Differential-Geometric Aspects of Constrained System Dynamics

Kołodziejczyk

2010

Multibody Syst Dyn

Self Cite

Cranes are underactuated systems with less control inputs than degrees of freedom. Dynamics and control of such systems is a challenging task, and the existence of solution to the inverse dynamics simulation problem in which an r-degree-of-freedom system with m actuators, m < r, is subject to m specified motion task (servo-constraints) is conditioned upon the system is differentially flat (all the system states and control inputs can be algebraically expressed in terms of the outputs and their time derivatives up to a certain order). The outputs are often designed as specified in time load coordinates to model a rest-to-rest maneuver along a trajectory in the working space, from the initial load position to its desired destination. The flatness-based methodology results then in the required control inputs determined in terms of the fourth time derivatives of the imposed outputs, and the derivations are featured by substantial complexity. The DAE formulation motivated in this contribution offers a more convenient approach to the prediction of dynamics and control of cranes executing prescribed load motions, and only the second time derivatives of the specified outputs are involved. While most of the inverse simulation formulations, both flatness-based and DAE ones, are performed using independent state variables, the use of dependent coordinates and velocities may lead to substantial modeling simplifications and gains in computational efficiency. An improved DAE formulation of this type is presented in this paper.

Section: Governing Equationsmentioning

confidence: 99%

Section: Governing Equationsmentioning

confidence: 99%

Improved DAE formulation for inverse dynamics simulation of cranes

Kołodziejczyk

2010

Multibody Syst Dyn

Self Cite

“…(9) represents the servo-constraint. As noticed by Blajer (1997a); Kolodziejczyk (2004, 2007) the servo-constraint problem Eqs. (8)- (9) is mathematically equivalent to Eqs.…”

Section: Servo-constraints In Multibody Systemsmentioning

confidence: 91%

Analysis of servo-constraint problems for underactuated multibody systems

Seifried

2013

Mech. Sci.

Abstract. Underactuated multibody systems have fewer control inputs than degrees of freedom. In trajectory tracking control of such systems an accurate and efficient feedforward control is often necessary. For multibody systems feedforward control by model inversion can be designed using servo-constraints. So far servo-constraints have been mostly applied to differentially flat underactuated mechanical systems. Differentially flat systems can be inverted purely by algebraic manipulations and using a finite number of differentiations of the desired output trajectory. However, such algebraic solutions are often hard to find and therefore the servo-constraint approach provides an efficient and practical solution method. Recently first results on servo-constraint problems of non-flat underactuated multibody systems have been reported. Hereby additional dynamics arise, so-called internal dynamics, yielding a dynamical system as inverse model. In this paper the servo-constraint problem is analyzed for both, differentially flat and non-flat systems. Different arising important phenomena are demonstrated using two illustrative examples. Also strategies for the numerical solution of servo-constraint problems are discussed.

“…In short, while the traditional joint coordinate scheme [32,33] uses the relationships between the (dependent) absolute coordinates p and the (independent) joint coordinates q, which are p = g(q) + η(t) for the case at hand and express the joint constraint equations given explicitly [32], the augmented form of the relationships is…”

Section: Dynamic Equations In Joint Coordinatesmentioning

confidence: 99%

Influence of selected modeling and computational issues on muscle force estimates

Czaplicki²,

Dziewiecki

et al. 2010

Multibody Syst Dyn

Self Cite

Knowledge of muscle forces and joint reaction forces during human movement can provide insight into the underlying control and tissue loading. Since direct measurement of the internal loads is generally not feasible, non-invasive methods based on musculoskeletal modeling and computer simulations have been extensively developed. By applying observed motion data to the musculoskeletal models, inverse dynamic analysis allow to determine the resultant joint torques, transformed then into estimates of individual muscle forces by means of different optimization procedures. Assessment of the joint reaction forces and other internal loads is further possible. Comparison of the muscle force estimates obtained for different modeling assumptions and parameters in the model can be valuable for the improvement of validity of the model-based estimations. The present study is another contribution to this field. Using a sagittal plane model of an upper limb with a weight carried in hand, and applying the data of recorded flexion and extension movement of the upper limb, the resultant muscular forces are predicted using different modeling assumptions and simulation tools. This study relates to different coordinates (joint and natural coordinates) used to built the mathematical model, muscle path modeling, muscle decomposition (change in number of the modeled muscles), and different optimization methods used to share the joint torques into individual muscles.