Navigation in Lorentz Finsler geometry induces isoparametric hypersurfaces.
problem Defining and analyzing isoparametric hypersurfaces in Lorentz Finsler geometry.
method Using a navigation process with a Finsler metric and a tangent vector field, isoparametric functions and hypersurfaces are defined and analyzed.
result Local correspondences between isoparametric functions and hypersurfaces are established.
The paper classifies isoparametric hypersurfaces in Randers space forms.
problem Classifying isoparametric hypersurfaces in Randers space forms.
method Anisotropic submanifolds and isoparametric hypersurfaces in Randers space forms (N,F) with (h,W) were studied.
result The isoparametric hypersurfaces in a Randers space form (N,F) are the same as in Riemannian space, despite different isoparametric functions.
In this paper, I study the isoparametric hypersurfaces in a Randers sphere (Sn,F) of constant flag curvature, with the navigation datum (h,W). I prove that an isoparametric hypersurface M for the standard round sphere (Sn,h) which is tangent to W remains isoparametric for (Sn,F) after the navigation proc…
This paper studies three aspects around dimension datum: (1), a generalization of the dimension datum, which we call the tau-dimension datum; (2), dimension data of disconnected subgroups; (3), compactness of isospectral sets of normal homogeneous spaces.
The paper explores rational functions with 3 branching points on the Riemann sphere.
problem Existence of rational functions with specific branching points.
method Utilizes complex analysis to establish properties of rational functions.
result Identifies new types of exceptional branching data.
Given a smooth bounded domain Ø⊆R2, we consider the equation $\D v = 2 v_x \wedge v_y$ in Ø, where v:Ø→R3. We prescribe Dirichlet boundary datum, and consider the case in which this datum converges to zero. An asymptotic study of the corresponding Euler functional is performed, analyzing multiple…
Study of tori of revolution under Willmore flow converges to Clifford Torus.
problem Long-time behavior and convergence of Willmore flow for tori of revolution.
method Gradient flow of Willmore energy for tori of revolution, analyzing energy threshold and convergence to Clifford Torus.
result Convergence of Willmore flow to Clifford Torus for initial energy below 8π.
HRL4IN tackles interactive navigation tasks with mobile manipulators, improving efficiency and performance.
problem Interactive Navigation tasks require mobile manipulators to perform various actions, but choosing the right part of the embodiment is inefficient.
method HRL4IN uses a hierarchical reinforcement learning architecture to handle heterogeneous phases of navigation and manipulation, selecting the appropriate part of the embodiment for each phase.
result HRL4IN significantly outperforms flat PPO and HAC in terms of task performance and energy efficiency.
Introduces a natural parallel translation for navigation data.
problem Navigation data geometric representation and parallelism.
method Introduces a natural parallel translation using Riemannian parallelism.
result The natural parallel translation preserves the Randers norm and has a finite-dimensional holonomy group.
Challenge to separate Earth's magnetic field from vehicle's magnetic field for accurate navigation.
problem Separate Earth's magnetic field from vehicle's magnetic field for accurate magnetic navigation.
method Use machine learning (ML) and integrate physics of magnetic navigation (SciML) to remove aircraft magnetic field from total magnetic field.
result A model can be constructed to effectively remove aircraft magnetic field from the dataset.
VALAN is a framework for navigation agents in photo-realistic environments.
problem Developing agents for indoor navigation tasks.
method Deep reinforcement learning with SEED RL architecture.
result VALAN framework can solve a variety of RL problems.
The paper solves navigation problems on conic Kropina manifolds and establishes curvature relationships.
problem Navigation problems on conic Kropina manifolds.
method Analyzes the solution of navigation problems and establishes curvature relationships.
result The solution to navigation problems on conic Kropina manifolds must be either a Randers metric or a Kropina metric.
Robotic navigation improves with RL and ultrasound images.
problem Improving accuracy in robotic navigation for ultrasound-guided procedures.
method Combines deep Q-networks with ultrasound images and binary classifier.
result Significantly improved navigation accuracy compared to pure RL and SL.
Deep RL improves robot navigation in images.
problem Applying deep RL to visual navigation in realistic environments.
method Extended A2C algorithm with auxiliary tasks for segmentation, depth prediction, and target prediction.
result Method outperforms state-of-the-art visual navigation methods.
Improved robot navigation using multi-head attention for natural language instructions.
problem Improving robot navigation in unfamiliar environments.
method Proposes a multi-head attention mechanism blending layer in a neural network model.
result Significant performance gains in translating instructions for unseen environments.
