scholarly journals A general framework for modeling and dynamic simulation of multibody systems using factor graphs

2021 ◽  
Author(s):  
Jose-Luis Blanco-Claraco ◽  
Antonio Leanza ◽  
Giulio Reina
Keyword(s):  
Multibody Systems ◽  
General Framework ◽  
Inverse Dynamics ◽  
Factor Graph ◽  
Factor Graphs ◽  
Nonlinear Minimization ◽  
Comparable Accuracy ◽  
Reference Implementation ◽  
Complex Mechanical Systems ◽  
Intuitive Interpretation

AbstractIn this paper, we present a novel general framework grounded in the factor graph theory to solve kinematic and dynamic problems for multibody systems. Although the motion of multibody systems is considered to be a well-studied problem and various methods have been proposed for its solution, a unified approach providing an intuitive interpretation is still pursued. We describe how to build factor graphs to model and simulate multibody systems using both, independent and dependent coordinates. Then, batch optimization or a fixed lag smoother can be applied to solve the underlying optimization problem that results in a highly sparse nonlinear minimization problem. The proposed framework has been tested in extensive simulations and validated against a commercial multibody software. We release a reference implementation as an open-source C++ library, based on the GTSAM framework, a well-known estimation library. Simulations of forward and inverse dynamics are presented, showing comparable accuracy with classical approaches. The proposed factor graph-based framework has the potential to be integrated into applications related with motion estimation and parameter identification of complex mechanical systems, ranging from mechanisms to vehicles, or robot manipulators.

Trajectory Tracking of Underactuated Multibody Systems

2011 ◽  
Author(s):  
Stefan Reichl ◽  
Wolfgang Steiner
Keyword(s):  
Trajectory Tracking ◽  
Multibody Systems ◽  
Degrees Of Freedom ◽  
Inverse Dynamics ◽  
Feedforward Control ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Differential Algebraic Equations ◽  
State Variables ◽  
Algebraic Equations

This work presents three different approaches in inverse dynamics for the solution of trajectory tracking problems in underactuated multibody systems. Such systems are characterized by less control inputs than degrees of freedom. The first approach uses an extension of the equations of motion by geometric and control constraints. This results in index-five differential-algebraic equations. A projection method is used to reduce the systems index and the resulting equations are solved numerically. The second method is a flatness-based feedforward control design. Input and state variables can be parameterized by the flat outputs and their time derivatives up to a certain order. The third approach uses an optimal control algorithm which is based on the minimization of a cost functional including system outputs and desired trajectory. It has to be distinguished between direct and indirect methods. These specific methods are applied to an underactuated planar crane and a three-dimensional rotary crane.

Multibody Dynamics in Generalized Divide and Conquer Algorithm (GDCA) Scheme

2011 ◽  
Author(s):  
Mohammad Poursina ◽  
Kurt S. Anderson
Keyword(s):  
Multibody Systems ◽  
Inverse Dynamics ◽  
Original System ◽  
Parent Body ◽  
Divide And Conquer ◽  
Loop Control ◽  
Generalized Coordinates ◽  
Divide And Conquer Algorithm ◽  
Generalized Force ◽  
New Formulation

Generalized divide and conquer algorithm (GDCA) is presented in this paper. In this new formulation, generalized forces appear explicitly in handle equations in addition to the spatial forces, absolute and generalized coordinates which have already been used in the original version of DCA. To accommodate these generalized forces in handle equations, a transformation is presented in this paper which provides an equivalent spatial force as an explicit function of a given generalized force. Each generalized force is then replaced by its equivalent spatial force applied from the appropriate parent body to its child body at the connecting joint without violating the dynamics of the original system. GDCA can be widely used in multibody problems in which a part of the forcing information is provided in generalized format. Herein, the application of the GDCA in controlling multibody systems in which the known generalized forces are fedback to the system is explained. It is also demonstrated that in inverse dynamics and closed-loop control problems in which the imposed constraints are often expressed in terms of generalized coordinates, a set of unknown generalized forces must be considered in the dynamics of system. As such, using both spatial and generalized forces, GDCA can be widely used to model these complicated multibody systems if it is desired to benefit from the computational advantages of the DCA.

