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Existing navigation systems mostly consider "success" when the robot reaches within 1m radius to a goal. This precision is insufficient for emerging applications where the robot needs to be positioned precisely relative to an object for downstream tasks, such as docking, inspection, and manipulation. To this end, we design and implement Aim-My-Robot (AMR), a local navigation system that enables a robot to reach any object in its vicinity at the desired relative pose, with centimeter-level precision. AMR achieves high precision and robustness by leveraging multi-modal perception, precise action prediction, and is trained on large-scale photorealistic data generated in simulation. AMR shows strong sim2real transfer and can adapt to different robot kinematics and unseen objects with little to no fine-tuning.

We focus on agile, continuous, and terrain-adaptive jumping of quadrupedal robots in discontinuous terrains such as stairs and stepping stones. Unlike single-step jumping, continuous jumping requires accurately executing highly dynamic motions over long horizons, which is challenging for existing approaches. To accomplish this task, we design a hierarchical learning and control framework, which consists of a learned heightmap predictor for robust terrain perception, a reinforcement-learning-based centroidal-level motion policy for versatile and terrain-adaptive planning, and a low-level model-based leg controller for accurate motion tracking. In addition, we minimize the sim-to-real gap by accurately modeling the hardware characteristics. Our framework enables a Unitree Go1 robot to perform agile and continuous jumps on human-sized stairs and sparse stepping stones, for the first time to the best of our knowledge. In particular, the robot can cross two stair steps in each jump and completes a 3.5m long, 2.8m high, 14-step staircase in 4.5 seconds. Moreover, the same policy outperforms baselines in various other parkour tasks, such as jumping over single horizontal or vertical discontinuities. Experiment videos can be found at https://yxyang.github.io/jumping_cod/, Comment: Website: https://yxyang.github.io/jumping_cod/

In this paper, we propose a weak Galerkin finite element method (WG) for solving singularly perturbed convection-diffusion problems on a Bakhvalov-type mesh in 2D. Our method is flexible and allows the use of discontinuous approximation functions on the meshe. An error estimate is devised in a suitable norm and the optimal convergence order is obtained. Finally, numerical experiments are given to support the theory and to show the efficiency of the proposed method.

Reliable estimation of terrain traversability is critical for the successful deployment of autonomous systems in wild, outdoor environments. Given the lack of large-scale annotated datasets for off-road navigation, strictly-supervised learning approaches remain limited in their generalization ability. To this end, we introduce a novel, image-based self-supervised learning method for traversability prediction, leveraging a state-of-the-art vision foundation model for improved out-of-distribution performance. Our method employs contrastive representation learning using both human driving data and instance-based segmentation masks during training. We show that this simple, yet effective, technique drastically outperforms recent methods in predicting traversability for both on- and off-trail driving scenarios. We compare our method with recent baselines on both a common benchmark as well as our own datasets, covering a diverse range of outdoor environments and varied terrain types. We also demonstrate the compatibility of resulting costmap predictions with a model-predictive controller. Finally, we evaluate our approach on zero- and few-shot tasks, demonstrating unprecedented performance for generalization to new environments. Videos and additional material can be found here: https://sites.google.com/view/visual-traversability-learning., Comment: ICRA 2024; 8 pages

We introduce LiDAR-UDA, a novel two-stage self-training-based Unsupervised Domain Adaptation (UDA) method for LiDAR segmentation. Existing self-training methods use a model trained on labeled source data to generate pseudo labels for target data and refine the predictions via fine-tuning the network on the pseudo labels. These methods suffer from domain shifts caused by different LiDAR sensor configurations in the source and target domains. We propose two techniques to reduce sensor discrepancy and improve pseudo label quality: 1) LiDAR beam subsampling, which simulates different LiDAR scanning patterns by randomly dropping beams; 2) cross-frame ensembling, which exploits temporal consistency of consecutive frames to generate more reliable pseudo labels. Our method is simple, generalizable, and does not incur any extra inference cost. We evaluate our method on several public LiDAR datasets and show that it outperforms the state-of-the-art methods by more than $3.9\%$ mIoU on average for all scenarios. Code will be available at https://github.com/JHLee0513/LiDARUDA., Comment: Accepted ICCV 2023 (Oral)

