A Linear-Time Variational Integrator for Multibody Systems

Lee, Jeong-Seok; Liu, C. Karen; Park, Frank C.; Srinivasa, Siddhartha S.

doi:10.1007/978-3-030-43089-4_23

Cited by 11 publications

(25 citation statements)

References 9 publications

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“…Within the discrete mechanics literature, extensions exist to apply the variational integrator to multi-body systems with a nonconstant mass matrix. However, these extensions are nontrivial and involve solving a root-finding problem within each integration step (Lee et al 2020).…”

Section: 32mentioning

confidence: 99%

Combining Physics and Deep Learning to learn Continuous-Time Dynamics Models

Lutter¹,

Peters²

2021

Preprint

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Deep learning has been widely used within learning algorithms for robotics. One disadvantage of deep networks is that these networks are black-box representations. Therefore, the learned approximations ignore the existing knowledge of physics or robotics. Especially for learning dynamics models, these black-box models are not desirable as the underlying principles are well understood and the standard deep networks can learn dynamics that violate these principles. To learn dynamics models with deep networks that guarantee physically plausible dynamics, we introduce physics-inspired deep networks that combine first principles from physics with deep learning. We incorporate Lagrangian mechanics within the model learning such that all approximated models adhere to the laws of physics and conserve energy. Deep Lagrangian Networks (DeLaN) parametrize the system energy using two networks. The parameters are obtained by minimizing the squared residual of the Euler-Lagrange differential equation. Therefore, the resulting model does not require specific knowledge of the individual system, is interpretable, and can be used as a forward, inverse, and energy model. Previously these properties were only obtained when using system identification techniques that require knowledge of the kinematic structure. We apply DeLaN to learning dynamics models and apply these models to control simulated and physical rigid body systems. The results show that the proposed approach obtains dynamics models that can be applied to physical systems for real-time control. Compared to standard deep networks, the physics-inspired models learn better models and capture the underlying structure of the dynamics.

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Section: 32mentioning

confidence: 99%

Combining Physics and Deep Learning to learn Continuous-Time Dynamics Models

Lutter¹,

Peters²

2021

Preprint

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“…e error is defined as ε, as shown in equation 19, where τ is the actual moment function of the dynamic model and τ t is the amount of moment change in the mathematical model. When the accuracy of the dynamic model can be improved, it is considered that the correction function τ ′ exists so that equation (20) is established. e ε ′ is defined as the error value after the kinetic model improves the accuracy, as shown in equation 20:…”

Section: Improved Dynamic Model Analysis and Modelingmentioning

confidence: 99%

“…e expression of the correction function τ ′ derived from equations (19) and (20) is shown in equation 21, where Δε is the amount of change in the model error:…”

Section: Improved Dynamic Model Analysis and Modelingmentioning

confidence: 99%

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Establishing the Improved Dynamic Model for the Extracorporeal Ultrasonic Lithotripsy Medical Cooperative Robot

Xiao

Gong

et al. 2020

Mathematical Problems in Engineering

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The calculus is one of the common diseases with high incidence. The effective treatment method is extracorporeal ultrasonic lithotripsy. At present, it is low about the intelligent and automatic level of the lithotripter, and it has gradually failed to meet the treatment needs. The extracorporeal ultrasonic lithotripsy medical cooperative robot can solve such problems effectively, and it is equally critical for accurate modeling studies of dynamic models. Based on the previous research and experimental basis, this paper proposes a correction theory to improve the accuracy of the dynamic model for the model error in collaborative robot work. The study first establishes the dynamic model and the solid model of the collaborative robot and then subtracts the value of the dynamic model from the solid model to obtain the modified equation. Finally, the accuracy of the dynamic model is improved by modifying the equation. The experiments show that the kinetic model correction theory is effective and can improve the accuracy of the dynamic model modeling after the correction of the torque equation. The experiments show that the improved dynamic model theory is effective and can improve the modeling accuracy of the dynamic model after the correction of the torque equation. The modified equation has the best correction effect in the 5th degree polynomial and can be used for the extracorporeal ultrasonic lithotripsy medical cooperative robot control.

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“…In the last few years, algorithms for calculating rigid body dynamics in linear time with variational integrators in minimal coordinates have been presented [13,7]. While these algorithms show promising results, mechanical structures with closed kinematic loops or nonholonomic (i.e.…”

Section: Introductionmentioning

confidence: 99%

Linear-Time Variational Integrators in Maximal Coordinates

Brüdigam,

Manchester

2020

Preprint

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Most dynamic simulation tools parameterize the configuration of multi-body robotic systems using minimal coordinates, also called generalized or joint coordinates. However, maximal-coordinate approaches have several advantages over minimal-coordinate parameterizations, including native handling of closed kinematic loops and nonholonomic constraints. This paper describes a linear-time variational integrator that is formulated in maximal coordinates. Due to its variational formulation, the algorithm does not suffer from constraint drift and has favorable energy and momentum conservation properties. A sparse matrix factorization technique allows the dynamics of a loop-free articulated mechanism with n links to be computed in O(n) (linear) time. Additional constraints that introduce loops can also be handled by the algorithm without incurring much computational overhead. Experimental results show that our approach offers speed competitive with state-of-the-art minimal-coordinate algorithms while outperforming them in several scenarios, especially when dealing with closed loops and configuration singularities.

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A Linear-Time Variational Integrator for Multibody Systems

Cited by 11 publications

References 9 publications

Combining Physics and Deep Learning to learn Continuous-Time Dynamics Models

Combining Physics and Deep Learning to learn Continuous-Time Dynamics Models

Establishing the Improved Dynamic Model for the Extracorporeal Ultrasonic Lithotripsy Medical Cooperative Robot

Linear-Time Variational Integrators in Maximal Coordinates

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