Dynamics of Serial Multibody Systems Using the Decoupled Natural Orthogonal Complement Matrices

1999 ◽  
Vol 66 (4) ◽  
pp. 986-996 ◽  
Author(s):  
S. K. Saha
Keyword(s):  
Multibody Systems ◽  
Degrees Of Freedom ◽  
Inverse Dynamics ◽  
Equations Of Motion ◽  
Kinematic Chain ◽  
Rigid Bodies ◽  
Dynamic Equations ◽  
Orthogonal Complement ◽  
Forward Dynamics ◽  
Velocity Constraints

Constrained dynamic equations of motion of serial multibody systems consisting of rigid bodies in a serial kinematic chain are derived in this paper. First, the Newton-Euler equations of motion of the decoupled rigid bodies of the system at hand are written. Then, with the aid of the decoupled natural orthogonal complement (DeNOC) matrices associated with the velocity constraints of the connecting bodies, the Euler-Lagrange independent equations of motion are derived. The De NOC is essentially the decoupled form of the natural orthogonal complement (NOC) matrix, introduced elsewhere. Whereas the use of the latter provides recursive order n—n being the degrees-of-freedom of the system at hand—inverse dynamics and order n3 forward dynamics algorithms, respectively, the former leads to recursive order n algorithms for both the cases. The order n algorithms are desirable not only for their computational efficiency but also for their numerical stability, particularly, in forward dynamics and simulation, where the system’s accelerations are solved from the dynamic equations of motion and subsequently integrated numerically. The algorithms are illustrated with a three-link three-degrees-of-freedom planar manipulator and a six-degrees-of-freedom Stanford arm.

scholarly journals Variational Message Passing and Local Constraint Manipulation in Factor Graphs

Entropy ◽  
2021 ◽  
Vol 23 (7) ◽  
pp. 807
Author(s):  
İsmail Şenöz ◽  
Thijs van de Laar ◽  
Dmitry Bagaev ◽  
Bert de de Vries
Keyword(s):  
Free Energy ◽  
Latent Variables ◽  
Message Passing ◽  
Factor Graph ◽  
Estimation Accuracy ◽  
Attractive Alternative ◽  
Factor Graphs ◽  
Data Set ◽  
Bethe Free Energy ◽  
Model Evidence

Accurate evaluation of Bayesian model evidence for a given data set is a fundamental problem in model development. Since evidence evaluations are usually intractable, in practice variational free energy (VFE) minimization provides an attractive alternative, as the VFE is an upper bound on negative model log-evidence (NLE). In order to improve tractability of the VFE, it is common to manipulate the constraints in the search space for the posterior distribution of the latent variables. Unfortunately, constraint manipulation may also lead to a less accurate estimate of the NLE. Thus, constraint manipulation implies an engineering trade-off between tractability and accuracy of model evidence estimation. In this paper, we develop a unifying account of constraint manipulation for variational inference in models that can be represented by a (Forney-style) factor graph, for which we identify the Bethe Free Energy as an approximation to the VFE. We derive well-known message passing algorithms from first principles, as the result of minimizing the constrained Bethe Free Energy (BFE). The proposed method supports evaluation of the BFE in factor graphs for model scoring and development of new message passing-based inference algorithms that potentially improve evidence estimation accuracy.

Inverse Dynamics of Constrained Multibody Systems

1990 ◽  
Vol 57 (3) ◽  
pp. 750-757 ◽  
Author(s):  
J. T. Wang
Keyword(s):  
Multibody Systems ◽  
Inverse Dynamics ◽  
Multibody System ◽  
Coefficient Matrix ◽  
Force Term ◽  
Constraint Forces ◽  
Kinematic Constraints ◽  
Constrained Multibody Systems ◽  
Orthogonal Complement Matrix ◽  
Partial Velocity

A method for analyzing constrained multibody systems is presented. The method is applicable to a class of problems in which the multibody system is subjected to both force and kinematic constraints. This class of problems cannot be solved by using the classical methods. The method is based upon the concept of partial velocity and generalized forces of Kane’s method to permit the choice of constraint forces for fulfilling both kinematic and force constraints. Thus, the constraint forces or moments at convenient points or bodies may be specified in any desired form. For many applications, the method also allows analysts to choose a constant coefficient matrix for the undetermined force term to greatly reduce the burden of repeatedly computing its orthogonal complement matrix in solving the differential algebraic dynamic equations. Two examples illustrating the concepts are presented.

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