Simultaneous optimal system and controller design for multibody systems with joint friction using direct sensitivities

Verulkar, Adwait; Sandu, Corina; Sandu, Adrian; Dopico, Daniel

doi:10.1007/s11044-024-10030-4

Title: Simultaneous optimal system and controller design for multibody systems with joint friction using direct sensitivities

Journal Article · 21 October 2024 · Multibody System Dynamics

DOI: https://doi.org/10.1007/s11044-024-10030-4 · OSTI ID:2473169

Verulkar, Adwait; Sandu, Corina; Sandu, Adrian; Dopico, Daniel

Abstract Real-world multibody systems are often subject to phenomena like friction, joint clearances, and external events. These phenomena can significantly impact the optimal design of the system and its controller. This work addresses the gradient-based optimization methodology for multibody dynamic systems with joint friction using a direct sensitivity approach. The Brown–McPhee model has been used to characterize the joint friction in the system. This model is suitable for the study due to its accuracy for dynamic simulation and its compatibility with sensitivity analysis. This novel methodology supports codesign of the multibody system and its controller, which is especially relevant for applications like robotics and servo-mechanical systems, where the actuation and design are highly dependent on each other. Numerical results are obtained using a software package written in Julia with state-of-the-art libraries for automatic differentiation and differential equations. Three case studies are provided to demonstrate the attractive properties of simultaneous optimal design and control approach for certain applications.

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Sponsoring Organization:: USDOE

OSTI ID:: 2473169

Journal Information:: Multibody System Dynamics, Journal Name: Multibody System Dynamics; ISSN 1384-5640

Publisher:: Springer Science + Business MediaCopyright Statement

Country of Publication:: Netherlands

Language:: English

References (61)

