Abstract This study deals with an application of constrained formulation to a nonlinear sloshing problem based on the Arbitrary Lagrangian-Eulerian finite element method (ALE). The ALE method incorporates a discretized form of equations of motion with mesh updating algorithms in order to prevent a problem of mesh distortion. This paper focuses on an analytical aspect of such treatments as constrained systems in the formulation of the ALE method. Since the mesh updating algorithms give algebraic relations for nodal coordinates, this study treats these relations as constraints. Then, we introduce formulation for constrained systems based on the method of Lagrange multipliers. As a result of this formulation, equations of motion are given by differential algebraic equations (DAEs) consisting of differential equations for time evolution of physical quantities and algebraic equations (constraints). The present method can be classified into a kind of augmented formulation. In particular, the present approach is motivated by the inherent simplicity of the DAEs. Moreover, we present a matrix size reduction technique used in the Newton-Raphson method in order to remove a part of the redundant degrees of freedom in the iterative procedures, because the resulting set of DAEs involves a larger number of unknowns than the minimal number of degrees of freedom due to the introduction of the constrained formulation. In addition, this study presents a method to introduce damping effects defined in the modal space into the FEM models. The proposed approach is validated by comparisons with experimental data in the time domain analysis.
{"title":"Application of the Constrained Formulation to the Nonlinear Sloshing Problem Based On the ALE Method","authors":"Kensuke Hara","doi":"10.1115/1.4063722","DOIUrl":"https://doi.org/10.1115/1.4063722","url":null,"abstract":"Abstract This study deals with an application of constrained formulation to a nonlinear sloshing problem based on the Arbitrary Lagrangian-Eulerian finite element method (ALE). The ALE method incorporates a discretized form of equations of motion with mesh updating algorithms in order to prevent a problem of mesh distortion. This paper focuses on an analytical aspect of such treatments as constrained systems in the formulation of the ALE method. Since the mesh updating algorithms give algebraic relations for nodal coordinates, this study treats these relations as constraints. Then, we introduce formulation for constrained systems based on the method of Lagrange multipliers. As a result of this formulation, equations of motion are given by differential algebraic equations (DAEs) consisting of differential equations for time evolution of physical quantities and algebraic equations (constraints). The present method can be classified into a kind of augmented formulation. In particular, the present approach is motivated by the inherent simplicity of the DAEs. Moreover, we present a matrix size reduction technique used in the Newton-Raphson method in order to remove a part of the redundant degrees of freedom in the iterative procedures, because the resulting set of DAEs involves a larger number of unknowns than the minimal number of degrees of freedom due to the introduction of the constrained formulation. In addition, this study presents a method to introduce damping effects defined in the modal space into the FEM models. The proposed approach is validated by comparisons with experimental data in the time domain analysis.","PeriodicalId":54858,"journal":{"name":"Journal of Computational and Nonlinear Dynamics","volume":"250 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136352590","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract The intrinsic formulation for geometrically-nonlinear beam dynamics provides a compact and versatile description of slender beam-like structures. With nonlinearities limited to second-order couplings in the formulation, it has been an attractive choice in formulating nonlinear reduced-order models for dynamic analysis and control design in aeroelasticity problems involving large displacements and rotations. Owing to its rotation-free formalism, the intrinsic formulation has not been formulated to accommodate multibody constraints, limiting its use against multibody structures with kinematic constraints. This work aims to address such weakness as we present developments in introducing multibody constraints into the full and reduced-order intrinsic equations while still preserving the beneficial traits of the method. We describe the resolution of displacement-level constraints using index-1 approach and adaptation of constraint stabilisation strategies to the intrinsic formulation using state projection. The numerical behaviour of the full- and reduced-order implementations are assessed using test cases with large static and dynamic deformations with time-domain simulations to demonstrate validity of the approach.
