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Optimal Control of Flexible Multibody Systems using the Adjoint Method
| Content Provider | Semantic Scholar |
|---|---|
| Author | Nachbagauer, Karin Lauß, Thomas Oberpeilsteiner, Stefan |
| Copyright Year | 2017 |
| Abstract | Optimal control problems of multibody systems are often defined for mechanical systems, as e.g. industrial robots, in order to follow a specific trajectory or to increase the overall performance. Modern robot design will include promising lightweight techniques in order reduce mass and energy consumptions in production lines. Therefore, optimal control problems have to be defined for flexible multibody systems in which the flexible components have to be able to describe large deformations during dynamic analysis. In the present study, the absolute nodal coordinate formulation (ANCF), which has been developed particularly for solving large deformation problems in multibody dynamics [1], is utilized. In contrast to classical nonlinear finite elements in literature, the ANCF does not use rotational degrees of freedom and therefore does not necessarily suffer from singularities emerging from angular parameterizations. The benefits of the ANCF are as well the isoparametric approach and the existence of a consistent displacement field. Moreover, the most essential advantage of the ANCF is the fact that the mass matrix remains constant with respect to the generalized coordinates during the entire dynamic simulation. The equations of motion of the constrained flexible multibody system can be expressed as a system of differential algebraic equations including the nonlinear elastic force terms in the ANCF. A beam finite element described in the ANCF with bending, axial and shear deformation properties is used which accounts for cross section deformation in order to avoid locking. This proposed element is available and tested extensively in literature, see e.g. [2, 3]. In general, the optimal control problem could be defined as an optimization task described by minimizing a cost function. The gradient of this cost function can be computed very efficiently also in complex multibody systems when incorporating the adjoint method, see e.g. [4] for a detailed derivation of the adjoint equations deduced from the system of differential algebraic equations in index 3 notation. Due to the fact that the ANCF includes a constant mass matrix with vanishing derivative, the equations reduce to a simpler form, also pointed out in [5]. There, as well a gradient-based optimization approach using adjoint equations for flexible ANCF bodies has been presented [5], with special focus on sensitivity analysis. A first and second order adjoint sensitivity analysis in the framework of the ANCF is as well studied in [6] and [7], respectively. In [6], the effect of Young’s modulus on elastic deformation of a planar single pendulum is presented. In [7] the dramatically decrease in computational costs for a large number of design variables is shown when comparing the adjoint method and the direct differentiation method. The direct differentiation method and the adjoint method for sensitivity analysis is as well compared in [8]. Moreover, sensitivity analysis for multibody systems formulated on a Lie group using the direct differentiation and the adjoint method can be found in [9]. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://imsd2018.tecnico.ulisboa.pt/Web_Abstracts_IMSD2018/pdf/WEB_ABSTRACTS/IMSD2018_paper_33.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
