Lie Group Integrators for Animation and Control of Vehicles
To appear in ACM Transactions on Graphics (TOG) 2009
Abstract: This paper 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.
PDF: Lie Group Integrators for Animation and Control of Vehicles
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Acknowledgements
The authors wish to thank Jerrold E. Marsden for inspiration and guidance, Gaurav Sukhatme for his assistance and support, and the reviewers for their feedback. This research project was partially funded by the NSF (ITR DMS-043145, CCF-0811373, and CMMI-0757106), DOE (DE-FG02-04ER25657), the Caltech IST Center for the Mathematics of Information, and Pixar Animation Studios.
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