Path planning for nonholonomic systems with drift (original) (raw)

Control of nonholonomic systems with drift terms

1997

In the present paper nonholonomic systems with drift terms are studied. The discussion is focused on a class of Lagrangian systems with a cyclic coordinate. We present an approach to open{loop path planning in which the system evolution is studied on manifolds of dimension equal to the number of control inputs. A control algorithm is derived and it is applied to the examples of a hopping robot and a planar diver. A similar algorithm is derived for the study of what states can be reached within a given time. An exponentially stabilizing feedback controller is derived for tracking of the planned trajectories. The results are illustrated with simulations.

Steering of a class of nonholonomic systems with drift terms

Automatica, 1999

In the present paper nonholonomic systems with drift terms are studied. The discussion is focused on a class of Lagrangian systems with a cyclic coordinate. We present an approach to open-loop path planning in which the system evolution is studied on manifolds of dimension equal to the number of control inputs. A control procedure is derived and it is applied to the planar diver.

Constrained motion planning of nonholonomic systems

Systems & Control Letters, 2011

This paper addresses the constrained motion planning problem for nonholonomic systems represented by driftless control systems with output. The problem consists in defining a control function driving the system output to a desirable point at a given time instant, whereas state and control variables remain over the control horizon within prescribed bounds. The state and control constraints are handled by extending the control system with a pair of state equations driven by the violation of constraints, and adding regularizing perturbations. For the regularized system a Jacobian motion planning algorithm is designed, called imbalanced. Solution of example constrained motion planning problem for the rolling ball illustrates theoretical concepts.

Controllability and motion planning for noncatastatic nonholonomic control systems

Mathematical and Computer Modelling, 1996

motion planning problem for a class of noncatsstatic nonholonomic control systems is considered. Under appropriate controllability assumptions we determine an open loop control function which steers the system from a specified initial state to a specified final state over a specified time interval. The method is based on combining second order averaging technique and a finite dimensional root finding technique.

Nonholonomic Motion Planning for Mobile Manipulators

Robotics and Automation, …, 2002

Abstract|A nonholonomic motion planner for mobile manipulators moving in cluttered environments is presented. The approach is based on a discontinous feedback law under the infuence of a special potential eld. Convergence is shown via Lyapunov's direct method. Utilizing redundancy, the methodology allows the system to perform secondary, con guration dependent, objectives such as singularity avoidance. It introduces an e cient feedback scheme for real time navigation of nonholonomic systems.

Steering for a Class of Dynamic Nonholonomic Systems

1999

In this paper we derive control algorithms for a class of dynamic nonholonomic steering problems, characterized as mechanical systems with nonholonomic constraints and symmetries. Recent research in geometric mechanics has led to a single, simplified framework that describes this class of systems, which includes examples such as wheeled mobile robots; undulatory robotic and biological locomotion systems, such as paramecia, inchworms, and snakes; and the reorientation of satellites and underwater vehicles. This geometric framework has also been applied to more unusual examples, such as the snakeboard robot, bicycles, the wobblestone, and the reorientation of a falling cat. We use this geometric framework as a basis for developing two types of control algorithms for such systems. The first is geared towards local controllability, using a perturbation approach to establish results similar to steering using sinusoids. The second method utilizes these results in applying more traditional steering algorithms for mobile robots, and is directed towards generating more non-local control methods of steering for this class of systems.

Nonholonomic motion planning: Steering using sinusoids

Automatic Control, IEEE Transactions …, 1993

In this paper, we investigate methods for steering systems with nonholonomic constraints between arbitrary configurations. Early work by Brockett derives the optimal controls for a set of canonical systems in which the tangent space to the configuration manifold is spanned by the input vector fields and their first order Lie brackets. Using Brockett's result as motivation, we derive suboptimal trajectories for systems which are not in canonical form and consider systems in which it takes more than one level of bracketing to achieve controllability. These trajectories use sinusoids at integrally related frequencies to achieve motion at a given bracketing level. We define a class of systems which can be steered using sinusoids (chained systems) and give conditions under which a class of two-input systems can be converted into this form.

Feedback Control and Nonlinear Controllability of Nonholonomic Systems

2003

In this thesis we study the methods for motion planning for nonholonomic systems. These systems are characterized by nonholonomic constraints on their generalized velocities. The motion planning problem with constraints on the velocities is transformed into a control problem having fewer control inputs than the degrees of freedom. The main focus of the thesis is on the study of motion planning and design of the feedback control laws for an autonomous underwater vehicle: a nonholonomic system. The nonlinear controllability issues for the system are also studied. For the design of feedback cont rollers, the system is transformed into chained and power forms.