Controllability and motion planning for noncatastatic nonholonomic control systems (original) (raw)

Path planning for nonholonomic systems with drift

Proceedings of the 1997 American Control Conference (Cat. No.97CH36041), 1997

In this paper we study nonholonomic systems with drift terms. The discussion is focused on a class of Lagrangian systems with a cyclic coordinate. An approach to open{loop path planning is presented. A control algorithm is derived and applied to the example of a 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.

Motion Planning of Nonholonomic Systems – Nondeterministic Endogenous Configuration Space Approach

Lecture Notes in Control and Information Sciences, 2012

This paper presents a new nondeterministic motion planning algorithm for nonholonomic systems. Such systems are represented by driftless control system with outputs. Presented approach combines two different methods: the endogenous configuration space approach and the Particle Filters. The former, fully deterministic, originally has been dedicated to motion planning problem for mobile manipulators. The latter, stochastic approach was designed for solving optimal estimation problems in non-linear non-Gaussian systems. A mixture of these methods results in a nondeterministic endogenous configuration space approach that outperforms the traditional one in regions, where the classical inverse Jacobian algorithm loses convergence. In accordance with the Particle Filters approach new algorithm consists of three major steps: prediction, update and resampling. In contrast to its original version, the presented algorithm contains an additional step of dividing particles into different subsets. Each subset is processed in a different way during prediction phase. Performance of the new algorithm has been illustrated by solving the motion planning problem for the rolling ball.

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.

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.

A unified control architecture for navigation of nonholonomic systems

Proceedings of the 2011 American Control Conference, 2011

The paper presents a unified control architecture for motion planning and navigation of constrained systems. It provides a systematic approach for planning any motion that may be specified by equations of algebraic or differential constraints. It is based upon one dynamic control model for constrained systems, which is not sensitive to the constraint kind and order. The preplanned reference motion may be executed by nonlinear control algorithms.

On motion planning of nonholonomic mobile robots

2000

ABSTRACT Mobile robots that consist of a mobile platform with one or many manipulators, are of great interest in a number of applications. This paper presents a methodology for generating paths and trajectories for both the mobile platform and the manipulator that will take a system from an initial configuration to a pre-specified final one, without violating the nonholonomic constraint. The generated paths are of polynomial nature and therefore are continuous and smooth.

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.