Modelling dynamical systems with equality state-space constraints

Modelling dynamical systems with equality state-space constraints

ten Dam, A.A.

National Aerospace Laboratory NLR

1990-07-01

A mathematical theory for modelling dynamical systems with equality state-space constraints is presented. The dynamic behaviour of these systems is represented by a combination of differential and algebraic equations. It Is shown that the freedom offered by control is essential to obtain other, mathematically equivalent formulations. The notion of applicable control is introduced for the systems under consideration. A characterisation for all applicable controls of constrained dynamical systems is presented. The theory also covers the case of mechanical systems with equality state-space constraints. The equations of motions as derived in classical mechanics can be obtained from the formulations presented in this report by a suitable choice of parameters or by further restrictions on the class of applicable controls. Furthermore, It is shown that in the case of mechanical systems, from a mathematical point of view, holonomlc and nonholonomic constraints are merely special cases. The theory is Illustrated by modelling constrained manipulator motions. Here the kinematic relation between Joints and end-effector is treated as an additional constraint. A number of test cases are considered. Decomposition of a model in submodels as well as easy exchange of submodels, important for the development and evaluation of (sub)models, is supported by the theory presented hare. The models derived here can form the basis for the development of planning and (feedback) control schemes for dynamical systems subject to equality state-space constraints. Furthermore, the models are useful especially if the time evolution of a constrained dynamical system is to be found by means of digital simulation. With the aid of one of the models stable numerical integration of dynamical systems with equality state-space constraints can be accomplished. This will be elaborated in a separate report.

dynamical systems
constraints
nonholonomic equations
dynamic models
robot dynamics
manipulators
end effectors
trajectory planning
Euler-Lagrange equation
Jacobi matrix method
control theory

http://resolver.tudelft.nl/uuid:036659d2-35ba-4dfa-9ef0-41dc669321a6

Nationaal Lucht- en Ruimtevaartlaboratorium

Campus only

NLR Technical Publication TP 89418 U

Aerospace Engineering Reports

report

(c) 1990 National Aerospace Laboratory NLR