Pub Date : 2023-10-06DOI: 10.1007/s11044-023-09934-4
Matthias Schubert, Rodrigo T. Sato Martín de Almagro, Karin Nachbagauer, Sina Ober-Blöbaum, Sigrid Leyendecker
Abstract Direct methods for the simulation of optimal control problems apply a specific discretization to the dynamics of the problem, and the discrete adjoint method is suitable to calculate corresponding conditions to approximate an optimal solution. While the benefits of structure preserving or geometric methods have been known for decades, their exploration in the context of optimal control problems is a relatively recent field of research. In this work, the discrete adjoint method is derived for variational integrators yielding structure preserving approximations of the dynamics firstly in the ODE case and secondly for the case in which the dynamics is subject to holonomic constraints. The convergence rates are illustrated by numerical examples. Thirdly, the discrete adjoint method is applied to geometrically exact beam dynamics, represented by a holonomically constrained PDE.
{"title":"Discrete adjoint method for variational integration of constrained ODEs and its application to optimal control of geometrically exact beam dynamics","authors":"Matthias Schubert, Rodrigo T. Sato Martín de Almagro, Karin Nachbagauer, Sina Ober-Blöbaum, Sigrid Leyendecker","doi":"10.1007/s11044-023-09934-4","DOIUrl":"https://doi.org/10.1007/s11044-023-09934-4","url":null,"abstract":"Abstract Direct methods for the simulation of optimal control problems apply a specific discretization to the dynamics of the problem, and the discrete adjoint method is suitable to calculate corresponding conditions to approximate an optimal solution. While the benefits of structure preserving or geometric methods have been known for decades, their exploration in the context of optimal control problems is a relatively recent field of research. In this work, the discrete adjoint method is derived for variational integrators yielding structure preserving approximations of the dynamics firstly in the ODE case and secondly for the case in which the dynamics is subject to holonomic constraints. The convergence rates are illustrated by numerical examples. Thirdly, the discrete adjoint method is applied to geometrically exact beam dynamics, represented by a holonomically constrained PDE.","PeriodicalId":49792,"journal":{"name":"Multibody System Dynamics","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135350416","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-06DOI: 10.1007/s11044-023-09935-3
Suo Zhang, Yunkai Gao, James Yang
{"title":"Dynamic modeling and analysis of vehicle scissor door mechanism with mixed clearance based on a hybrid contact force model","authors":"Suo Zhang, Yunkai Gao, James Yang","doi":"10.1007/s11044-023-09935-3","DOIUrl":"https://doi.org/10.1007/s11044-023-09935-3","url":null,"abstract":"","PeriodicalId":49792,"journal":{"name":"Multibody System Dynamics","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135350420","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-06DOI: 10.1007/s11044-023-09939-z
Prashant G. Iyer
{"title":"Modelling of a 12-DoF Parachute–Riser–Payload system dynamics using Kane’s method","authors":"Prashant G. Iyer","doi":"10.1007/s11044-023-09939-z","DOIUrl":"https://doi.org/10.1007/s11044-023-09939-z","url":null,"abstract":"","PeriodicalId":49792,"journal":{"name":"Multibody System Dynamics","volume":"53 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135351056","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-06DOI: 10.1007/s11044-023-09938-0
Urbano Lugrís, Manuel Pérez-Soto, Florian Michaud, Javier Cuadrado
Abstract Optical motion capture is an essential tool for the study and analysis of human movement. Currently, most manufacturers of motion-capture systems provide software applications for reconstructing the movement in real time, thus allowing for on-the-fly visualization. The captured kinematics can be later used as input data for a further musculoskeletal analysis. However, in advanced biofeedback applications, the results of said analysis, such as joint torques, ground-reaction forces, muscle efforts, and joint-reaction forces, are also required in real time. In this work, an extended Kalman filter (EKF) previously developed by the authors for real-time, whole-body motion capture and reconstruction is augmented with inverse dynamics and muscle-efforts optimization, enabling the calculation and visualization of the latter, along with joint-reaction forces, while capturing the motion. A modified version of the existing motion-capture algorithm provides the positions, velocities, and accelerations at every time step. Then, the joint torques are calculated by solving the inverse-dynamics problem, using force-plate measurements along with previously estimated body-segment parameters. Once the joint torques are obtained, an optimization problem is solved, in order to obtain the muscle forces that provide said torques while minimizing an objective function. This is achieved by a very efficient quadratic programming algorithm, thoroughly tuned for this specific problem. With this procedure, it is possible to capture and label the optical markers, reconstruct the motion of the model, solve the inverse dynamics, and estimate the individual muscle forces, all while providing real-time visualization of the results.
