Motion equations in redundant coordinates with application to inverse dynamics of constrained mechanical systems

2011 ◽  
Vol 67 (4) ◽  
pp. 2527-2541 ◽  
Author(s):  
A. Müller
Keyword(s):  
Inverse Dynamics ◽  
Mechanical Systems ◽  
Motion Equations ◽  
Constrained Mechanical Systems

An Alternative Formulation of Motion Equations in Redundant Coordinates for the Inverse Dynamics of Constrained Mechanical Systems

2011 ◽  
Author(s):  
Andreas Mu¨ller
Keyword(s):  
Inverse Dynamics ◽  
Mass Matrix ◽  
Alternative Formulation ◽  
Constrained System ◽  
Motion Equations ◽  
Constrained Mechanical Systems ◽  
Implementation Effort ◽  
Regular Configuration ◽  
Minimal Coordinates ◽  
Coordinate Partitioning

The basis for any model-based control of dynamical systems is an efficient formulation of the motion equations. These are preferably expressed in terms of independent coordinates. In other words the coordinates of a constrained system are split into a set of dependent and independent ones. It is well-known that such coordinate partitioning is not globally valid. A remedy is to switch between different possible sets of minimal coordinates. This drastically increases the numerical complexity and implementation effort, however. In this paper a formulation of the motion equations in redundant coordinates is presented for general non-holonomic systems. This gives rise to a redundant system of differential equations. The formulation is valid in any regular configuration. Because of the singular mass matrix it is not directly applicable for solving the forward dynamics but is tailored for solving the inverse dynamics. An inverse dynamics solution is presented for general full-actuated systems.

Differential-Geometric Methods in Multibody Dynamics and Control

2005 ◽  
Author(s):  
P. Maißer
Keyword(s):  
Configuration Space ◽  
High Performance ◽  
Multibody System ◽  
Equations Of Motion ◽  
Geometric Approach ◽  
Motion Equations ◽  
Constrained Mechanical Systems ◽  
Dynamics And Control ◽  
Set Up ◽  
Lagrangian Motion

This paper presents a differential-geometric approach to the multibody system dynamics regarded as a point dynamics in a n-dimensional configuration space Rn. This configuration space becomes a Riemannian space Vn the metric of which is defined by the kinetic energy of the multibody system (MBS). Hence, all concepts and statements of the Riemannian geometry can be used to study the dynamics of MBS. One of the key points is to set up the non-linear Lagrangian motion equations of tree-like MBS as well as of constrained mechanical systems, the perturbed equations of motion, and the motion equations of hybrid MBS in a derivative-free manner. Based on this approach transformation properties can be investigated for application in real-time simulation, control theory, Hamilton mechanics, the construction of first integrals, stability etc. Finally, a general Lyapunov-stable force control law for underactuated systems is given that demonstrates the power of the approach in high-performance sports applications.

scholarly journals Numerical solution for consistent initial conditions of constrained mechanical systems

2003 ◽  
Vol 25 (3) ◽  
pp. 170-185
Author(s):  
Dinh Van Phong
Keyword(s):  
Numerical Solution ◽  
Initial Conditions ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Differential Algebraic Equations ◽  
System Of Equations ◽  
Algebraic Equations ◽  
Flexible Approach ◽  
Constrained Mechanical Systems ◽  
Consistent Initial Values

The article deals with the problem of consistent initial values of the system of equations of motion which has the form of the system of differential-algebraic equations. Direct treating the equations of mechanical systems with particular properties enables to study the system of DAE in a more flexible approach. Algorithms and examples are shown in order to illustrate the considered technique.

scholarly journals Stabilization of Constrained Mechanical Systems with DAEs and Invariant Manifolds

1995 ◽  
Vol 23 (2) ◽  
pp. 135-157 ◽  
Author(s):  
Uri M. Ascher ◽  
Hongsheng Chin ◽  
Linda R. Petzold ◽  
Sebastian Reich
Keyword(s):  
Invariant Manifolds ◽  
Mechanical Systems ◽  
Constrained Mechanical Systems

On the Use of the Canonical Equations of Motion for the Dynamic Analysis of Constrained Multibody Systems

1992 ◽  
Author(s):  
E. Bayo ◽  
J. M. Jimenez
Keyword(s):  
Dynamic Analysis ◽  
Multibody Systems ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Numerical Algorithms ◽  
Constrained Multibody Systems ◽  
Constrained Mechanical Systems ◽  
First Order ◽  
Canonical Variables ◽  
Lagrange’S Multipliers

Abstract We investigate in this paper the different approaches that can be derived from the use of the Hamiltonian or canonical equations of motion for constrained mechanical systems with the intention of responding to the question of whether the use of these equations leads to more efficient and stable numerical algorithms than those coming from acceleration based formalisms. In this process, we propose a new penalty based canonical description of the equations of motion of constrained mechanical systems. This technique leads to a reduced set of first order ordinary differential equations in terms of the canonical variables with no Lagrange’s multipliers involved in the equations. This method shows a clear advantage over the previously proposed acceleration based formulation, in terms of numerical efficiency. In addition, we examine the use of the canonical equations based on independent coordinates, and conclude that in this second case the use of the acceleration based formulation is more advantageous than the canonical counterpart.

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