Learning and planning high-dimensional physical trajectories via structured Lagrangians

— We consider the problem of finding sufficiently simple models of high-dimensional physical systems that are consistent with observed trajectories, and using these models to synthesize new trajectories. Our approach models physical trajectories as least-time trajectories realized by free particles moving along the geodesics of a curved manifold, reminiscent of the way light rays obey Fermat’s principle of least time. Finding these trajectories, unfortunately, requires finding a minimumcost path in a high-dimensional space, which is generally a computationally intractable problem. In this work we show that this high-dimensional planning problem can often be solved nearly optimally in practice via deterministic search, as long as we can find a certain low-dimensional structure in the Lagrangian that describes our observed trajectories. This lowdimensional structure additionally makes it feasible to learn an estimate of a Lagrangian that is consistent with the observed trajectori...

• Type: Journal
• Year: 2010
• Where: ICRA
• Authors: Paul Vernaza, Daniel D. Lee, Seung-Joon Yi
• Keywords: ICRA 2010, Least-time Trajectories, Observed Trajectories, Robotics, Trajectories