Structure-preserving Method for Reconstructing Unknown Hamiltonian Systems from Trajectory Data

We present a numerical approach for approximating unknown Hamiltonian systems using observation data. A distinct feature of the proposed method is that it is structure-preserving, in the sense that it enforces conservation of the reconstructed Hamiltonian. This is achieved by directly approximating the underlying unknown Hamiltonian, rather than the right-hand-side of the governing equations. We present the technical details of the proposed algorithm and its error estimate, along with a practical de-noising procedure to cope with noisy data. A set of numerical examples are then presented to demonstrate the structure-preserving property and effectiveness of the algorithm.

A General Optimization-based Framework for Global Pose Estimation with Multiple Sensors

Accurate state estimation is a fundamental problem for autonomous robots. To achieve locally accurate and globally drift-free state estimation, multiple sensors with complementary properties are usually fused together. Local sensors (camera, IMU, LiDAR, etc) provide precise pose within a small region, while global sensors (GPS, magnetometer, barometer, etc) supply noisy but globally drift-free localization in a large-scale environment. In this paper, we propose a sensor fusion framework to fuse local states with global sensors, which achieves locally accurate and globally drift-free pose estimation. Local estimations, produced by existing VO/VIO approaches, are fused with global sensors in a pose graph optimization. Within the graph optimization, local estimations are aligned into a global coordinate. Meanwhile, the accumulated drifts are eliminated. We evaluate the performance of our system on public datasets and with real-world experiments. Results are compared against other state-of-the-art algorithms. We highlight that our system is a general framework, which can easily fuse various global sensors in a unified pose graph optimization. Our implementations are open source\footnote{https://github.com/HKUST-Aerial-Robotics/VINS-Fusion}.

A General Optimization-based Framework for Local Odometry Estimation with Multiple Sensors

Nowadays, more and more sensors are equipped on robots to increase robustness and autonomous ability. We have seen various sensor suites equipped on different platforms, such as stereo cameras on ground vehicles, a monocular camera with an IMU (Inertial Measurement Unit) on mobile phones, and stereo cameras with an IMU on aerial robots. Although many algorithms for state estimation have been proposed in the past, they are usually applied to a single sensor or a specific sensor suite. Few of them can be employed with multiple sensor choices. In this paper, we proposed a general optimization-based framework for odometry estimation, which supports multiple sensor sets. Every sensor is treated as a general factor in our framework. Factors which share common state variables are summed together to build the optimization problem. We further demonstrate the generality with visual and inertial sensors, which form three sensor suites (stereo cameras, a monocular camera with an IMU, and stereo cameras with an IMU). We validate the performance of our system on public datasets and through real-world experiments with multiple sensors. Results are compared against other state-of-the-art algorithms. We highlight that our system is a general framework, which can easily fuse various sensors in a pose graph optimization. Our implementations are open source\footnote{https://github.com/HKUST-Aerial-Robotics/VINS-Fusion}.

Data Driven Governing Equations Approximation Using Deep Neural Networks

We present a numerical framework for approximating unknown governing equations using observation data and deep neural networks (DNN). In particular, we propose to use residual network (ResNet) as the basic building block for equation approximation. We demonstrate that the ResNet block can be considered as a one-step method that is exact in temporal integration. We then present two multi-step methods, recurrent ResNet (RT-ResNet) method and recursive ReNet (RS-ResNet) method. The RT-ResNet is a multi-step method on uniform time steps, whereas the RS-ResNet is an adaptive multi-step method using variable time steps. All three methods presented here are based on integral form of the underlying dynamical system. As a result, they do not require time derivative data for equation recovery and can cope with relatively coarsely distributed trajectory data. Several numerical examples are presented to demonstrate the performance of the methods.

Estimating Metric Poses of Dynamic Objects Using Monocular Visual-Inertial Fusion

A monocular 3D object tracking system generally has only up-to-scale pose estimation results without any prior knowledge of the tracked object. In this paper, we propose a novel idea to recover the metric scale of an arbitrary dynamic object by optimizing the trajectory of the objects in the world frame, without motion assumptions. By introducing an additional constraint in the time domain, our monocular visual-inertial tracking system can obtain continuous six degree of freedom (6-DoF) pose estimation without scale ambiguity. Our method requires neither fixed multi-camera nor depth sensor settings for scale observability, instead, the IMU inside the monocular sensing suite provides scale information for both camera itself and the tracked object. We build the proposed system on top of our monocular visual-inertial system (VINS) to obtain accurate state estimation of the monocular camera in the world frame. The whole system consists of a 2D object tracker, an object region-based visual bundle adjustment (BA), VINS and a correlation analysis-based metric scale estimator. Experimental comparisons with ground truth demonstrate the tracking accuracy of our 3D tracking performance while a mobile augmented reality (AR) demo shows the feasibility of potential applications.