{"title":"Human motion capture, reconstruction, and musculoskeletal analysis in real time","authors":"Urbano Lugrís, Manuel Pérez-Soto, Florian Michaud, Javier Cuadrado","doi":"10.1007/s11044-023-09938-0","DOIUrl":"https://doi.org/10.1007/s11044-023-09938-0","url":null,"abstract":"Abstract Optical motion capture is an essential tool for the study and analysis of human movement. Currently, most manufacturers of motion-capture systems provide software applications for reconstructing the movement in real time, thus allowing for on-the-fly visualization. The captured kinematics can be later used as input data for a further musculoskeletal analysis. However, in advanced biofeedback applications, the results of said analysis, such as joint torques, ground-reaction forces, muscle efforts, and joint-reaction forces, are also required in real time. In this work, an extended Kalman filter (EKF) previously developed by the authors for real-time, whole-body motion capture and reconstruction is augmented with inverse dynamics and muscle-efforts optimization, enabling the calculation and visualization of the latter, along with joint-reaction forces, while capturing the motion. A modified version of the existing motion-capture algorithm provides the positions, velocities, and accelerations at every time step. Then, the joint torques are calculated by solving the inverse-dynamics problem, using force-plate measurements along with previously estimated body-segment parameters. Once the joint torques are obtained, an optimization problem is solved, in order to obtain the muscle forces that provide said torques while minimizing an objective function. This is achieved by a very efficient quadratic programming algorithm, thoroughly tuned for this specific problem. With this procedure, it is possible to capture and label the optical markers, reconstruct the motion of the model, solve the inverse dynamics, and estimate the individual muscle forces, all while providing real-time visualization of the results.","PeriodicalId":49792,"journal":{"name":"Multibody System Dynamics","volume":"166 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135346761","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-06DOI: 10.1007/s11044-023-09932-6
L. Bartali, E. Grabovic, M. Gabiccini
Abstract Minimum-lap-time planning (MLTP) problems, which entail finding optimal trajectories for race cars on racetracks, have received significant attention in the recent literature. They are commonly addressed as optimal control problems (OCPs) and are numerically discretized using direct collocation methods. Subsequently, they are solved as nonlinear programs (NLPs). The conventional approach to solving MLTP problems is serial , whereby the resulting NLP is solved all at once. However, for problems characterized by a large number of variables, distributed optimization algorithms, such as the alternating direction method of multipliers (ADMM), may represent a viable option, especially when multicore CPU architectures are available. This study presents a consensus-based ADMM approach tailored to solving MLTP problems through a distributed optimization algorithm. The algorithm partitions the problem into smaller subproblems based on different sectors of a track, distributing them among multiple processors. ADMM is then used to ensure consensus among the distributed computational processes. In particular, here the term “consensus” denotes the requirement for each subproblem to achieve mutual agreement across the junction areas. The paper also outlines specific strategies leveraging domain knowledge to improve the convergence of the distributed algorithm. The ADMM approach is validated against the serial approach, and numerical results are presented for both single-lap and multilap scenarios. In both cases, the ADMM approach proves superior for problem dimensions of 70k+ variables compared to serial methods. In planning scenarios with complex vehicle models on long track horizons, i.e., for problems with 1M+ variables, the efficiency gain of the ADMM approach is substantial, and it becomes the only viable option to maintain computational times within acceptable limits.