Simultaneous optimization approach for combined control–structural design versus the conventional sequential optimization method Alavi, Arsalan; Dolatabadi, Mohammad; Mashhadi, Javad Structural and Multidisciplinary Optimization, Vol. 63, Issue 3 https://doi.org/10.1007/s00158-020-02765-3	journal	November 2020
On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming Wächter, Andreas; Biegler, Lorenz T. Mathematical Programming, Vol. 106, Issue 1 https://doi.org/10.1007/s10107-004-0559-y	journal	April 2005
Construction of Rosenbrock–Wanner method Rodas5P and numerical benchmarks within the Julia Differential Equations package Steinebach, Gerd BIT Numerical Mathematics, Vol. 63, Issue 2 https://doi.org/10.1007/s10543-023-00967-x	journal	April 2023
Analysis of Joint Clearances in Multibody Systems Orden, J. C. García Multibody System Dynamics, Vol. 13, Issue 4 https://doi.org/10.1007/s11044-005-3989-2	journal	May 2005
Multibody dynamics simulation of planar linkages with Dahl friction Pennestrì, E.; Valentini, P. P.; Vita, L. Multibody System Dynamics, Vol. 17, Issue 4 https://doi.org/10.1007/s11044-007-9047-5	journal	February 2007
Multibody dynamics with redundant constraints and singular mass matrix: existence, uniqueness, and determination of solutions for accelerations and constraint forces García de Jalón, J.; Gutiérrez-López, M. D. Multibody System Dynamics, Vol. 30, Issue 3 https://doi.org/10.1007/s11044-013-9358-7	journal	March 2013
Modeling and analysis of friction including rolling effects in multibody dynamics: a review Marques, Filipe; Flores, Paulo; Claro, J. C. Pimenta Multibody System Dynamics, Vol. 45, Issue 2 https://doi.org/10.1007/s11044-018-09640-6	journal	August 2018
Adjoint sensitivity analysis of hybrid multibody dynamical systems Corner, Sebastien; Sandu, Adrian; Sandu, Corina Multibody System Dynamics, Vol. 49, Issue 4 https://doi.org/10.1007/s11044-020-09726-0	journal	February 2020
Discrete adjoint variable method for the sensitivity analysis of ALI3-P formulations López Varela, Álvaro; Sandu, Corina; Sandu, Adrian Multibody System Dynamics https://doi.org/10.1007/s11044-023-09911-x	journal	June 2023
CasADi: a software framework for nonlinear optimization and optimal control Andersson, Joel A. E.; Gillis, Joris; Horn, Greg Mathematical Programming Computation, Vol. 11, Issue 1 https://doi.org/10.1007/s12532-018-0139-4	journal	July 2018
Stabilization of constraints and integrals of motion in dynamical systems Baumgarte, J. Computer Methods in Applied Mechanics and Engineering, Vol. 1, Issue 1 https://doi.org/10.1016/0045-7825(72)90018-7	journal	June 1972
Optimization of multibody dynamics using object oriented programming and a mixed numerical-symbolic penalty formulation Pagalday, J. M.; Avello, A. Mechanism and Machine Theory, Vol. 32, Issue 2 https://doi.org/10.1016/S0094-114X(96)00037-7	journal	February 1997
Efficient sensitivity analysis of large-scale differential-algebraic systems Feehery, William F.; Tolsma, John E.; Barton, Paul I. Applied Numerical Mathematics, Vol. 25, Issue 1 https://doi.org/10.1016/S0168-9274(97)00050-0	journal	October 1997
Software and algorithms for sensitivity analysis of large-scale differential algebraic systems Li, Shengtai; Petzold, Linda Journal of Computational and Applied Mathematics, Vol. 125, Issue 1-2 https://doi.org/10.1016/S0377-0427(00)00464-7	journal	December 2000
Stiff differential equations solved by Radau methods Hairer, Ernst; Wanner, Gerhard Journal of Computational and Applied Mathematics, Vol. 111, Issue 1-2 https://doi.org/10.1016/S0377-0427(99)00134-X	journal	November 1999
Sensitivity analysis of differential-algebraic equations and partial differential equations Petzold, Linda; Li, Shengtai; Cao, Yang Computers & Chemical Engineering, Vol. 30, Issue 10-12 https://doi.org/10.1016/j.compchemeng.2006.05.015	journal	September 2006
Modeling and optimization with Optimica and JModelica.org—Languages and tools for solving large-scale dynamic optimization problems Åkesson, J.; Årzén, K. -E.; Gäfvert, M. Computers & Chemical Engineering, Vol. 34, Issue 11 https://doi.org/10.1016/j.compchemeng.2009.11.011	journal	November 2010
Jacobian-free Newton–Krylov methods: a survey of approaches and applications Knoll, D. A.; Keyes, D. E. Journal of Computational Physics, Vol. 193, Issue 2 https://doi.org/10.1016/j.jcp.2003.08.010	journal	January 2004
On the unique solvability of a direct dynamics problem for mechanisms with redundant constraints and Coulomb friction in joints Frączek, Janusz; Wojtyra, Marek Mechanism and Machine Theory, Vol. 46, Issue 3 https://doi.org/10.1016/j.mechmachtheory.2010.11.003	journal	March 2011
