Designing Sparse Reliable Pose-Graph SLAM: A Graph-Theoretic Approach

In this paper, we aim to design sparse D-optimal (determinantoptimal) pose-graph SLAM problems through the synthesis of sparse graphs with the maximum weighted number of spanning trees. Characterizing graphs with the maximum number of spanning trees is an open problem in general. To tackle this problem, several new theoretical results are established in this paper, including the monotone log-submodularity of the weighted number of spanning trees. By exploiting these structures, we design a complementary pair of near-optimal efficient approximation algorithms with provable guarantees. Our theoretical results are validated using random graphs and a publicly available pose-graph SLAM dataset.Comment: WAFR 201

Surface Ocean Enstrophy, Kinetic Energy Fluxes and Spectra from Satellite Altimetry

Enstrophy, kinetic energy (KE) fluxes and spectra are estimated in different parts of the mid-latitudinal oceans via altimetry data. To begin with, using geostrophic currents derived from sea-surface height anomaly data provided by AVISO, we confirm the presence of a strong inverse flux of surface KE at scales larger than approximately 250 km. We then compute enstrophy fluxes to help develop a clearer picture of the underlying dynamics at smaller scales, i.e., 250 km to 100 km. Here, we observe a robust enstrophy cascading regime, wherein the enstrophy shows a large forward flux and the KE spectra follow an approximate $k^{-3.5}$ power-law. Given the rotational character of the flow, not only is this large scale inverse KE and smaller scale forward enstrophy transfer scenario consistent with expectations from idealized studies of three-dimensional rapidly-rotating and strongly-stratified turbulence, it also agrees with detailed analyses of spectra and fluxes in the upper level midlatitude troposphere. Decomposing the currents into components with greater and less than 100 day variability (referred to as seasonal and eddy, respectively), we find that, in addition to the eddy-eddy contribution, the seasonal-eddy and seasonal-seasonal fluxes play a significant role in the inverse (forward) flux of KE (enstrophy) at scales larger (smaller) than about 250 km. Taken together, we suspect, it is quite possible that, from about 250 km to 100 km, the altimeter is capturing the relatively steep portion of a surface oceanic counterpart of the upper tropospheric Nastrom-Gage spectrum.Comment: 10 pages, 7 figure

Generating Behaviorally Diverse Policies with Latent Diffusion Models

Recent progress in Quality Diversity Reinforcement Learning (QD-RL) has enabled learning a collection of behaviorally diverse, high performing policies. However, these methods typically involve storing thousands of policies, which results in high space-complexity and poor scaling to additional behaviors. Condensing the archive into a single model while retaining the performance and coverage of the original collection of policies has proved challenging. In this work, we propose using diffusion models to distill the archive into a single generative model over policy parameters. We show that our method achieves a compression ratio of 13x while recovering 98% of the original rewards and 89% of the original coverage. Further, the conditioning mechanism of diffusion models allows for flexibly selecting and sequencing behaviors, including using language. Project website: https://sites.google.com/view/policydiffusion/hom

Physics-based Simulation of Continuous-Wave LIDAR for Localization, Calibration and Tracking

Light Detection and Ranging (LIDAR) sensors play an important role in the perception stack of autonomous robots, supplying mapping and localization pipelines with depth measurements of the environment. While their accuracy outperforms other types of depth sensors, such as stereo or time-of-flight cameras, the accurate modeling of LIDAR sensors requires laborious manual calibration that typically does not take into account the interaction of laser light with different surface types, incidence angles and other phenomena that significantly influence measurements. In this work, we introduce a physically plausible model of a 2D continuous-wave LIDAR that accounts for the surface-light interactions and simulates the measurement process in the Hokuyo URG-04LX LIDAR. Through automatic differentiation, we employ gradient-based optimization to estimate model parameters from real sensor measurements.Comment: Published at ICRA 202

Conditionally Combining Robot Skills using Large Language Models

This paper combines two contributions. First, we introduce an extension of the Meta-World benchmark, which we call "Language-World," which allows a large language model to operate in a simulated robotic environment using semi-structured natural language queries and scripted skills described using natural language. By using the same set of tasks as Meta-World, Language-World results can be easily compared to Meta-World results, allowing for a point of comparison between recent methods using Large Language Models (LLMs) and those using Deep Reinforcement Learning. Second, we introduce a method we call Plan Conditioned Behavioral Cloning (PCBC), that allows finetuning the behavior of high-level plans using end-to-end demonstrations. Using Language-World, we show that PCBC is able to achieve strong performance in a variety of few-shot regimes, often achieving task generalization with as little as a single demonstration. We have made Language-World available as open-source software at https://github.com/krzentner/language-world/