A surface integral algorithm for the motion planning of nonholonomic mechanical systems
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Authors
Anderson, David P.
Subjects
Holonomic
Nonholonomic
Scleronomic
Motion constraints
Degrees of freedom
Generalized coordinates
Motion planning
Nonholonomic
Scleronomic
Motion constraints
Degrees of freedom
Generalized coordinates
Motion planning
Advisors
Mukherjee, Ranjan
Date of Issue
1992-12
Date
December 1992
Publisher
Monterey, California. Naval Postgraduate School
Language
en_US
Abstract
The number of coordinates needed to completely describe the configuration of a holonomic mechanical system is equal to the number of degrees of freedom possessed by that system. In contrast, nonholonomic systems always require more coordinates for their description than there are degrees of freedom due to the nonintegrable nature of the governing velocity constraints. The task of nonholonomic motion planning applied to a given system is to develop trajectories of the independent coordinate variables such that the system is driven to some desired point in its configuration space. An algorithm for constructing these trajectories is presented. In this algorithm, the independent variable are first converged to their desired values. The dependent variables are subsequently converged using closed trajectories of the independent variables. The requisite closed trajectories are planned using Stoke's Theorem which converts the problem of finding a closed path in the space of the independent variables to that of finding a surface area in that same space such that the dependent variable converge to their desired values as the independent variables traverse along the boundary of the surface area. The use of Stoke's Theorem simplifies the motion planning process and also answers important questions pertaining to the system. The salient features of the algorithm are apparent in the two examples discussed: a planar space robot and a disk rolling without slipping on a flat surface.
Type
Thesis
Description
Series/Report No
Department
Mechanical Engineering
Organization
Naval Postgraduate School
Identifiers
NPS Report Number
Sponsors
Funder
Format
60 p.
Citation
Distribution Statement
Approved for public release; distribution is unlimited.
Rights
This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.