A comprehensive survey of the analytical, numerical and experimental methodologies for dynamics of multibody mechanical systems with clearance or imperfect joints Tian, Qiang; Flores, Paulo; Lankarani, Hamid M. Mechanism and Machine Theory, Vol. 122 https://doi.org/10.1016/j.mechmachtheory.2017.12.002	journal	April 2018
Adjoint method for optimal control of multibody systems in the Hamiltonian setting Pikuliński, Maciej; Malczyk, Paweł Mechanism and Machine Theory, Vol. 166 https://doi.org/10.1016/j.mechmachtheory.2021.104473	journal	December 2021
Contact-impact events with friction in multibody dynamics: Back to basics Flores, Paulo; Ambrósio, Jorge; Lankarani, Hamid M. Mechanism and Machine Theory, Vol. 184 https://doi.org/10.1016/j.mechmachtheory.2023.105305	journal	June 2023
Modeling and sensitivity analysis methodology for hybrid dynamical system Corner, Sebastien; Sandu, Corina; Sandu, Adrian Nonlinear Analysis: Hybrid Systems, Vol. 31 https://doi.org/10.1016/j.nahs.2018.07.003	journal	February 2019
A Regularized Contact Model with Asymmetric Damping and Dwell-Time Dependent Friction Gonthier, Yves; McPhee, John; Lange, Christian Multibody System Dynamics, Vol. 11, Issue 3 https://doi.org/10.1023/B:MUBO.0000029392.21648.bc	journal	April 2004
Dynamic Analysis for Planar Multibody Mechanical Systems with Lubricated Joints Flores, Paulo; Ambrósio, Jorge; Claro, J. Pimenta Multibody System Dynamics, Vol. 12, Issue 1 https://doi.org/10.1023/B:MUBO.0000042901.74498.3a	journal	August 2004
Stiff neural ordinary differential equations Kim, Suyong; Ji, Weiqi; Deng, Sili Chaos: An Interdisciplinary Journal of Nonlinear Science, Vol. 31, Issue 9 https://doi.org/10.1063/5.0060697	journal	September 2021
A Topology-Based Approach for Exploiting Sparsity in Multibody Dynamics in Cartesian Formulation* Serban, Radu; Negrut, Dan; Haug, Edward J. Mechanics of Structures and Machines, Vol. 25, Issue 3 https://doi.org/10.1080/08905459708905295	journal	January 1997
Simulation of spatial multibody systems with friction Haug, Edward J. Mechanics Based Design of Structures and Machines, Vol. 46, Issue 3 https://doi.org/10.1080/15397734.2017.1377086	journal	March 2018
A Simplex Method for Function Minimization Nelder, J. A.; Mead, R. The Computer Journal, Vol. 7, Issue 4 https://doi.org/10.1093/comjnl/7.4.308	journal	January 1965
Parameter estimation for mechanical systems via an explicit representation of uncertainty Blanchard, Emmanuel; Sandu, Adrian; Sandu, Corina Engineering Computations, Vol. 26, Issue 5 https://doi.org/10.1108/02644400910970185	journal	July 2009
A new model for control of systems with friction Canudas de Wit, C.; Olsson, H.; Astrom, K. J. IEEE Transactions on Automatic Control, Vol. 40, Issue 3 https://doi.org/10.1109/9.376053	journal	March 1995
A Comparison of Automatic Differentiation and Continuous Sensitivity Analysis for Derivatives of Differential Equation Solutions Ma, Yingbo; Dixit, Vaibhav; Innes, Michael J. 2021 IEEE High Performance Extreme Computing Conference (HPEC) https://doi.org/10.1109/HPEC49654.2021.9622796	conference	September 2021
Optimization based full body control for the atlas robot Feng, Siyuan; Whitman, Eric; Xinjilefu, X. 2014 IEEE-RAS International Conference on Humanoid Robots https://doi.org/10.1109/HUMANOIDS.2014.7041347	conference	November 2014
Particle swarm optimization Kennedy, J.; Eberhart, R. Proceedings of ICNN'95 - International Conference on Neural Networks https://doi.org/10.1109/ICNN.1995.488968	conference	January 1995
Dynamics of Multibody Systems With Spherical Clearance Joints Flores, P.; Ambrósio, J.; Claro, J. C. P. Journal of Computational and Nonlinear Dynamics, Vol. 1, Issue 3 https://doi.org/10.1115/1.2198877	journal	March 2006
Optimal Design of Mechanical Systems With Constraint Violation Stabilization Method Chang, C. O.; Nikravesh, P. E. Journal of Mechanisms, Transmissions, and Automation in Design, Vol. 107, Issue 4 https://doi.org/10.1115/1.3260751	journal	December 1985
A Polynomial Chaos-Based Kalman Filter Approach for Parameter Estimation of Mechanical Systems Blanchard, Emmanuel D.; Sandu, Adrian; Sandu, Corina Journal of Dynamic Systems, Measurement, and Control, Vol. 132, Issue 6 https://doi.org/10.1115/1.4002481	journal	November 2010
Direct and Adjoint Sensitivity Analysis of Ordinary Differential Equation Multibody Formulations Dopico, Daniel; Zhu, Yitao; Sandu, Adrian Journal of Computational and Nonlinear Dynamics, Vol. 10, Issue 1 https://doi.org/10.1115/1.4026492	journal	September 2014
Dynamic Response Optimization of Complex Multibody Systems in a Penalty Formulation Using Adjoint Sensitivity Zhu, Yitao; Dopico, Daniel; Sandu, Corina Journal of Computational and Nonlinear Dynamics, Vol. 10, Issue 3 https://doi.org/10.1115/1.4029601	journal	May 2015
