Lie Group Integrators for Animation and Control of Vehicles - Talk (2/4)

This video is a conference presentation of the paper "Lie Group Integrators for Animation and Control of Vehicles" given by Keenan Crane in August 2009 -- see http://www.cs.caltech.edu/~keenan/project_lgiacv.html for more information

Accompanying slides can be found here: http://www.cs.caltech.edu/~keenan/pdf/vehicle_slides_siggraph09.pdf


Lie Group Integrators for Animation and Control of Vehicles
Marin Kobilarov, Keenan Crane, Mathieu Desbrun (Caltech)

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.

Category:

Science & Technology

Tags:

• computer graphics
• animation
• simulation
• vehicles
• numerical integration
• optimal control
• Lie groups
• nonholonomic mechancs
• geometric mechanics
• variational principles
• SIGGRAPH
• Caltech

[keenancrane]

@MrManifolder For the car, one copy of S1 represents the angle of the rear axle and the other copy represents the (tangent of the) angle of the front wheels relative to the orientation of the car. The SE(2) component gives the position and direction of the car in the plane. So the overall configuration space is the same as for the snakeboard, but you will of course get very different dynamics!

[MrManifolder]

Your excellent paper says that the car, like the above snake board, also has configuration space Q = S^1 X S^1 X SE(2). Just to confirm, is that because one S^1 Lie group is for each front wheel and then the SE(2) Lie group is for the chassis?

Thanks! Keep up the great work!