An explicit control design scheme is
proposed for the class of controllable systems whose degree of nonholonomy is
equal to 1. It is shown that the trajectories of the closed-loop system
converge exponentially to any given neighborhood of the reference curve
provided that the solutions are defined in the sense of sampling. This
convergence property is also illustrated numerically by several examples of
nonholonomic systems of degrees 1 and 2.Comment: This is the author's version of the manuscript accepted for
publication in the Proceedings of the 2019 European Control Conference
(ECC'19
Trajectory generation for the N-trailer problem using Goursat normal form
Develops the machinery of exterior differential forms, more particularly the Goursat normal form for a Pfaffian system, for solving nonholonomic motion planning problems, i.e., motion planning for systems with nonintegrable velocity constraints. The authors use this technique to solve the problem of steering a mobile robot with n trailers. The authors present an algorithm for finding a family of transformations which will convert the system of rolling constraints on the wheels of the robot with n trailers into the Goursat canonical form. Two of these transformations are studied in detail. The Goursat normal form for exterior differential systems is dual to the so-called chained-form for vector fields that has been studied previously. Consequently, the authors are able to give the state feedback law and change of coordinates to convert the N-trailer system into chained-form. Three methods for planning trajectories for chained-form systems using sinusoids, piecewise constants, and polynomials as inputs are presented. The motion planning strategy is therefore to first convert the N-trailer system into Goursat form, use this to find the chained-form coordinates, plan a path for the corresponding chained-form system, and then transform the resulting trajectory back into the original coordinates. Simulations and frames of movie animations of the N-trailer system for parallel parking and backing into a loading dock using this strategy are included
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