NDLI: Triangularizing kinematic constraint equations using Gröbner bases for real-time dynamic simulation

Content Provider	Springer Nature Link
Author	Uchida, Thomas McPhee, John
Copyright Year	2011
Abstract	Real-time simulation is an essential component of hardware- and operator-in-the-loop applications, such as driving simulators, and can greatly facilitate the design, implementation, and testing of dynamic controllers. Such applications may involve multibody systems containing closed kinematic chains, which are most readily modeled using a set of redundant generalized coordinates. The governing dynamic equations for such systems are differential-algebraic in nature—that is, they consist of a set of ordinary differential equations coupled with a set of nonlinear algebraic constraint equations—and can be difficult to solve in real time. In this work, the equations of motion are formulated symbolically using linear graph theory. The embedding technique is applied to eliminate the Lagrange multipliers from the dynamic equations and obtain one ordinary differential equation for each independent acceleration. The theory of Gröbner bases is then used to triangularize the kinematic constraint equations, thereby producing a recursively solvable system for calculating the dependent generalized coordinates given values of the independent coordinates. The proposed approach can be used to generate computationally efficient simulation code that avoids the use of iteration, which makes it particularly suitable for real-time applications.
Starting Page	335
Ending Page	356
Page Count	22
File Format	PDF
ISSN	13845640
Journal	Multibody System Dynamics
Volume Number	25
Issue Number	3
e-ISSN	1573272X
Language	English
Publisher	Springer Netherlands
Publisher Date	2011-01-19
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Closed kinematic chains Computational efficiency Differential-algebraic equations Kinematic loops Symbolic computation Automotive Engineering Mechanical Engineering Electrical Engineering Optimization Vibration, Dynamical Systems, Control
Content Type	Text
Resource Type	Article
Subject	Control and Optimization Mechanical Engineering Aerospace Engineering Modeling and Simulation Computer Science Applications

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