6,348 research outputs found
Stein Variational Guided Model Predictive Path Integral Control: Proposal and Experiments with Fast Maneuvering Vehicles
This paper presents a novel Stochastic Optimal Control (SOC) method based on
Model Predictive Path Integral control (MPPI), named Stein Variational Guided
MPPI (SVG-MPPI), designed to handle rapidly shifting multimodal optimal action
distributions. While MPPI can find a Gaussian-approximated optimal action
distribution in closed form, i.e., without iterative solution updates, it
struggles with multimodality of the optimal distributions, such as those
involving non-convex constraints for obstacle avoidance. This is due to the
less representative nature of the Gaussian. To overcome this limitation, our
method aims to identify a target mode of the optimal distribution and guide the
solution to converge to fit it. In the proposed method, the target mode is
roughly estimated using a modified Stein Variational Gradient Descent (SVGD)
method and embedded into the MPPI algorithm to find a closed-form
"mode-seeking" solution that covers only the target mode, thus preserving the
fast convergence property of MPPI. Our simulation and real-world experimental
results demonstrate that SVG-MPPI outperforms both the original MPPI and other
state-of-the-art sampling-based SOC algorithms in terms of path-tracking and
obstacle-avoidance capabilities. Source code:
https://github.com/kohonda/proj-svg_mppiComment: 7 pages, 5 figure
Large amplitude behavior of the Grinfeld instability: a variational approach
In previous work, we have performed amplitude expansions of the continuum
equations for the Grinfeld instability and carried them to high orders.
Nevertheless, the approach turned out to be restricted to relatively small
amplitudes. In this article, we use a variational approach in terms of
multi-cycloid curves instead. Besides its higher precision at given order, the
method has the advantages of giving a transparent physical meaning to the
appearance of cusp singularities and of not being restricted to interfaces
representable as single-valued functions. Using a single cycloid as ansatz
function, the entire calculation can be performed analytically, which gives a
good qualitative overview of the system. Taking into account several but few
cycloid modes, we obtain remarkably good quantitative agreement with previous
numerical calculations. With a few more modes taken into consideration, we
improve on the accuracy of those calculations. Our approach extends them to
situations involving gravity effects. Results on the shape of steady-state
solutions are presented at both large stresses and amplitudes. In addition,
their stability is investigated.Comment: subm. to EPJ
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