A Geometric Approach to Solving Problems of Control Constraints: Theory and a DAE Framework

Blajer, Wojciech; Kołodziejczyk, Krzysztof

doi:10.1023/b:mubo.0000040800.40045.51

Cited by 115 publications

(155 citation statements)

References 26 publications

Supporting

Mentioning

154

Contrasting

Order By: Relevance

“…The flatness-based methodology results in the required control inputs determined in terms of the fourth time derivatives of the imposed outputs, and the related derivations are featured by substantial complexity. The DAE formulation proposed in [5], and motivated in this contribution as well, offers an alternative and more convenient approach to the prediction of dynamics and control of cranes executing prescribed payload motions, where only the second time derivatives of the specified outputs are involved, and the solution consists in numerical estimation of crane's states and control inputs in the specified motion.…”

mentioning

confidence: 99%

Improved DAE formulation for inverse dynamics simulation of cranes

Blajer

Kołodziejczyk

2010

Multibody Syst Dyn

Self Cite

View full text Add to dashboard 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.

show abstract

mentioning

confidence: 99%

Improved DAE formulation for inverse dynamics simulation of cranes

Blajer

Kołodziejczyk

2010

Multibody Syst Dyn

Self Cite

View full text Add to dashboard Cite

show abstract

“…Recall that the equations of motion (1a)-(1c) form a DAE of index 5. As in [5,Ex. 3], the following parameters were used within the computations:…”

Section: Two-car Examplementioning

confidence: 99%

“…The servo-constraint problem of this section was originally formulated in terms of minimal coordinates in [5] and was recast in redundant coordinates in [10]; see Fig. 5.…”

Section: Overhead Cranementioning

confidence: 99%

“…In this paper, we consider a two-car example [8,Sect. II], its generalization to n connected cars, and an overhead crane example [5,Ex. 4].…”

mentioning

confidence: 99%

“…This constraint makes the model equations a system of differential-algebraic equations (DAE) even though the dynamics of the system may be given in the form of an ODE. Even more, the resulting DAE is typically of high index so that for its application in simulations, we need to employ a suitable index reduction [1,5,7]. Apart from the numerical difficulties that come with high index DAEs, an immediate drawback of the DAE approach is that a solution to the problem can only exist if the target trajectory is sufficiently smooth.…”

mentioning

confidence: 99%

See 2 more Smart Citations

Simulation of multibody systems with servo constraints through optimal control

Altmann

Heiland

2016

Multibody Syst Dyn

View full text Add to dashboard Cite

We consider mechanical systems where the dynamics are partially constrained to prescribed trajectories. An example for such a system is a building crane with a load and the requirement that the load moves on a certain path.Enforcing this condition directly in form of a servo constraint leads to differentialalgebraic equations (DAEs) of arbitrarily high index. Typically, the model equations are of index 5, which already poses high regularity conditions. If we relax the servo constraints and consider the system from an optimal control point of view, the strong regularity conditions vanish, and the solution can be obtained by standard techniques.By means of the well-known n-car example and an overhead crane, the theoretical and expected numerical difficulties of the direct DAE and the alternative modeling approach are illustrated. We show how the formulation of the problem in an optimal control context works and address the solvability of the optimal control system. We discuss that the problematic DAE behavior is still inherent in the optimal control system and show how its evidences depend on the regularization parameters of the optimization.

show abstract

Application of stable inversion to flexible manipulators modeled by the absolute nodal coordinate formulation

Drücker

Seifried

2023

GAMM-Mitteilungen

View full text Add to dashboard Cite

Compared to conventional robots, flexible manipulators offer many advantages, such as faster end‐effector velocities and less energy consumption. However, their flexible structure can lead to undesired oscillations. Therefore, the applied control strategy should account for these elasticities. A feedforward controller based on an inverse model of the system is an efficient way to improve the performance. However, unstable internal dynamics arise for many common flexible robots and stable inversion must be applied. In this contribution, an approximation of the original stable inversion approach is proposed. The approximation simplifies the problem setup, since the internal dynamics do not need to be derived explicitly for the definition of the boundary conditions. From a practical point of view, this makes the method applicable to more complex systems with many unactuated degrees of freedom. Flexible manipulators modeled by the absolute nodal coordinate formulation (ANCF) are considered as an application example.

show abstract

A Geometric Approach to Solving Problems of Control Constraints: Theory and a DAE Framework

Cited by 115 publications

References 26 publications

Improved DAE formulation for inverse dynamics simulation of cranes

Improved DAE formulation for inverse dynamics simulation of cranes

Simulation of multibody systems with servo constraints through optimal control

Application of stable inversion to flexible manipulators modeled by the absolute nodal coordinate formulation

Contact Info

Product

Resources

About