Attention mechanism has shown great performance and efficiency in a lot of deep learning models, in which relative position encoding plays a crucial role. However, when introducing attention to manifolds, there is no canonical local coordinate system to parameterize neighborhoods.

Attention mechanism has shown great performance and efficiency in a lot of deep learning models, in which relative position encoding plays a crucial role. However, when introducing attention to manifolds, there is no canonical local coordinate system to parameterize neighborhoods. To address this issue, we propose an equivariant transformer to make our model agnostic to the orientation of local coordinate systems (\textit{i.e.}, gauge equivariant), which employs multi-head self-attention to jointly incorporate both position-based and content-based information. To enhance expressive ability, we adopt regular field of cyclic groups as feature fields in intermediate layers, and propose a novel method to parallel transport the feature vectors in these fields. In addition, we project the position vector of each point onto its local coordinate system to disentangle the orientation of the coordinate system in ambient space (\textit{i.e.}, global coordinate system), achieving rotation invariance. To the best of our knowledge, we are the first to introduce gauge equivariance to self-attention, thus name our model Gauge Equivariant Transformer (GET), which can be efficiently implemented on triangle meshes. Extensive experiments show that GET achieves state-of-the-art performance on two common recognition tasks.

Understanding the computational power of mobile robot systems is a fundamental challenge in distributed computing. While prior work has focused on pairwise separations between models, we explore how robot capabilities, light observability, and scheduler synchrony interact in more complex ways. We first show that the Exponential Times Expansion (ETE) problem is solvable only in the strongest model -- fully-synchronous robots with full mutual lights ($\mathcal{LUMT}^F$). We then introduce the Hexagonal Edge Traversal (HET) and TAR(d)* problems to demonstrate how internal memory and lights interact with synchrony: under weak synchrony, internal memory alone is insufficient, while full synchrony can substitute for both lights and memory. In the asynchronous setting, we classify problems such as LP-MLCv, VEC, and ZCC to show fine-grained separations between $\mathcal{FSTA}$ and $\mathcal{FCOM}$ robots. We also analyze Vertex Traversal Rendezvous (VTR) and Leave Place Convergence (LP-Cv), illustrating the limitations of internal memory in symmetric settings. These results extend the known separation map of 14 canonical robot models, revealing structural phenomena only visible through higher-order comparisons. Our work provides new impossibility criteria and deepens the understanding of how observability, memory, and synchrony collectively shape the computational power of mobile robots.

Sampling is a fundamental and arguably very important task with numerous applications in Machine Learning.

Self-localization is an important technology for automating bulldozers. Conventional bulldozer self-localization systems rely on RTK-GNSS (Real Time Kinematic-Global Navigation Satellite Systems). However, RTK-GNSS signals are sometimes lost in certain mining conditions. Therefore, self-localization methods that do not depend on RTK-GNSS are required. In this paper, we propose a machine learning-based self-localization method for bulldozers. The proposed method consists of two steps: estimating local velocities using a machine learning model from internal sensors, and incorporating these estimates into an Extended Kalman Filter (EKF) for global localization. We also created a novel dataset for bulldozer odometry and conducted experiments across various driving scenarios, including slalom, excavation, and driving on slopes. The result demonstrated that the proposed self-localization method suppressed the accumulation of position errors compared to kinematics-based methods, especially when slip occurred. Furthermore, this study showed that bulldozer-specific sensors, such as blade position sensors and hydraulic pressure sensors, contributed to improving self-localization accuracy.

Attention mechanism has shown great performance and efficiency in a lot of deep learning models, in which relative position encoding plays a crucial role. However, when introducing attention to manifolds, there is no canonical local coordinate system to parameterize neighborhoods. To address this issue, we propose an equivariant transformer to make our model agnostic to the orientation of local coordinate systems (\textit{i.e.}, gauge equivariant), which employs multi-head self-attention to jointly incorporate both position-based and content-based information. To enhance expressive ability, we adopt regular field of cyclic groups as feature fields in intermediate layers, and propose a novel method to parallel transport the feature vectors in these fields. In addition, we project the position vector of each point onto its local coordinate system to disentangle the orientation of the coordinate system in ambient space (\textit{i.e.}, global coordinate system), achieving rotation invariance.

A metamorphic robotic system (MRS) consists of anonymous modules, each of which autonomously moves in the 2D square grid by sliding and rotation with keeping connectivity among the modules. Existing literature considers distributed coordination among modules so that they collectively form a single MRS. In this paper, we consider distributed coordination for two MRSs. We first present a rendezvous algorithm that makes the two MRSs gather so that each module can observe all the other modules. Then, we present a merge algorithm that makes the two MRSs assemble and establish connectivity after rendezvous is finished. These two algorithms assume that each MRS consists of five modules, that do not have a common coordinate system. Finally, we show that five modules for each MRS is necessary to solve the rendezvous problem. To the best of our knowledge, our result is the first result on distributed coordination of multiple MRSs.

The paper focuses on modeling and experimental evaluation of a quadcopter team configurable coordination guided by a single quadruped robot. We consider the quadcopter team as particles of a two-dimensional deformable body and propose a two-dimensional affine transformation model for safe and collision-free configurable coordination of this heterogeneous robotic system. The proposed affine transformation is decomposed into translation, that is specified by the quadruped global position, and configurable motion of the quadcopters, which is determined by a nonsingular Jacobian matrix so that the quadcopter team can safely navigate a constrained environment while avoiding collision. We propose two methods to experimentally evaluate the proposed heterogeneous robot coordination model. The first method measures real positions of quadcopters, quadruped, and environmental objects all with respect to the global coordinate system. On the other hand, the second method measures position with respect to the local coordinate system fixed on the dog robot which in turn enables safe planning the Jacobian matrix of the quadcopter team while the world is virtually approached the robotic system.