Robot dynamics: A recursive algorithm for efficient calculation of Christoffel symbols

Safeea, Mohammad; Neto, Pedro; Béarée, Richard

doi:10.1016/j.mechmachtheory.2019.103589

Cited by 12 publications

(4 citation statements)

References 27 publications

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“…Note that, with this model, the volume is not preserved locally when the tentacle deforms, but the overall change in volume is limited to 2% for extreme deformations. The Coriolis terms are computed thanks to Christoffel symbols [23]. The gravitational field, together with the buoyancy force field can be expressed as:…”

Section: Modelling and System Identificationmentioning

confidence: 99%

An Experimental Validation of the Polynomial Curvature Model: Identification and Optimal Control of a Soft Underwater Tentacle

Stella

Obayashi

Santina

et al. 2022

IEEE Robot. Autom. Lett.

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The control possibilities for soft robots have long been hindered by the lack of accurate yet computationally treatable dynamic models of soft structures. Polynomial curvature models propose a solution to this quest for continuum slender structures. Nevertheless, the results produced with this class of models have been so far essentially theoretical. With the present work, we aim to provide a much-needed experimental validation to these recent theories. To this end, we focus on soft tentacles immersed in water. First, we propose an extension of the affine curvature model to underwater structures, considering the drag forces arising from the fluid-solid interaction. Then, we extensively test the model's capability to describe the system behavior across several shapes and working conditions. Finally, we validate model-based control policies, proposing and solving an optimal control problem for directional underwater swimming. Using the model we show an average increase of more than 3.5 times the swimming speed of a sinusoidal baseline controller, with some tentacles showing an improvement in excess of 5.5 times the baseline.

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Section: Modelling and System Identificationmentioning

confidence: 99%

An Experimental Validation of the Polynomial Curvature Model: Identification and Optimal Control of a Soft Underwater Tentacle

Stella

Obayashi

Santina

et al. 2022

IEEE Robot. Autom. Lett.

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“…Supplemental Derivation for Equation (19) Toward simplifying (18), consider the following summation lemma: Lemma 1. Let body i with the following set…”

Section: And J K}mentioning

confidence: 99%

“…From this Coriolis matrix algorithm, we also derive a new method for the calculation of the Christoffel symbols of the first kind, without requiring any symbolic partial derivatives in the algorithm itself. A related algorithm was recently proposed in [18] that is applicable for kinematic chains with revolute joints. By adopting a coordinate-free development, the work herein is more general (e.g., enabling application to branched systems with prismatic joints, or combinations of prismatic and revolute joints, etc.).…”

Section: Introductionmentioning

confidence: 99%

Numerical Methods to Compute the Coriolis Matrix and Christoffel Symbols for Rigid-Body Systems

Echeandia,

Wensing

2020

Preprint

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The growth of model-based control strategies for robotics platforms has led to the need for additional rigid-bodydynamics algorithms to support their operation. Toward addressing this need, this article summarizes efficient numerical methods to compute the Coriolis matrix and underlying Christoffel Symbols (of the first kind) for tree-structure rigid-body systems. The resulting algorithms can be executed purely numerically, without requiring any partial derivatives that would be required in symbolic techniques that do not scale. Properties of the presented algorithms share recursive structure in common with classical methods such as the Composite-Rigid-Body Algorithm. The algorithms presented are of the lowest possible order: O(N d) for the Coriolis Matrix and O(N d 2 ) for the Christoffel symbols, where N is the number of bodies and d is the depth of the kinematic tree. A method of order O(N d) is also provided to compute the time derivative of the mass matrix. A numerical implementation of these algorithms in C/C++ is benchmarked showing computation times on the order of 10-20 µs for the computation of C and 40 − 120 µs for the computation of the Christoffel symbols for systems with 20 degrees of freedom. These results demonstrate feasibility for the adoption of these numerical methods within control loops that need to operate at 1kHz rates or higher, as is commonly required for model-based control applications.

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“…The geometric center of the moving platform is taken as the origin of the O1-X1Y1Z1. According to the transform matrix of each branch to the end of the A transform matrix [22], we have:…”

Section: Finding the Derivation Relative To Time T At Both Sides Of Fmentioning

confidence: 99%

Dimension Synthesis of a 3T2R Labelling Robot with Hybrid Mechanism

Deng¹,

Liu²,

Zhang³

2019

JESA

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This paper proposes a novel 3T2R labelling robot with hybrid mechanism for the end-faces of round steels. The hybrid mechanism consists of a three degrees-of-freedom (DOFs) translation (3T) parallel mechanism and a two DOFs rotation (2R) mechanism. Based on the Jacobian matrix of the hybrid mechanism, the author analyzed the influence of each dimension parameter on three performance indices, namely, kinematics, transmission and stiffness of the mechanism, under the constraints of the workspace. Based on the Pareto frontier approach, the Non-dominated Sorting Genetic Algorithm II (NSGA-II) was adopted to find the optimal values of the three performance indices, and identify the dimension parameters that bring the best overall performance of the whole mechanism. The research results shed new light on the design of light weight labelling robot. Journal homepage: http://iieta.org/journals/jesa P Q q J J J J J J J J J −   ==    J J J . (7) 0 0 c 0 J J J l l J J J l s J J J l max -1 min = J K   = J JJ J

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Robot dynamics: A recursive algorithm for efficient calculation of Christoffel symbols

Cited by 12 publications

References 27 publications

An Experimental Validation of the Polynomial Curvature Model: Identification and Optimal Control of a Soft Underwater Tentacle

An Experimental Validation of the Polynomial Curvature Model: Identification and Optimal Control of a Soft Underwater Tentacle

Numerical Methods to Compute the Coriolis Matrix and Christoffel Symbols for Rigid-Body Systems

Dimension Synthesis of a 3T2R Labelling Robot with Hybrid Mechanism

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