Reducing Parameter Space for Neural Network Training

For neural networks (NNs) with rectified linear unit (ReLU) or binary activation functions, we show that their training can be accomplished in a reduced parameter space. Specifically, the weights in each neuron can be trained on the unit sphere, as opposed to the entire space, and the threshold can be trained in a bounded interval, as opposed to the real line. We show that the NNs in the reduced parameter space are mathematically equivalent to the standard NNs with parameters in the whole space. The reduced parameter space shall facilitate the optimization procedure for the network training, as the search space becomes (much) smaller. We demonstrate the improved training performance using numerical examples.

Online Temporal Calibration for Monocular Visual-Inertial Systems

Accurate state estimation is a fundamental module for various intelligent applications, such as robot navigation, autonomous driving, virtual and augmented reality. Visual and inertial fusion is a popular technology for 6-DOF state estimation in recent years. Time instants at which different sensors' measurements are recorded are of crucial importance to the system's robustness and accuracy. In practice, timestamps of each sensor typically suffer from triggering and transmission delays, leading to temporal misalignment (time offsets) among different sensors. Such temporal offset dramatically influences the performance of sensor fusion. To this end, we propose an online approach for calibrating temporal offset between visual and inertial measurements. Our approach achieves temporal offset calibration by jointly optimizing time offset, camera and IMU states, as well as feature locations in a SLAM system. Furthermore, the approach is a general model, which can be easily employed in several feature-based optimization frameworks. Simulation and experimental results demonstrate the high accuracy of our calibration approach even compared with other state-of-art offline tools. The VIO comparison against other methods proves that the online temporal calibration significantly benefits visual-inertial systems. The source code of temporal calibration is integrated into our public project, VINS-Mono.

Stereo Vision-based Semantic 3D Object and Ego-motion Tracking for Autonomous Driving

We propose a stereo vision-based approach for tracking the camera ego-motion and 3D semantic objects in dynamic autonomous driving scenarios. Instead of directly regressing the 3D bounding box using end-to-end approaches, we propose to use the easy-to-labeled 2D detection and discrete viewpoint classification together with a light-weight semantic inference method to obtain rough 3D object measurements. Based on the object-aware-aided camera pose tracking which is robust in dynamic environments, in combination with our novel dynamic object bundle adjustment (BA) approach to fuse temporal sparse feature correspondences and the semantic 3D measurement model, we obtain 3D object pose, velocity and anchored dynamic point cloud estimation with instance accuracy and temporal consistency. The performance of our proposed method is demonstrated in diverse scenarios. Both the ego-motion estimation and object localization are compared with the state-of-of-the-art solutions.

Relocalization, Global Optimization and Map Merging for Monocular Visual-Inertial SLAM

The monocular visual-inertial system (VINS), which consists one camera and one low-cost inertial measurement unit (IMU), is a popular approach to achieve accurate 6-DOF state estimation. However, such locally accurate visual-inertial odometry is prone to drift and cannot provide absolute pose estimation. Leveraging history information to relocalize and correct drift has become a hot topic. In this paper, we propose a monocular visual-inertial SLAM system, which can relocalize camera and get the absolute pose in a previous-built map. Then 4-DOF pose graph optimization is performed to correct drifts and achieve global consistent. The 4-DOF contains x, y, z, and yaw angle, which is the actual drifted direction in the visual-inertial system. Furthermore, the proposed system can reuse a map by saving and loading it in an efficient way. Current map and previous map can be merged together by the global pose graph optimization. We validate the accuracy of our system on public datasets and compare against other state-of-the-art algorithms. We also evaluate the map merging ability of our system in the large-scale outdoor environment. The source code of map reuse is integrated into our public code, VINS-Mono.

VINS-Mono: A Robust and Versatile Monocular Visual-Inertial State Estimator

A monocular visual-inertial system (VINS), consisting of a camera and a low-cost inertial measurement unit (IMU), forms the minimum sensor suite for metric six degrees-of-freedom (DOF) state estimation. However, the lack of direct distance measurement poses significant challenges in terms of IMU processing, estimator initialization, extrinsic calibration, and nonlinear optimization. In this work, we present VINS-Mono: a robust and versatile monocular visual-inertial state estimator.Our approach starts with a robust procedure for estimator initialization and failure recovery. A tightly-coupled, nonlinear optimization-based method is used to obtain high accuracy visual-inertial odometry by fusing pre-integrated IMU measurements and feature observations. A loop detection module, in combination with our tightly-coupled formulation, enables relocalization with minimum computation overhead.We additionally perform four degrees-of-freedom pose graph optimization to enforce global consistency. We validate the performance of our system on public datasets and real-world experiments and compare against other state-of-the-art algorithms. We also perform onboard closed-loop autonomous flight on the MAV platform and port the algorithm to an iOS-based demonstration. We highlight that the proposed work is a reliable, complete, and versatile system that is applicable for different applications that require high accuracy localization. We open source our implementations for both PCs and iOS mobile devices.