A Continuous Velocity-Based Friction Model for Dynamics and Control With Physically Meaningful Parameters Brown, Peter; McPhee, John Journal of Computational and Nonlinear Dynamics, Vol. 11, Issue 5 https://doi.org/10.1115/1.4033658	journal	June 2016
Direct Sensitivity Analysis of Multibody Systems: A Vehicle Dynamics Benchmark Callejo, Alfonso; Dopico, Daniel Journal of Computational and Nonlinear Dynamics, Vol. 14, Issue 2 https://doi.org/10.1115/1.4041960	journal	January 2019
Computation of Direct Sensitivities of Spatial Multibody Systems With Joint Friction Verulkar, Adwait; Sandu, Corina; Dopico, Daniel Journal of Computational and Nonlinear Dynamics, Vol. 17, Issue 7 https://doi.org/10.1115/1.4054110	journal	April 2022
Direct Sensitivity Analysis of Spatial Multibody Systems With Joint Friction Using Index-1 Formulation Verulkar, Adwait; Sandu, Corina; Dopico, Daniel Volume 9: 17th International Conference on Multibody Systems, Nonlinear Dynamics, and Control (MSNDC) https://doi.org/10.1115/DETC2021-68777	conference	August 2021
Efficient Bipedal Robots Based on Passive-Dynamic Walkers Collins, S. Science, Vol. 307, Issue 5712 https://doi.org/10.1126/science.1107799	journal	February 2005
Automatic Selection of Methods for Solving Stiff and Nonstiff Systems of Ordinary Differential Equations Petzold, Linda SIAM Journal on Scientific and Statistical Computing, Vol. 4, Issue 1 https://doi.org/10.1137/0904010	journal	March 1983
A Limited Memory Algorithm for Bound Constrained Optimization Byrd, Richard H.; Lu, Peihuang; Nocedal, Jorge SIAM Journal on Scientific Computing, Vol. 16, Issue 5 https://doi.org/10.1137/0916069	journal	September 1995
Evaluating Derivatives Griewank, Andreas; Walther, Andrea https://doi.org/10.1137/1.9780898717761	book	January 2008
Solving Nonlinear Equations with Newton's Method Kelley, C. T. Fundamentals of Algorithms (series) https://doi.org/10.1137/1.9780898718898	book	January 2003
Sparse Matrix-Matrix Products Executed Through Coloring McCourt, Michael; Smith, Barry; Zhang, Hong SIAM Journal on Matrix Analysis and Applications, Vol. 36, Issue 1 https://doi.org/10.1137/13093426X	journal	January 2015
A Technique for Accelerating the Convergence of Restarted GMRES Baker, A. H.; Jessup, E. R.; Manteuffel, T. SIAM Journal on Matrix Analysis and Applications, Vol. 26, Issue 4 https://doi.org/10.1137/S0895479803422014	journal	January 2005
SUNDIALS: Suite of nonlinear and differential/algebraic equation solvers Hindmarsh, Alan C.; Brown, Peter N.; Grant, Keith E. ACM Transactions on Mathematical Software, Vol. 31, Issue 3 https://doi.org/10.1145/1089014.1089020	journal	September 2005
A Recursive Algebraic Coloring Technique for Hardware-efficient Symmetric Sparse Matrix-vector Multiplication Alappat, Christie; Basermann, Achim; Bishop, Alan R. ACM Transactions on Parallel Computing, Vol. 7, Issue 3 https://doi.org/10.1145/3399732	journal	June 2020
High-performance symbolic-numerics via multiple dispatch Gowda, Shashi; Ma, Yingbo; Cheli, Alessandro ACM Communications in Computer Algebra, Vol. 55, Issue 3 https://doi.org/10.1145/3511528.3511535	journal	September 2021
ADIFOR–Generating Derivative Codes from Fortran Programs Bischof, Christian; Carle, Alan; Corliss, George Scientific Programming, Vol. 1, Issue 1 https://doi.org/10.1155/1992/717832	journal	January 1992
Polynomial chaos-based parameter estimation methods applied to a vehicle system Blanchard, E. D.; Sandu, A.; Sandu, C. Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics, Vol. 224, Issue 1 https://doi.org/10.1243/14644193JMBD204	journal	July 2009
Description and use of LSODE, the Livemore Solver for Ordinary Differential Equations Radhakrishnan, K.; Hindmarsh, A. C. https://doi.org/10.2172/15013302	report	December 1993
User guide for MINPACK-1. [In FORTRAN] More, J.; Garbow, B.; Hillstrom, K. https://doi.org/10.2172/6997568	report	August 1980
Composing Modeling And Simulation With Machine Learning In Julia Rackauckas, Chris; Gwozdz, Maja; Jain, Anand 2022 Annual Modeling and Simulation Conference (ANNSIM) https://doi.org/10.23919/ANNSIM55834.2022.9859453	conference	July 2022
Simultaneous Combined Optimal Design and Control Formulation for Aircraft Hybrid-Electric Propulsion Systems Nakka, Sai Krishna Sumanth; Alexander-Ramos, Michael J. Journal of Aircraft, Vol. 58, Issue 1 https://doi.org/10.2514/1.C035678	journal	January 2021
Dynamic Modeling of the Dissipative Contact and Friction Forces of a Passive Biped-Walking Robot Corral, Eduardo; García, M. J. Gómez; Castejon, Cristina Applied Sciences, Vol. 10, Issue 7 https://doi.org/10.3390/app10072342	journal	March 2020
Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence Holland, John H. The MIT Press https://doi.org/10.7551/mitpress/1090.001.0001	book	January 1992

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