Some Applications of Automatic Differentiation to Rigid, Flexible, and Constrained Multibody Dynamics

Griffith, D. Todd; Turner, James D.; Junkins, John L.

doi:10.1115/detc2005-85640

Cited by 7 publications

(3 citation statements)

References 5 publications

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“…There is considerable research on how to use Auto-Diff to model and simulate Rigid Body systems, e.g. [16], [17], [18]. However, this work is focused on solving the RBD differential equations in order to obtain equations of motions rather than explicitly computing their derivatives.…”

Section: Related Workmentioning

confidence: 99%

Automatic differentiation of rigid body dynamics for optimal control and estimation

et al. 2017

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Many algorithms for control, optimization and estimation in robotics depend on derivatives of the underlying system dynamics, e.g. to compute linearizations, sensitivities or gradient directions. However, we show that when dealing with Rigid Body Dynamics, these derivatives are difficult to derive analytically and to implement efficiently. To overcome this issue, we extend the modelling tool 'RobCoGen' to be compatible with Automatic Differentiation. Additionally, we propose how to automatically obtain the derivatives and generate highly efficient source code. We highlight the flexibility and performance of the approach in two application examples. First, we show a Trajectory Optimization example for the quadrupedal robot HyQ, which employs auto-differentiation on the dynamics including a contact model. Second, we present a hardware experiment in which a 6 DoF robotic arm avoids a randomly moving obstacle in a go-to task by fast, dynamic replanning. This paper is an extended version of [1].

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Section: Related Workmentioning

confidence: 99%

Automatic differentiation of rigid body dynamics for optimal control and estimation

et al. 2017

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“…Here, part of the chain rule is calculated via finite differencing e.g. for the direct method: [38,44,62,138] direct differentiation [24,111,132,[137][138][139]159] adjoint variable method [6, 20, 21, 26, 44, 60, 72-74, 81, 84, 100, 101, 105, 106, 123, 149, 159] complex step method [20,21,26] automatic differentiation [4,25,63] The complex-step method of sensitivity analysis in which the perturbation is carried out with the imaginary value j x i originates in [95,96,130],…”

Section: General Sensitivity Analysismentioning

confidence: 99%

“…This method has found limited application to the differentiation of the primal equations of flexible multibody systems e.g. [4,25,63]. However, automatic differentiation can be used to compute partial terms of the system parameters in the sensitivity equations [4], see Sect.…”

Section: General Sensitivity Analysismentioning

confidence: 99%

A review of flexible multibody dynamics for gradient-based design optimization

2021

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Design optimization of flexible multibody dynamics is critical to reducing weight and therefore increasing efficiency and lowering costs of mechanical systems. Simulation of flexible multibody systems, though, typically requires high computational effort which limits the usage of design optimization, especially when gradient-free methods are used and thousands of system evaluations are required. Efficient design optimization of flexible multibody dynamics is enabled by gradient-based optimization methods in concert with analytical sensitivity analysis. The present study summarizes different formulations of the equations of motion of flexible multibody dynamics. Design optimization techniques are introduced, and applications to flexible multibody dynamics are categorized. Efficient sensitivity analysis is the centerpiece of gradient-based design optimization, and sensitivity methods are introduced. The increased implementation effort of analytical sensitivity analysis is rewarded with high computational efficiency. An exemplary solution strategy for system and sensitivity evaluations is shown with the analytical direct differentiation method. Extensive literature sources are shown related to recent research activities.

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