{"title":"Multibody Constraints in the Geometrically-Nonlinear Intrinsic Formulation","authors":"Yinan Wang, Keisuke Otsuka","doi":"10.1115/1.4063724","DOIUrl":"https://doi.org/10.1115/1.4063724","url":null,"abstract":"Abstract The intrinsic formulation for geometrically-nonlinear beam dynamics provides a compact and versatile description of slender beam-like structures. With nonlinearities limited to second-order couplings in the formulation, it has been an attractive choice in formulating nonlinear reduced-order models for dynamic analysis and control design in aeroelasticity problems involving large displacements and rotations. Owing to its rotation-free formalism, the intrinsic formulation has not been formulated to accommodate multibody constraints, limiting its use against multibody structures with kinematic constraints. This work aims to address such weakness as we present developments in introducing multibody constraints into the full and reduced-order intrinsic equations while still preserving the beneficial traits of the method. We describe the resolution of displacement-level constraints using index-1 approach and adaptation of constraint stabilisation strategies to the intrinsic formulation using state projection. The numerical behaviour of the full- and reduced-order implementations are assessed using test cases with large static and dynamic deformations with time-domain simulations to demonstrate validity of the approach.","PeriodicalId":54858,"journal":{"name":"Journal of Computational and Nonlinear Dynamics","volume":"109 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136294331","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract A novel numerical scheme for the time-fractional Kuramoto-Sivashinsky equation is presented in this article. A modification of the Atangana-Baleanu Caputo derivative known as the modified Atangana-Baleanu Caputo operator is introduced for the time-fractional derivative. A Taylor series-based formula is used to derive a second-order accurate approximation to the modified Atangana-Baleanu Caputo derivative. A linear combination of the quintic $B$-spline basis functions is used to approximate the functions in spatial direction. Moreover, through rigorous analysis, it has been proved that the present scheme is unconditionally stable and convergent. Finally, two test problems are solved numerically to demonstrate the proposed method's superconvergence and accuracy.
{"title":"Modified Atangana-Baleanu Caputo Operator for Time-Fractional Kuramoto-Sivashinsky Equation via Quintic B-Splines","authors":"Komal Deswal, Renu Choudhary, Devendra Kumar","doi":"10.1115/1.4063554","DOIUrl":"https://doi.org/10.1115/1.4063554","url":null,"abstract":"Abstract A novel numerical scheme for the time-fractional Kuramoto-Sivashinsky equation is presented in this article. A modification of the Atangana-Baleanu Caputo derivative known as the modified Atangana-Baleanu Caputo operator is introduced for the time-fractional derivative. A Taylor series-based formula is used to derive a second-order accurate approximation to the modified Atangana-Baleanu Caputo derivative. A linear combination of the quintic $B$-spline basis functions is used to approximate the functions in spatial direction. Moreover, through rigorous analysis, it has been proved that the present scheme is unconditionally stable and convergent. Finally, two test problems are solved numerically to demonstrate the proposed method's superconvergence and accuracy.","PeriodicalId":54858,"journal":{"name":"Journal of Computational and Nonlinear Dynamics","volume":"54 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135193336","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract As a semi-analytical approach, the incremental harmonic balance (IHB) method is widely implemented for solving steady-state (including both periodic and quasi-periodic) responses through an iteration process. The iteration is carried out through a Jacobian matrix (JM) and a residual vector, both updated in each iteration. Though the JM is known to be singular at certain bifurcation points, the singularity is still an open question and could play a pivotal role in real applications. In this study, we define and calculate an expanded JM (EJM) by applying an expanded solution expression in the IHB iteration. The singularity of the EJM at several different bifurcation points is proved in a general manner, according to the bifurcation theory for equilibria in nonlinear dynamical systems. Given the possible bifurcation type, furthermore, the singularity is applied to locate the corresponding bifurcation point directly and precisely. Considered are the cases of the period-doubling, symmetry breaking, and Neimark-Sacker bifurcations of periodic and/or quasi-periodic responses.