We consider the singularly perturbed fourth-order boundary value problem $\varepsilon ^{2}\Delta ^{2}u-\Delta u=f $ on the unit square $\Omega \subset \mathbb{R}^2$, with boundary conditions $u = \partial u / \partial n = 0$ on $\partial \Omega$, where $\varepsilon \in (0, 1)$ is a small parameter. The problem is solved numerically by means of a weak Galerkin(WG) finite element method, which is highly robust and flexible in the element construction by using discontinuous piecewise polynomials on finite element partitions consisting of polygons of arbitrary shape. The resulting WG finite element formulation is symmetric, positive definite, and parameter-free. Under reasonable assumptions on the structure of the boundary layers that appear in the solution, a family of suitable Shishkin meshes with $N^2$ elements is constructed ,convergence of the method is proved in a discrete $H^2$ norm for the corresponding WG finite element solutions and numerical results are presented.

We present CAJun, a novel hierarchical learning and control framework that enables legged robots to jump continuously with adaptive jumping distances. CAJun consists of a high-level centroidal policy and a low-level leg controller. In particular, we use reinforcement learning (RL) to train the centroidal policy, which specifies the gait timing, base velocity, and swing foot position for the leg controller. The leg controller optimizes motor commands for the swing and stance legs according to the gait timing to track the swing foot target and base velocity commands using optimal control. Additionally, we reformulate the stance leg optimizer in the leg controller to speed up policy training by an order of magnitude. Our system combines the versatility of learning with the robustness of optimal control. By combining RL with optimal control methods, our system achieves the versatility of learning while enjoys the robustness from control methods, making it easily transferable to real robots. We show that after 20 minutes of training on a single GPU, CAJun can achieve continuous, long jumps with adaptive distances on a Go1 robot with small sim-to-real gaps. Moreover, the robot can jump across gaps with a maximum width of 70cm, which is over 40% wider than existing methods., Comment: Please visit https://yxyang.github.io/cajun/ for additional results

Jumping is essential for legged robots to traverse through difficult terrains. In this work, we propose a hierarchical framework that combines optimal control and reinforcement learning to learn continuous jumping motions for quadrupedal robots. The core of our framework is a stance controller, which combines a manually designed acceleration controller with a learned residual policy. As the acceleration controller warm starts policy for efficient training, the trained policy overcomes the limitation of the acceleration controller and improves the jumping stability. In addition, a low-level whole-body controller converts the body pose command from the stance controller to motor commands. After training in simulation, our framework can be deployed directly to the real robot, and perform versatile, continuous jumping motions, including omni-directional jumps at up to 50cm high, 60cm forward, and jump-turning at up to 90 degrees. Please visit our website for more results: https://sites.google.com/view/learning-to-jump., Comment: To be presented at L4DC 2023

Effective use of camera-based vision systems is essential for robust performance in autonomous off-road driving, particularly in the high-speed regime. Despite success in structured, on-road settings, current end-to-end approaches for scene prediction have yet to be successfully adapted for complex outdoor terrain. To this end, we present TerrainNet, a vision-based terrain perception system for semantic and geometric terrain prediction for aggressive, off-road navigation. The approach relies on several key insights and practical considerations for achieving reliable terrain modeling. The network includes a multi-headed output representation to capture fine- and coarse-grained terrain features necessary for estimating traversability. Accurate depth estimation is achieved using self-supervised depth completion with multi-view RGB and stereo inputs. Requirements for real-time performance and fast inference speeds are met using efficient, learned image feature projections. Furthermore, the model is trained on a large-scale, real-world off-road dataset collected across a variety of diverse outdoor environments. We show how TerrainNet can also be used for costmap prediction and provide a detailed framework for integration into a planning module. We demonstrate the performance of TerrainNet through extensive comparison to current state-of-the-art baselines for camera-only scene prediction. Finally, we showcase the effectiveness of integrating TerrainNet within a complete autonomous-driving stack by conducting a real-world vehicle test in a challenging off-road scenario.

The semantics of the environment, such as the terrain type and property, reveals important information for legged robots to adjust their behaviors. In this work, we present a framework that learns semantics-aware locomotion skills from perception for quadrupedal robots, such that the robot can traverse through complex offroad terrains with appropriate speeds and gaits using perception information. Due to the lack of high-fidelity outdoor simulation, our framework needs to be trained directly in the real world, which brings unique challenges in data efficiency and safety. To ensure sample efficiency, we pre-train the perception model with an off-road driving dataset. To avoid the risks of real-world policy exploration, we leverage human demonstration to train a speed policy that selects a desired forward speed from camera image. For maximum traversability, we pair the speed policy with a gait selector, which selects a robust locomotion gait for each forward speed. Using only 40 minutes of human demonstration data, our framework learns to adjust the speed and gait of the robot based on perceived terrain semantics, and enables the robot to walk over 6km without failure at close-to-optimal speed.

