We propose a diffusion approximation method to the continuous-state Markov decision processes that can be utilized to address autonomous navigation and control in unstructured off-road environments. In contrast to most decision-theoretic planning frameworks that assume fully known state transition models, we design a method that eliminates such a strong assumption that is often extremely difficult to engineer in reality. We first take the second-order Taylor expansion of the value function. The Bellman optimality equation is then approximated by a partial differential equation, which only relies on the first and second moments of the transition model. By combining the kernel representation of the value function, we design an efficient policy iteration algorithm whose policy evaluation step can be represented as a linear system of equations characterized by a finite set of supporting states. We first validate the proposed method through extensive simulations in 2 D obstacle avoidance and 2.5 D terrain navigation problems. The results show that the proposed approach leads to a much superior performance over several baselines. We then develop a system that integrates our decision-making framework with onboard perception and conduct real-world experiments in both cluttered indoor and unstructured outdoor environments. The results from the physical systems further demonstrate the applicability of our method in challenging real-world environments.
- Award ID(s):
- 2134178
- NSF-PAR ID:
- 10434221
- Date Published:
- Journal Name:
- International Conference on Learning Representations
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Understanding the geometry of collision-free configuration space (C-free) in the presence of Cartesian-space obstacles is an essential ingredient for collision-free motion planning. While it is possible to check for collisions at a point using standard algorithms, to date no practical method exists for computing C-free regions with rigorous certificates due to the complexity of mapping Cartesian-space obstacles through the kinematics. In this work, we present the first to our knowledge rigorous method for approximately decomposing a rational parametrization of C-free into certified polyhedral regions. Our method, called C-Iris (C-space Iterative Regional Inflation by Semidefinite programming), generates large, convex polytopes in a rational parameterization of the configuration space which are rigorously certified to be collision-free. Such regions have been shown to be useful for both optimization-based and randomized motion planning. Based on convex optimization, our method works in arbitrary dimensions, only makes assumptions about the convexity of the obstacles in the 3D Cartesian space, and is fast enough to scale to realistic problems in manipulation. We demonstrate our algorithm’s ability to fill a non-trivial amount of collision-free C-space in several 2-DOF examples where the C-space can be visualized, as well as the scalability of our algorithm on a 7-DOF KUKA iiwa, a 6-DOF UR3e, and 12-DOF bimanual manipulators. An implementation of our algorithm is open-sourced in Drake . We furthermore provide examples of our algorithm in interactive Python notebooks .
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Abstract Motivation Neural networks have been widely used to analyze high-throughput microscopy images. However, the performance of neural networks can be significantly improved by encoding known invariance for particular tasks. Highly relevant to the goal of automated cell phenotyping from microscopy image data is rotation invariance. Here we consider the application of two schemes for encoding rotation equivariance and invariance in a convolutional neural network, namely, the group-equivariant CNN (G-CNN), and a new architecture with simple, efficient conic convolution, for classifying microscopy images. We additionally integrate the 2D-discrete-Fourier transform (2D-DFT) as an effective means for encoding global rotational invariance. We call our new method the Conic Convolution and DFT Network (CFNet).
Results We evaluated the efficacy of CFNet and G-CNN as compared to a standard CNN for several different image classification tasks, including simulated and real microscopy images of subcellular protein localization, and demonstrated improved performance. We believe CFNet has the potential to improve many high-throughput microscopy image analysis applications.
Availability and implementation Source code of CFNet is available at: https://github.com/bchidest/CFNet.
Supplementary information Supplementary data are available at Bioinformatics online.
- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- The DOI is not currently available.