{"title":"The Singularity of Expanded Jacobian Matrix in IHB Method Directly Locates Bifurcation Points of Steady State Responses","authors":"Y.M. Chen, J.K. Liu","doi":"10.1115/1.4063400","DOIUrl":"https://doi.org/10.1115/1.4063400","url":null,"abstract":"Abstract As a semi-analytical approach, the incremental harmonic balance (IHB) method is widely implemented for solving steady-state (including both periodic and quasi-periodic) responses through an iteration process. The iteration is carried out through a Jacobian matrix (JM) and a residual vector, both updated in each iteration. Though the JM is known to be singular at certain bifurcation points, the singularity is still an open question and could play a pivotal role in real applications. In this study, we define and calculate an expanded JM (EJM) by applying an expanded solution expression in the IHB iteration. The singularity of the EJM at several different bifurcation points is proved in a general manner, according to the bifurcation theory for equilibria in nonlinear dynamical systems. Given the possible bifurcation type, furthermore, the singularity is applied to locate the corresponding bifurcation point directly and precisely. Considered are the cases of the period-doubling, symmetry breaking, and Neimark-Sacker bifurcations of periodic and/or quasi-periodic responses.","PeriodicalId":54858,"journal":{"name":"Journal of Computational and Nonlinear Dynamics","volume":"48 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135342818","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Discussion on the paper “A Numerical Scheme for Fractional Mixed Convection Flow Over Flat and Oscillatory Plates, Yasir Nawaz, Muhammad Shoaib Arif, Kamaleldin Abodayeh, Journal of Computational and Nonlinear Dynamics, July 2022, Vol. 17, 071008”","authors":"A. Pantokratoras","doi":"10.1115/1.4063336","DOIUrl":"https://doi.org/10.1115/1.4063336","url":null,"abstract":"\u0000 Some serious errors exist in the above paper.","PeriodicalId":54858,"journal":{"name":"Journal of Computational and Nonlinear Dynamics","volume":"44 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78557053","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
According to traffic flow theory, traffic is affected not only by road conditions such as bottlenecks, the environment, interruptions, and so on but also by the driver's behavior. To control and manage increasingly complex traffic networks, it also becomes necessary to study the effects of driver characteristics significantly. In this research, a novel car-following model is proposed which considers both the driver's cautious and aggressive instincts for optimal and relative velocity integrals. To analyze the stability of the new model, a small perturbation method was used. Further, the modified Korteweg-de Vries equations were established with the help of a reductive perturbation method. In bifurcation analysis, we examine the existence and stability of Hopf bifurcation in various systems. This helps to gain deeper insight into the behavior of these dynamical systems and can be used to develop more efficient control strategies. Numerical simulations and theoretical analyses both show that the aspects of the enhanced model related to driver characteristics have a major effect on traffic flow stability. Additionally, the model can adeptly handle traffic congestion and quickly return to its normal state if any disruption occurs.
{"title":"Bifurcation Analysis Of Driver's Characteristics In Car-Following Model","authors":"Sunita Yadav, Poonam Redhu","doi":"10.1115/1.4063338","DOIUrl":"https://doi.org/10.1115/1.4063338","url":null,"abstract":"\u0000 According to traffic flow theory, traffic is affected not only by road conditions such as bottlenecks, the environment, interruptions, and so on but also by the driver's behavior. To control and manage increasingly complex traffic networks, it also becomes necessary to study the effects of driver characteristics significantly. In this research, a novel car-following model is proposed which considers both the driver's cautious and aggressive instincts for optimal and relative velocity integrals. To analyze the stability of the new model, a small perturbation method was used. Further, the modified Korteweg-de Vries equations were established with the help of a reductive perturbation method. In bifurcation analysis, we examine the existence and stability of Hopf bifurcation in various systems. This helps to gain deeper insight into the behavior of these dynamical systems and can be used to develop more efficient control strategies. Numerical simulations and theoretical analyses both show that the aspects of the enhanced model related to driver characteristics have a major effect on traffic flow stability. Additionally, the model can adeptly handle traffic congestion and quickly return to its normal state if any disruption occurs.","PeriodicalId":54858,"journal":{"name":"Journal of Computational and Nonlinear Dynamics","volume":"32 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80389307","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The primary aim of this research is to establish the time dependent diffusion coefficient in a one dimensional time fractional diffusion equation in Caputo sense by means of newly defined Monic Laquerre wavelets (MLW) and collocation points. We first give the definition of MLW by taking Monic Laquerre polynomials into account. Later, time fractional diffusion problem is reduced into a system of ordinary fractional and algebraic equations by utilizing MLW. Residual power series method and the over-measured data are applied to this system to determine the solution and the unknown time dependent coefficient together in series form. In the end, illustrative examples are presented to show the stability and accuracy of the proposed wavelet method for the inverse problem of determining unknown time dependent coefficient in fractional diffusion problems. The reliability of the proposed algorithm for the inverse problems is supported by high degree of accuracy in given examples.