The problem of pursuing a moving target is always one of the main topics in navigation. In the literatures, there are two well-known algorithms called Pure Pursuit and Pure Rendezvous navigation in the 3-dimensional space R3. In this paper, these two methods are combined to introduce a novel family of pursu…
Ancient solutions found for a specific flow on symplectic half-flat structures.
problem Existence of solutions for a particular geometric flow.
method Analyzes Type IIA flow on symplectic half-flat SU(3)-structures.
result Existence of ancient, immortal, and eternal solutions under suitable conditions.
Mobile robot navigation in complex and dynamic environments is a challenging but important problem. Reinforcement learning approaches fail to solve these tasks efficiently due to reward sparsities, temporal complexities and high-dimensionality of sensorimotor spaces which are inherent in such problems. We present a nov…
We prove that the Calabi-Yau equation on the Kodaira-Thurston manifold has a unique solution for every S1-invariant initial datum.
SLAM-net learns to navigate visually in challenging indoor environments.
problem Challenges in SLAM for visual robot navigation, especially in noisy conditions.
method Differentiable SLAM Network (SLAM-net) that encodes a particle filter SLAM algorithm in a differentiable graph and learns components through backpropagation.
result Significantly outperforms ORB-SLAM in noisy conditions and improves the Habitat Challenge 2020 PointNav task.
Proves existence of multi-phase flows from arbitrary initial data.
problem Non-uniqueness issue in Brakke flows.
method Global existence proof for multi-phase mean curvature flow.
result Validates explicit identity for evolving grain volumes.
Improves AI agents' 3D navigation by learning from failures and 3D spatial relationships.
problem Challenges in data efficiency, obstacle avoidance, and generalization in 3D visual navigation.
method Incorporates attention on 3D spatial relationships and a target skill extension module into DRL framework.
result Significantly improves navigation performance and generalization across targets and scenes.
Bayesian model for energy consumption helps electric vehicles navigate efficiently.
problem Limited battery capacity in electric vehicles makes energy efficient navigation challenging.
method Developed an online learning framework using Bayesian models and exploration strategies like Thompson Sampling.
result Established rigorous regret bounds for Thompson Sampling in both single-agent and multi-agent settings.
A Bayesian treatment of latent directed graph structure for non-iid data is provided where each child datum is sampled with a directed conditional dependence on a single unknown parent datum. The latent graph structure is assumed to lie in the family of directed out-tree graphs which leads to efficient Bayesian inferen…
This work analyzes minimum-time navigation on Riemannian manifolds using Finsler geometry.
problem Minimum-time navigation on Riemannian manifolds.
method Finsler geometry, introducing superwind concept, extending (α,β)-metrics. result Time-minimizing geodesics and necessary/sufficient conditions for strong convexity.
The paper explains geometric correspondences for homothetic navigation.
problem Understanding geodesic and Jacobi field correspondences in homothetic navigation.
method Providing conceptual explanations and shortcuts to formulas.
result Directly seeing local correspondence between isoparametric functions or hypersurfaces.
To a branched cover between closed, connected and orientable surfaces one associates a "branch datum", which consists of the two surfaces, the total degree d, and the partitions of d given by the collections of local degrees over the branching points. This datum must satisfy the Riemann-Hurwitz formula. A "candidate su…
Deep learning agent improves pedestrian navigation in urban environments.
problem Autonomous driving among pedestrians in urban areas.
method Multi-objective deep reinforcement learning using a deep Q-learning variant.
result The multi-objective DQN agent outperforms single-objective DQN in various environments.
Meta-algorithm reduces exploration steps in changing CMPs.
problem Navigating in environments where transition probabilities change abruptly.
method MNM learning meta-algorithm, exploration steps as performance measure.
result Upper bound on exploration steps in terms of changes.
Global existence and convergence of heat flow for p-harmonic maps.
problem Global existence and convergence of heat flow for p-harmonic maps between manifolds.
method Analysis of heat flow equations for p-harmonic maps.
result Global existence and convergence of heat flow for p-harmonic maps under certain conditions.
Bayesian model for energy-efficient EV navigation.
problem Limited battery capacity in electric vehicles.
method Bayesian modeling and online learning framework with exploration strategies.
result Established rigorous regret bounds for Thompson Sampling.
Solves time-minimizing navigation on a mountain slope using Riemann-Finsler geometry.
problem Time-minimizing navigation on a mountain slope under gravity.
method Riemann-Finsler geometry, Zermelo navigation problem, anisotropic deformation of the background Riemannian metric, rescaled gravitational wind.
result A new Finsler metric for optimal navigation on slippery mountain slopes.
