research-article

Lie group integrators for animation and control of vehicles

Authors:

Marin Kobilarov,

Mathieu DesbrunAuthors Info & Claims

ACM Transactions on Graphics (TOG), Volume 28, Issue 2

Article No.: 16, Pages 1 - 14

https://doi.org/10.1145/1516522.1516527

Published: 13 May 2009 Publication History

Abstract

This article is concerned with the animation and control of vehicles with complex dynamics such as helicopters, boats, and cars. Motivated by recent developments in discrete geometric mechanics, we develop a general framework for integrating the dynamics of holonomic and nonholonomic vehicles by preserving their state-space geometry and motion invariants. We demonstrate that the resulting integration schemes are superior to standard methods in numerical robustness and efficiency, and can be applied to many types of vehicles. In addition, we show how to use this framework in an optimal control setting to automatically compute accurate and realistic motions for arbitrary user-specified constraints.

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Cited By

Soliman YPadilla MGross OKnöppel FPinkall USchröder P(2024)Going with the FlowACM Transactions on Graphics10.1145/365816443:4(1-12)Online publication date: 19-Jul-2024
https://dl.acm.org/doi/10.1145/3658164
Surya Prakash NSeo JSreenath KChoi JHorowitz R(2024)Deep Geometric Potential Functions for Tracking on Manifolds2024 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)10.1109/IROS58592.2024.10801512(i-viii)Online publication date: 14-Oct-2024
https://doi.org/10.1109/IROS58592.2024.10801512
Moiseev I(2024)Comparative Analysis of Physical Correctness of Models Using Classical and Variational Integrators2024 International Conference on Industrial Engineering, Applications and Manufacturing (ICIEAM)10.1109/ICIEAM60818.2024.10553825(1151-1158)Online publication date: 20-May-2024
https://doi.org/10.1109/ICIEAM60818.2024.10553825
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Index Terms

Lie group integrators for animation and control of vehicles
1. Computing methodologies
  1. Computer graphics
    1. Animation
  2. Modeling and simulation
    1. Simulation types and techniques
      1. Simulation by animation

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Published In

cover image ACM Transactions on Graphics

ACM Transactions on Graphics Volume 28, Issue 2

April 2009

129 pages

ISSN:0730-0301

EISSN:1557-7368

DOI:10.1145/1516522

Issue’s Table of Contents

Copyright © 2009 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Association for Computing Machinery

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Publication History

Published: 13 May 2009

Accepted: 01 January 2009

Revised: 01 November 2008

Received: 01 July 2008

Published in TOG Volume 28, Issue 2

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Cited By

Soliman YPadilla MGross OKnöppel FPinkall USchröder P(2024)Going with the FlowACM Transactions on Graphics10.1145/365816443:4(1-12)Online publication date: 19-Jul-2024
https://dl.acm.org/doi/10.1145/3658164
Surya Prakash NSeo JSreenath KChoi JHorowitz R(2024)Deep Geometric Potential Functions for Tracking on Manifolds2024 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)10.1109/IROS58592.2024.10801512(i-viii)Online publication date: 14-Oct-2024
https://doi.org/10.1109/IROS58592.2024.10801512
Moiseev I(2024)Comparative Analysis of Physical Correctness of Models Using Classical and Variational Integrators2024 International Conference on Industrial Engineering, Applications and Manufacturing (ICIEAM)10.1109/ICIEAM60818.2024.10553825(1151-1158)Online publication date: 20-May-2024
https://doi.org/10.1109/ICIEAM60818.2024.10553825
del Valle CAngelidakis VRoy SMuñoz JPöschel T(2024)SPIRAL: An efficient algorithm for the integration of the equation of rotational motionComputer Physics Communications10.1016/j.cpc.2023.109077297(109077)Online publication date: Apr-2024
https://doi.org/10.1016/j.cpc.2023.109077
Coiffier GCorman E(2023)The Method of Moving Frames for Surface Global ParametrizationACM Transactions on Graphics10.1145/360428242:5(1-18)Online publication date: 20-Sep-2023
https://dl.acm.org/doi/10.1145/3604282
Csomay-Shanklin NDorobantu VAmes A(2023)Nonlinear Model Predictive Control of a 3D Hopping Robot: Leveraging Lie Group Integrators for Dynamically Stable Behaviors2023 IEEE International Conference on Robotics and Automation (ICRA)10.1109/ICRA48891.2023.10160873(12106-12112)Online publication date: 29-May-2023
https://doi.org/10.1109/ICRA48891.2023.10160873
Caruso MFernández JTori CZuccalli M(2023)Lagrangian reduction of forced discrete mechanical systemsJournal of Physics A: Mathematical and Theoretical10.1088/1751-8121/aceae356:35(355202)Online publication date: 8-Aug-2023
https://doi.org/10.1088/1751-8121/aceae3
Hou SLu XGao WJiang SZhang X(2022)Interactive Physically Based Simulation of Roadheader RobotArabian Journal for Science and Engineering10.1007/s13369-022-07335-x48:2(2441-2454)Online publication date: 30-Sep-2022
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Yi ZYue BDeng M(2022)Hamilton–Pontryagin spectral-collocation methods for the orbit propagationActa Mechanica Sinica10.1007/s10409-021-01138-3Online publication date: 30-Jan-2022
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Xie JChakraborty N(2021)Modeling and Prediction of Rigid Body Motion With Planar Non-Convex ContactJournal of Mechanisms and Robotics10.1115/1.404987713:4Online publication date: 9-Apr-2021
https://doi.org/10.1115/1.4049877
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