{"title":"On The Inverse Problem Of Time Dependent Coefficient In A Time Fractional Diffusion Problem By Newly Defined Monic Laquerre Wavelets","authors":"M. Bayrak, Ali Demir","doi":"10.1115/1.4063337","DOIUrl":"https://doi.org/10.1115/1.4063337","url":null,"abstract":"\u0000 The primary aim of this research is to establish the time dependent diffusion coefficient in a one dimensional time fractional diffusion equation in Caputo sense by means of newly defined Monic Laquerre wavelets (MLW) and collocation points. We first give the definition of MLW by taking Monic Laquerre polynomials into account. Later, time fractional diffusion problem is reduced into a system of ordinary fractional and algebraic equations by utilizing MLW. Residual power series method and the over-measured data are applied to this system to determine the solution and the unknown time dependent coefficient together in series form. In the end, illustrative examples are presented to show the stability and accuracy of the proposed wavelet method for the inverse problem of determining unknown time dependent coefficient in fractional diffusion problems. The reliability of the proposed algorithm for the inverse problems is supported by high degree of accuracy in given examples.","PeriodicalId":54858,"journal":{"name":"Journal of Computational and Nonlinear Dynamics","volume":"192 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85098146","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
S. Muñoz, P. Urda, Xinxi Yu, A. Mikkola, J. Escalona
A model-based methodology for the estimation of both lateral and vertical track irregularities is presented. This methodology, based on Kalman filter techniques, was developed for an independent and compact measuring system comprising an instrumented axle equipped with a limited set of low-cost sensors: a 3D gyroscope, a Linear Variable Differential Transformer (LVDT) distance sensor and an encoder. The instrumented axle can be used on any railway vehicle travelling at moderate forward speed to provide measurements in real-time. The proposed methodology, combined with the instrumented axle, enables precise and prompt measurement of track irregularities. An experimental campaign carried out on a 1:10 scale track facility at the University of Seville validated both the system and the methodology. In the testing, 80 meters of scaled track was measured at an operational speed of V = 0.65 m/s in just two minutes. Simulation estimates for track irregularities compared against the measured data from the testing showed a good performance of the proposed methodology, with maximum errors of 0.45 mm in the short wavelength range D1, the range most influential to vehicle dynamic behavior.
{"title":"Real-Time Measurement Of Track Irregularities Using An Instrumented Axle And Kalman Filtering Techniques","authors":"S. Muñoz, P. Urda, Xinxi Yu, A. Mikkola, J. Escalona","doi":"10.1115/1.4063339","DOIUrl":"https://doi.org/10.1115/1.4063339","url":null,"abstract":"\u0000 A model-based methodology for the estimation of both lateral and vertical track irregularities is presented. This methodology, based on Kalman filter techniques, was developed for an independent and compact measuring system comprising an instrumented axle equipped with a limited set of low-cost sensors: a 3D gyroscope, a Linear Variable Differential Transformer (LVDT) distance sensor and an encoder. The instrumented axle can be used on any railway vehicle travelling at moderate forward speed to provide measurements in real-time. The proposed methodology, combined with the instrumented axle, enables precise and prompt measurement of track irregularities. An experimental campaign carried out on a 1:10 scale track facility at the University of Seville validated both the system and the methodology. In the testing, 80 meters of scaled track was measured at an operational speed of V = 0.65 m/s in just two minutes. Simulation estimates for track irregularities compared against the measured data from the testing showed a good performance of the proposed methodology, with maximum errors of 0.45 mm in the short wavelength range D1, the range most influential to vehicle dynamic behavior.","PeriodicalId":54858,"journal":{"name":"Journal of Computational and Nonlinear Dynamics","volume":"20 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77478604","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
E. Okabe, Victor Paiva, Luis Silva-Teixeira, J. Izuka
In this work, three reinforcement learning algorithms (Proximal Policy Optimization, Soft Actor-Critic and Twin Delayed Deep Deterministic Policy Gradient) are employed to control a two link SCARA robot. This robot has three cables attached to its end-effector, which creates a triangular shaped workspace. Positioning the end-effector in the workspace is a relatively simple kinematic problem, but moving outside this region, although possible, requires a nonlinear dynamic model and a state-of-the-art controller. To solve this problem in a simple manner, reinforcement learning algorithms are used to find possible trajectories for three targets out of the workspace. Additionally, the SCARA mechanism offers two possible configurations for each end-effector position. The algorithm results are compared in terms of displacement error, velocity and standard deviation among ten trajectories provided by the trained network. The results indicate the Proximal Policy Algorithm as the most consistent in the analyzed situations. Still, the Soft Actor-Critic presented better solutions, and Twin Delayed Deep Deterministic Policy Gradient provided interesting and more unusual trajectories.