The paper develops a method to learn navigation costs from expert demonstrations in partially observable environments.
problem Learning navigation costs from expert demonstrations in partially observable environments.
method Develops a cost function representation composed of a probabilistic occupancy encoder and a cost encoder, optimized by differentiating the error between demonstrated controls and a control policy computed from the cost encoder.
result The method outperforms baseline IRL algorithms in robot navigation tasks, improving both training and test-time efficiency.
New algorithms solve time-dependent navigation problems, including zig-zag paths.
problem Finding optimal paths in moving water with varying speed profiles.
method Lorentz-Finsler geometry, novel computational algorithms.
result Optimal paths may involve zig-zag trajectories due to tacking behavior.
Improved UAV navigation and landing using deep learning.
problem Autonomous navigation and landing of UAVs with high accuracy.
method Multimodal fusion of visual and inertial sensor data using deep neural networks.
result 25% improvement in pose estimation accuracy compared to traditional methods.
OtoWorld helps agents learn to navigate by listening in interactive environments.
problem Training agents to navigate using auditory information.
method Interactive environment with agents learning to listen and navigate.
result Agents can win at OtoWorld, a navigation game with sound sources.
Proposes a new prior for deep generative models to capture latent properties.
problem Complex non-linear relationships between data and latent properties.
method Factorial mixture prior with Gaussian mixture models for quantization.
result Empirically evaluated method for learning discrete properties in unsupervised or semi-supervised settings.
Paper introduces timing-based adversarial attacks on DRL-based navigation systems.
problem Vulnerability of DRL-based navigation systems to adversarial attacks.
method Timing-based adversarial strategies using physical noise patterns.
result Adversarial timing attacks significantly degrade DRL-based navigation performance.
UAV uses RL to navigate, map, and detect targets in unknown environments.
problem Optimizing UAV trajectory for accurate mapping and target detection in unknown environments.
method Formulated as an MDP, UAV uses RL to infer navigation policy.
result UAV autonomously explores high target detection areas while reconstructing the environment.
This research introduces an autonomous robot navigation method using reinforcement learning.
problem Improving robot navigation in complex environments.
method Deep Q Network (DQN) and Proximal Policy Optimization (PPO) models for path planning and decision-making.
result The models enhance robot navigation ability and adaptive learning in unknown environments.
In this paper, we study Zermelo navigation on Riemannian manifolds and use that to solve a long standing problem in Finsler geometry. Namely, the complete classification of strongly convex Randers metrics of constant flag curvature.
Capsule Networks improve autonomous navigation in sparse environments.
problem Challenges in reinforcement learning for sparse reward environments.
method Caps-EM pairs CapsNets with Advantage Actor Critic, using fewer parameters.
result Caps-EM achieves significant time improvements and fewer parameters compared to competing methods.
Rational maps structure theorem with geometric decomposition and realizability proof.
problem Realizability of rational maps branch data.
method Geometric decomposition of pullback metric into footballs and application to realizability.
result Realizability of branch data for rational maps when k>l+1. The paper addresses errors in online selective conformal prediction and proposes new strategies to ensure valid inference.
problem Online selective conformal prediction's exchangeability issues and false coverage rate control problems.
method Evaluation and correction of existing calibration selection strategies, proposing new ones that preserve exchangeability.
result Novel calibration selection strategies ensure both selection-conditional coverage and FCR control.
Agents learn to communicate and solve navigation tasks efficiently.
problem Understanding and developing communication in artificial agents.
method Multi-agent navigation tasks in gridworld environments.
result Agents develop an interpretable communication protocol that optimally solves tasks.
We present a novel human-aware navigation approach, where the robot learns to mimic humans to navigate safely in crowds. The presented model, referred to as DeepMoTIon, is trained with pedestrian surveillance data to predict human velocity in the environment. The robot processes LiDAR scans via the trained network to n…
Consider an assistive system that guides visually impaired users through speech and haptic feedback to their destination. Existing robotic and ubiquitous navigation technologies (e.g., portable, ground, or wearable systems) often operate in a generic, user-agnostic manner. However, to minimize confusion and navigation …
VUSFA improves transfer learning for target-driven navigation in AI2THOR.
problem Improving transfer reinforcement learning for complex visual navigation tasks.
method Introducing SFDP and Variational Information Bottlenecks to A3C agent.
result VUSFA achieves state-of-the-art performance and generalizability.