{"title":"A consensus-based alternating direction method of multipliers approach to parallelize large-scale minimum-lap-time problems","authors":"L. Bartali, E. Grabovic, M. Gabiccini","doi":"10.1007/s11044-023-09932-6","DOIUrl":"https://doi.org/10.1007/s11044-023-09932-6","url":null,"abstract":"Abstract Minimum-lap-time planning (MLTP) problems, which entail finding optimal trajectories for race cars on racetracks, have received significant attention in the recent literature. They are commonly addressed as optimal control problems (OCPs) and are numerically discretized using direct collocation methods. Subsequently, they are solved as nonlinear programs (NLPs). The conventional approach to solving MLTP problems is serial , whereby the resulting NLP is solved all at once. However, for problems characterized by a large number of variables, distributed optimization algorithms, such as the alternating direction method of multipliers (ADMM), may represent a viable option, especially when multicore CPU architectures are available. This study presents a consensus-based ADMM approach tailored to solving MLTP problems through a distributed optimization algorithm. The algorithm partitions the problem into smaller subproblems based on different sectors of a track, distributing them among multiple processors. ADMM is then used to ensure consensus among the distributed computational processes. In particular, here the term “consensus” denotes the requirement for each subproblem to achieve mutual agreement across the junction areas. The paper also outlines specific strategies leveraging domain knowledge to improve the convergence of the distributed algorithm. The ADMM approach is validated against the serial approach, and numerical results are presented for both single-lap and multilap scenarios. In both cases, the ADMM approach proves superior for problem dimensions of 70k+ variables compared to serial methods. In planning scenarios with complex vehicle models on long track horizons, i.e., for problems with 1M+ variables, the efficiency gain of the ADMM approach is substantial, and it becomes the only viable option to maintain computational times within acceptable limits.","PeriodicalId":49792,"journal":{"name":"Multibody System Dynamics","volume":"48 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135351688","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-15DOI: 10.1007/s11044-023-09931-7
Ling Tao, Zhiqiang Feng
{"title":"Cushioning performance analysis of multilayered rubber materials with nonuniform friction coefficients of corrugated contact surface under the bipotential framework","authors":"Ling Tao, Zhiqiang Feng","doi":"10.1007/s11044-023-09931-7","DOIUrl":"https://doi.org/10.1007/s11044-023-09931-7","url":null,"abstract":"","PeriodicalId":49792,"journal":{"name":"Multibody System Dynamics","volume":"139 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135438204","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-13DOI: 10.1007/s11044-023-09929-1
Kun Li, Zuqing Yu, Peng Lan, Qinglong Tian, Nianli Lu
{"title":"ALE-ANCF circular cross-section beam element and its application on the dynamic analysis of cable-driven mechanism","authors":"Kun Li, Zuqing Yu, Peng Lan, Qinglong Tian, Nianli Lu","doi":"10.1007/s11044-023-09929-1","DOIUrl":"https://doi.org/10.1007/s11044-023-09929-1","url":null,"abstract":"","PeriodicalId":49792,"journal":{"name":"Multibody System Dynamics","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135741600","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-12DOI: 10.1007/s11044-023-09930-8
Pierangelo Masarati, M Jihad Ummul Quro, Andrea Zanoni
Abstract The formulation of (possibly redundantly) constrained system dynamics using coordinate projection onto a subspace locally tangent to the constraint manifold is revisited using the QR factorization of the constraint Jacobian matrix, using column pivoting to identify a suitable subspace, possibly detect any singular configurations that may arise, and extract it. The evolution of the QR factorization is integrated along with that of the constraint Jacobian matrix as the solution evolves, generalizing to redundant constraints a recently proposed true continuation algorithm that tracks the evolution of the subspace of independent coordinates. The resulting subspace does not visibly affect the quality of the solution, as it is merely a recombination of that resulting from the blind application of the QR factorization but avoids the artificial algorithmic irregularities or discontinuities in the generalized velocities that could otherwise result from arbitrary reparameterizations of the coordinate set, and identifies and discriminates any further possible motions that arise at singular configurations. The characteristics of the proposed subspace evolution approach are exemplified by solving simple problems with incremental levels of redundancy and singularity orders.
