Symbolic computer methods to automatically formulate vehicle simulation codes.

Abstract

This dissertation deals with the modeling and computer simulation of multibody systems composed of rigid bodies and massless force- and torque-producing elements. Multibody systems pertaining to ground vehicles are of particular interest. The dissertation includes (1) a software design for representing a multibody system in symbolic form as a set of computer data objects representing bodies, points, forces, etc, (2) a multibody formalism (i.e., a formal strategy for deriving equations of motion for a multibody system) that is valid for systems with various types of connections between bodies, (3) methods to manipulate symbolic expressions automatically within the multibody formalism, (4) the design of an interface to the analyst that permits the description of unconventional force- and moment-producing components, (5) methods for automatically generating constraint equations in symbolic form, and (6) a way to accommodate external numerical algorithms that may have already been developed. The methods are valid for systems of rigid bodies with holonomic and nonholonomic constraints, tree topologies, closed kinematical loops, and scleronomic or rheonomic constraints that are continuously differentiable. Symbol manipulation techniques are applied to (1) vector and dyadic algebraic expressions, (2) elements of the multibody system, and (3) pieces of numerical analysis code. A software package called AUTOSIM was written in the Lisp computer language to validate and demonstrate the methods. The analyst using AUTOSIM provides a description of (1) the multibody system layout, (2) output variables of interest, (3) "external" subroutines, and, for some systems, (4) descriptions of constraint conditions. Using the multibody formalism and symbol manipulation techniques, AUTOSIM automatically generates a complete, self-contained Fortran program that numerically computes the specified output variables in response to initial conditions, control inputs, and disturbances. Six case studies are included to illustrate the methods. These include two ground vehicles (one with rigid, nonslipping wheels, and one with slip angles and tire characteristics), a four-bar linkage, two spacecraft vehicles, and a robot manipulator with six links.