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Spherical harmonics are a favorable technique for 3D representation, employing a frequency-based approach through the spherical harmonic transform (SHT). Typically, SHT is performed using equiangular sampling grids. However, these grids are non-uniform on spherical surfaces and exhibit local anisotropy, a common limitation in existing spherical harmonic decomposition methods. This paper proposes a 3D representation method using Fibonacci Spherical Harmonics (FSH3D). We introduce a spherical Fibonacci grid (SFG), which is more uniform than equiangular grids for SHT in the frequency domain. Our method employs analytical weights for SHT on SFG, effectively assigning sampling errors to spherical harmonic degrees higher than the recovered band-limited function. This provides a novel solution for spherical harmonic transformation on non-equiangular grids. The key advantages of our FSH3D method include: 1) With the same number of sampling points, SFG captures more features without bias compared to equiangular grids; 2) The root mean square error of 32-degree spherical harmonic coefficients is reduced by approximately 34.6% for SFG compared to equiangular grids; and 3) FSH3D offers more stable frequency domain representations, especially for rotating functions. FSH3D enhances the stability of frequency domain representations under rotational transformations. Its application in 3D shape reconstruction and 3D shape classification results in more accurate and robust representations. Our code is publicly available at https://github.com/Miraclelzk/Fibonacci-Spherical-Harmonics., Comment: 11 pages, 11 figures

We present a novel approach for image-goal navigation, where an agent navigates with a goal image rather than accurate target information, which is more challenging. Our goal is to decouple the learning of navigation goal planning, collision avoidance, and navigation ending prediction, which enables more concentrated learning of each part. This is realized by four different modules. The first module maintains an obstacle map during robot navigation. The second predicts a long-term goal on the real-time map periodically, which can thus convert an image-goal navigation task to several point-goal navigation tasks. To achieve these point-goal navigation tasks, the third module plans collision-free command sets for navigating to these long-term goals. The final module stops the robot properly near the goal image. The four modules are designed or maintained separately, which helps cut down the search time during navigation and improves the generalization to previously unseen real scenes. We evaluate the method in both a simulator and in the real world with a mobile robot. The results in real complex environments show that our method attains at least a $17\%$ increase in navigation success rate and a $23\%$ decrease in navigation collision rate over some state-of-the-art models., Comment: 9 pages

We present a target-driven navigation system to improve mapless visual navigation in indoor scenes. Our method takes a multi-view observation of a robot and a target as inputs at each time step to provide a sequence of actions that move the robot to the target without relying on odometry or GPS at runtime. The system is learned by optimizing a combinational objective encompassing three key designs. First, we propose that an agent conceives the next observation before making an action decision. This is achieved by learning a variational generative module from expert demonstrations. We then propose predicting static collision in advance, as an auxiliary task to improve safety during navigation. Moreover, to alleviate the training data imbalance problem of termination action prediction, we also introduce a target checking module to differentiate from augmenting navigation policy with a termination action. The three proposed designs all contribute to the improved training data efficiency, static collision avoidance, and navigation generalization performance, resulting in a novel target-driven mapless navigation system. Through experiments on a TurtleBot, we provide evidence that our model can be integrated into a robotic system and navigate in the real world. Videos and models can be found in the supplementary material., Comment: accepted by IEEE Robotics and Automation Letters

To enhance the cross-target and cross-scene generalization of target-driven visual navigation based on deep reinforcement learning (RL), we introduce an information-theoretic regularization term into the RL objective. The regularization maximizes the mutual information between navigation actions and visual observation transforms of an agent, thus promoting more informed navigation decisions. This way, the agent models the action-observation dynamics by learning a variational generative model. Based on the model, the agent generates (imagines) the next observation from its current observation and navigation target. This way, the agent learns to understand the causality between navigation actions and the changes in its observations, which allows the agent to predict the next action for navigation by comparing the current and the imagined next observations. Cross-target and cross-scene evaluations on the AI2-THOR framework show that our method attains at least a $10\%$ improvement of average success rate over some state-of-the-art models. We further evaluate our model in two real-world settings: navigation in unseen indoor scenes from a discrete Active Vision Dataset (AVD) and continuous real-world environments with a TurtleBot.We demonstrate that our navigation model is able to successfully achieve navigation tasks in these scenarios. Videos and models can be found in the supplementary material., Comment: corresponding author: Kai Xu (kevin.kai.xu@gmail.com) and Jun Wang (wjun@nuaa.edu.cn), accepted by IEEE Robotics and Automation Letters

We propose improving the cross-target and cross-scene generalization of visual navigation through learning an agent that is guided by conceiving the next observations it expects to see. This is achieved by learning a variational Bayesian model, called NeoNav, which generates the next expected observations (NEO) conditioned on the current observations of the agent and the target view. Our generative model is learned through optimizing a variational objective encompassing two key designs. First, the latent distribution is conditioned on current observations and the target view, leading to a model-based, target-driven navigation. Second, the latent space is modeled with a Mixture of Gaussians conditioned on the current observation and the next best action. Our use of mixture-of-posteriors prior effectively alleviates the issue of over-regularized latent space, thus significantly boosting the model generalization for new targets and in novel scenes. Moreover, the NEO generation models the forward dynamics of agent-environment interaction, which improves the quality of approximate inference and hence benefits data efficiency. We have conducted extensive evaluations on both real-world and synthetic benchmarks, and show that our model consistently outperforms the state-of-the-art models in terms of success rate, data efficiency, and generalization., Comment: added experiments, accepted by AAAI, Corresponding author: Kai Xu (kevin.kai.xu@gmail.com)