Exact energy-momentum conserving algorithms and symplectic schemes for nonlinear dynamics
Computer Methods in Applied Mechanics and Engineering
SIAM Journal on Control and Optimization
NeuroAnimator: fast neural network emulation and control of physics-based models
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
Interactive manipulation of rigid body simulations
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Robot Motion Planning
A Mathematical Introduction to Robotic Manipulation
A Mathematical Introduction to Robotic Manipulation
Linear combination of transformations
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
SNOPT: An SQP Algorithm for Large-Scale Constrained Optimization
SIAM Journal on Optimization
Fast frictional dynamics for rigid bodies
ACM SIGGRAPH 2005 Papers
ACM SIGGRAPH 2005 Papers
Discrete geometric mechanics for variational time integrators
ACM SIGGRAPH 2006 Courses
Geometric, variational integrators for computer animation
Proceedings of the 2006 ACM SIGGRAPH/Eurographics symposium on Computer animation
Foundations of Computational Mathematics
Energy stability and fracture for frame rate rigid body simulations
Proceedings of the 2009 ACM SIGGRAPH/Eurographics Symposium on Computer Animation
Group-Valued regularization framework for motion segmentation of dynamic non-rigid shapes
SSVM'11 Proceedings of the Third international conference on Scale Space and Variational Methods in Computer Vision
Underwater rigid body dynamics
ACM Transactions on Graphics (TOG) - SIGGRAPH 2012 Conference Proceedings
Articulated motion segmentation of point clouds by group-valued regularization
EG 3DOR'12 Proceedings of the 5th Eurographics conference on 3D Object Retrieval
Group-Valued regularization for analysis of articulated motion
ECCV'12 Proceedings of the 12th international conference on Computer Vision - Volume Part I
EUROSCA'12 Proceedings of the 11th ACM SIGGRAPH / Eurographics conference on Computer Animation
Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation
Mathematical description of motion and deformation: from basics to graphics applications
SIGGRAPH Asia 2013 Courses
Stochastic modeling of immersed rigid-body dynamics
SIGGRAPH Asia 2013 Technical Briefs
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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.