{"title":"Cable SCARA Robot Controlled by a Neural Network Using Reinforcement Learning","authors":"E. Okabe, Victor Paiva, Luis Silva-Teixeira, J. Izuka","doi":"10.1115/1.4063222","DOIUrl":"https://doi.org/10.1115/1.4063222","url":null,"abstract":"\u0000 In this work, three reinforcement learning algorithms (Proximal Policy Optimization, Soft Actor-Critic and Twin Delayed Deep Deterministic Policy Gradient) are employed to control a two link SCARA robot. This robot has three cables attached to its end-effector, which creates a triangular shaped workspace. Positioning the end-effector in the workspace is a relatively simple kinematic problem, but moving outside this region, although possible, requires a nonlinear dynamic model and a state-of-the-art controller. To solve this problem in a simple manner, reinforcement learning algorithms are used to find possible trajectories for three targets out of the workspace. Additionally, the SCARA mechanism offers two possible configurations for each end-effector position. The algorithm results are compared in terms of displacement error, velocity and standard deviation among ten trajectories provided by the trained network. The results indicate the Proximal Policy Algorithm as the most consistent in the analyzed situations. Still, the Soft Actor-Critic presented better solutions, and Twin Delayed Deep Deterministic Policy Gradient provided interesting and more unusual trajectories.","PeriodicalId":54858,"journal":{"name":"Journal of Computational and Nonlinear Dynamics","volume":"3 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84167194","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The analytical sensitivity analysis, i.e., the analytical first-order partial derivatives of dynamical equations, is one key to improving descent-based optimization methods for motion planning and control of robots. This paper proposes an efficient algorithm that recursively evaluates the analytic gradient of the dynamical equations of a multibody system. The theory of projective geometric algebra (PGA) is used to generate the algorithm. It provides a systemic and geometrically intuitive interpretation for the multibody system dynamics, and the resulting algorithm is highly efficient, with concise formula. The algorithm is first applied to the open-chain system and extended for the cases when kinematic loops are contained. The runtime varying with respect to the degree of freedom (DOF) of the system is analyzed. The results are compared with that obtained from the algorithm based on spatial vector algebra (SVA) using open-source MATLAB codes. A 2-DOF serial robot, a 3-DOF robot with a kinematic loop and the PUMA560 robot are used for the validation of the minimum-effort motion planning, and it is verified that the proposed algorithm improves the efficiency.
{"title":"An Analytical Method For Sensitivity Analysis Of Rigid Multibody System Dynamics Using Projective Geometric Algebra","authors":"Guangzhen Sun, Ye Ding","doi":"10.1115/1.4063225","DOIUrl":"https://doi.org/10.1115/1.4063225","url":null,"abstract":"\u0000 The analytical sensitivity analysis, i.e., the analytical first-order partial derivatives of dynamical equations, is one key to improving descent-based optimization methods for motion planning and control of robots. This paper proposes an efficient algorithm that recursively evaluates the analytic gradient of the dynamical equations of a multibody system. The theory of projective geometric algebra (PGA) is used to generate the algorithm. It provides a systemic and geometrically intuitive interpretation for the multibody system dynamics, and the resulting algorithm is highly efficient, with concise formula. The algorithm is first applied to the open-chain system and extended for the cases when kinematic loops are contained. The runtime varying with respect to the degree of freedom (DOF) of the system is analyzed. The results are compared with that obtained from the algorithm based on spatial vector algebra (SVA) using open-source MATLAB codes. A 2-DOF serial robot, a 3-DOF robot with a kinematic loop and the PUMA560 robot are used for the validation of the minimum-effort motion planning, and it is verified that the proposed algorithm improves the efficiency.","PeriodicalId":54858,"journal":{"name":"Journal of Computational and Nonlinear Dynamics","volume":"134 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77375639","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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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