This paper proposes an equivariant neural network that takes data in any finite-dimensional semi-simple Lie algebra as input. The corresponding group acts on the Lie algebra as adjoint operations, making our proposed network adjoint-equivariant. Our framework generalizes the Vector Neurons, a simple $\mathrm{SO}(3)$-equivariant network, from 3-D Euclidean space to Lie algebra spaces, building upon the invariance property of the Killing form. Furthermore, we propose novel Lie bracket layers and geometric channel mixing layers that extend the modeling capacity. Experiments are conducted for the $\mathfrak{so}(3)$, $\mathfrak{sl}(3)$, and $\mathfrak{sp}(4)$ Lie algebras on various tasks, including fitting equivariant and invariant functions, learning system dynamics, point cloud registration, and homography-based shape classification. Our proposed equivariant network shows wide applicability and competitive performance in various domains.

This paper develops a novel slip estimator using the invariant observer design theory and Disturbance Observer (DOB). The proposed state estimator for mobile robots is fully proprioceptive and combines data from an inertial measurement unit and body velocity within a Right Invariant Extended Kalman Filter (RI-EKF). By embedding the slip velocity into SE3(3) matrix Lie group, the developed DOB-based RI-EKF provides real-time velocity and slip velocity estimates on different terrains. Experimental results using a Husky wheeled robot confirm the mathematical derivations and effectiveness of the proposed method in estimating the observable state variables. Open-source software is available for download and reproducing the presented results.

This paper reports on a novel nonparametric rigid point cloud registration framework, Semantic Continuous Visual Odometry (CVO), that jointly integrates geometric and semantic measurements such as color or semantic labels into the alignment process and does not require explicit data association. The point clouds are represented as nonparametric functions in a reproducible kernel Hilbert space. The alignment problem is formulated as maximizing the inner product between two functions, essentially a sum of weighted kernels, each of which exploits the local geometric and semantic features. As a result of the continuous models, analytical gradients can be computed, and a local solution can be obtained by optimization over the rigid body transformation group. Besides, we present a new point cloud alignment metric that is intrinsic to the proposed framework and takes into account geometric and semantic information. The evaluations using publicly available stereo and RGB-D datasets show that the proposed method outperforms state-of-the-art outdoor and indoor frame-to-frame registration methods. An open-source GPU implementation is also provided.

Stories are diverse and highly personalized, resulting in a large possible output space for story generation. Existing end-to-end approaches produce monotonous stories because they are limited to the vocabulary and knowledge in a single training dataset. This paper introduces KG-Story, a three-stage framework that allows the story generation model to take advantage of external Knowledge Graphs to produce interesting stories. KG-Story distills a set of representative words from the input prompts, enriches the word set by using external knowledge graphs, and finally generates stories based on the enriched word set. This distill-enrich-generate framework allows the use of external resources not only for the enrichment phase, but also for the distillation and generation phases. In this paper, we show the superiority of KG-Story for visual storytelling, where the input prompt is a sequence of five photos and the output is a short story. Per the human ranking evaluation, stories generated by KG-Story are on average ranked better than that of the state-of-the-art systems. Our code and output stories are available at https://github.com/zychen423/KE-VIST.

In this paper, Kalman filter is designed and implemented on a heat deformation tester (HDT) to estimate the LVDT sensor information from a noisy measured data sequence. In simulation and test, the output response of Kalman filter can separate noise from reference signal and the outcome is closely matched with reference signal. The response of low-pass IIR filter is smooth and can also separate noise but some time delay is presented. The mean squared error (MSE) of low-pass IIR filter is 0.6354 while the MSE of Kalman filter reduces to 0.1467, a significant improvement by 4 times. Also, the computational efficiency of Kalman filter is better than that of low-pass IIR filter in this application. Both filtering algorithms are implemented and programmed into a heat deformation tester (HDT). The performance is impressive.