Accurate recursive learning of uncertain diffeomorphism dynamics 2013-03-25

Adam Nilsson and Andrea Censi. Accurate recursive learning of uncertain diffeomorphism dynamics. In IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). Tokyo, Japan, November 2013. pdfdoi supp. material


Abstract: Diffeomorphisms dynamical systems are dynamical systems where the state is an image and each commands induce a diffeomorphism of the state. These systems can approximate the dynamics of robotic sensorimotor cascades well enough to be used for problems such as planning in observations space. Learning of an arbitrary diffeomorphism from pairs of images is a high dimensional learning problem. This paper describes two improvements to the methods presented in previous work. The previous method had required O(ρ⁴) memory as a function of the desired resolution ρ, which, in practice, was the main limitation to the resolution of the diffeomorphisms that could be learned. This paper describes an algorithm based on recursive refinement that lowers the memory requirement to O(ρ²) memory and O(ρ² log(ρ)) computation. Another improvement regards the estimation the diffeomorphism uncertainty, which is used to represent the sensor's limited field of view; the improved method obtains a more accurate estimation of the uncertainty by checking the consistency of a learned diffeomorphism and its independently learned inverse. The methods are tested on two robotic systems (a pan-tilt camera and a 5-DOF manipulator).

source code/logs to come soon

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