6D grasping in cluttered scenes is a longstanding problem in robotic manipulation. Open-loop manipulation pipelines may fail due to inaccurate state estimation, while most end-to-end grasping methods have not yet scaled to complex scenes with obstacles. In this work, we propose a new method for end-to-end learning of 6D grasping in cluttered scenes. Our hierarchical framework learns collision-free target-driven grasping based on partial point cloud observations. We learn an embedding space to encode expert grasping plans during training and a variational autoencoder to sample diverse grasping trajectories at test time. Furthermore, we train a critic network for plan selection and an option classifier for switching to an instance grasping policy through hierarchical reinforcement learning. We evaluate our method and compare against several baselines in simulation, as well as demonstrate that our latent planning can generalize to real-world cluttered-scene grasping tasks. Our videos and code can be found at https://sites.google.com/view/latent-grasping .

Learning high-level navigation behaviors has important implications: it enables robots to build compact visual memory for repeating demonstrations and to build sparse topological maps for planning in novel environments. Existing approaches only learn discrete, short-horizon behaviors. These standalone behaviors usually assume a discrete action space with simple robot dynamics, thus they cannot capture the intricacy and complexity of real-world trajectories. To this end, we propose Composable Behavior Embedding (CBE), a continuous behavior representation for long-horizon visual navigation. CBE is learned in an end-to-end fashion; it effectively captures path geometry and is robust to unseen obstacles. We show that CBE can be used to performing memory-efficient path following and topological mapping, saving more than an order of magnitude of memory than behavior-less approaches.

Visual topological navigation has been revitalized recently thanks to the advancement of deep learning that substantially improves robot perception. However, the scalability and reliability issue remain challenging due to the complexity and ambiguity of real world images and mechanical constraints of real robots. We present an intuitive solution to show that by accurately measuring the capability of a local controller, large-scale visual topological navigation can be achieved while being scalable and robust. Our approach achieves state-of-the-art results in trajectory following and planning in large-scale environments. It also generalizes well to real robots and new environments without retraining or finetuning.

An initial-boundary value problem with a Caputo time derivative of fractional order $\alpha\in(0,1)$ is considered, solutions of which typically exhibit a singular behaviour at an initial time. For this problem, we give a simple and general numerical-stability analysis using barrier functions, which yields sharp pointwise-in-time error bounds on quasi-graded temporal meshes with arbitrary degree of grading. L1-type and Alikhanov-type discretization in time are considered. In particular, those results imply that milder (compared to the optimal) grading yields optimal convergence rates in positive time. Semi-discretizations in time and full discretizations are addressed. The theoretical findings are illustrated by numerical experiments., Comment: arXiv admin note: text overlap with arXiv:1905.05070

End-to-end learning for autonomous navigation has received substantial attention recently as a promising method for reducing modeling error. However, its data complexity, especially around generalization to unseen environments, is high. We introduce a novel image-based autonomous navigation technique that leverages in policy structure using the Riemannian Motion Policy (RMP) framework for deep learning of vehicular control. We design a deep neural network to predict control point RMPs of the vehicle from visual images, from which the optimal control commands can be computed analytically. We show that our network trained in the Gibson environment can be used for indoor obstacle avoidance and navigation on a real RC car, and our RMP representation generalizes better to unseen environments than predicting local geometry or predicting control commands directly.

In this paper, we present the convergence analysis of the rectangular Morley element scheme utilised on the second order problem in arbitrary dimensions. Specifically, we prove that the convergence of the scheme is of $\mathcal{O}(h)$ order in energy norm and of $\mathcal{O}(h^2)$ order in $L^2$ norm on general $d$-rectangular grids. Moreover, when the grid is uniform, the convergence rate can be of $\mathcal{O}(h^2)$ order in energy norm, and the convergence rate in $L^2$ norm is still of $\mathcal{O}(h^2)$ order, which can not be improved. Numerical examples are presented to demonstrate our theoretical results., Comment: This paper has been withdrawn by the author due to some rewrittings of the proof