{"title":"Projection continuation for minimal coordinate set formulation and singularity detection of redundantly constrained system dynamics","authors":"Pierangelo Masarati, M Jihad Ummul Quro, Andrea Zanoni","doi":"10.1007/s11044-023-09930-8","DOIUrl":"https://doi.org/10.1007/s11044-023-09930-8","url":null,"abstract":"Abstract The formulation of (possibly redundantly) constrained system dynamics using coordinate projection onto a subspace locally tangent to the constraint manifold is revisited using the QR factorization of the constraint Jacobian matrix, using column pivoting to identify a suitable subspace, possibly detect any singular configurations that may arise, and extract it. The evolution of the QR factorization is integrated along with that of the constraint Jacobian matrix as the solution evolves, generalizing to redundant constraints a recently proposed true continuation algorithm that tracks the evolution of the subspace of independent coordinates. The resulting subspace does not visibly affect the quality of the solution, as it is merely a recombination of that resulting from the blind application of the QR factorization but avoids the artificial algorithmic irregularities or discontinuities in the generalized velocities that could otherwise result from arbitrary reparameterizations of the coordinate set, and identifies and discriminates any further possible motions that arise at singular configurations. The characteristics of the proposed subspace evolution approach are exemplified by solving simple problems with incremental levels of redundancy and singularity orders.","PeriodicalId":49792,"journal":{"name":"Multibody System Dynamics","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135825554","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-08-24DOI: 10.1007/s11044-023-09928-2
Álvaro López Varela, Daniel Dopico Dopico, Alberto Luaces Fernández
Abstract Sensitivity analysis represents a powerful tool for the optimization of multibody system dynamics. The performance of a gradient-based optimization algorithm is strongly tied to the dynamic and the sensitivity formulations considered. The accuracy and efficiency are critical to any optimization problem, thus they are key factors in the selection of the dynamic and sensitivity analysis approaches used to compute an objective function gradient. Semi-recursive methods usually outperform global methods in terms of computational time, even though they involve sometimes demanding recursive procedures. Semi-recursive methods are well suited to be combined with different constraints enforcement schemes as the augmented Lagrangian index-3 formulation with velocity and acceleration projections (ALI3-P), taking advantage of the robustness, accurate fulfillment of constraint equations and the low computational burden. The sensitivity analysis of the semi-recursive ALI3-P formulation is studied in this document by means of the direct differentiation method. As a result, a semi-recursive ALI3-P sensitivity formulation is developed for an arbitrary reference point selection, and then two particular versions are unfolded and implemented in the general purpose multibody library MBSLIM, using as reference point the center of mass (RTdyn0) or the global origin of coordinates (RTdyn1). Besides, the detailed derivatives of the recursive terms are provided, which will be useful not only for the direct sensitivity formulation presented herein, but also for other sensitivity formulations relying on the same recursive expressions. The implementation has been tested in two numerical experiments, a five-bar benchmark problem and a buggy vehicle.
{"title":"Augmented Lagrangian index-3 semi-recursive formulations with projections","authors":"Álvaro López Varela, Daniel Dopico Dopico, Alberto Luaces Fernández","doi":"10.1007/s11044-023-09928-2","DOIUrl":"https://doi.org/10.1007/s11044-023-09928-2","url":null,"abstract":"Abstract Sensitivity analysis represents a powerful tool for the optimization of multibody system dynamics. The performance of a gradient-based optimization algorithm is strongly tied to the dynamic and the sensitivity formulations considered. The accuracy and efficiency are critical to any optimization problem, thus they are key factors in the selection of the dynamic and sensitivity analysis approaches used to compute an objective function gradient. Semi-recursive methods usually outperform global methods in terms of computational time, even though they involve sometimes demanding recursive procedures. Semi-recursive methods are well suited to be combined with different constraints enforcement schemes as the augmented Lagrangian index-3 formulation with velocity and acceleration projections (ALI3-P), taking advantage of the robustness, accurate fulfillment of constraint equations and the low computational burden. The sensitivity analysis of the semi-recursive ALI3-P formulation is studied in this document by means of the direct differentiation method. As a result, a semi-recursive ALI3-P sensitivity formulation is developed for an arbitrary reference point selection, and then two particular versions are unfolded and implemented in the general purpose multibody library MBSLIM, using as reference point the center of mass (RTdyn0) or the global origin of coordinates (RTdyn1). Besides, the detailed derivatives of the recursive terms are provided, which will be useful not only for the direct sensitivity formulation presented herein, but also for other sensitivity formulations relying on the same recursive expressions. The implementation has been tested in two numerical experiments, a five-bar benchmark problem and a buggy vehicle.","PeriodicalId":49792,"journal":{"name":"Multibody System Dynamics","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135420527","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-24DOI: 10.1007/s11044-023-09927-3
J. Ambrósio, A. Mikkola
{"title":"Preface for the MUBO Special Issue on its 25th Anniversary","authors":"J. Ambrósio, A. Mikkola","doi":"10.1007/s11044-023-09927-3","DOIUrl":"https://doi.org/10.1007/s11044-023-09927-3","url":null,"abstract":"","PeriodicalId":49792,"journal":{"name":"Multibody System Dynamics","volume":"58 1","pages":"227 - 229"},"PeriodicalIF":3.4,"publicationDate":"2023-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47991737","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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