Doubly Robust Smoothing of Dynamical Processes via Outlier Sparsity Constraints

Coping with outliers contaminating dynamical processes is of major importance in various applications because mismatches from nominal models are not uncommon in practice. In this context, the present paper develops novel fixed-lag and fixed-interval smoothing algorithms that are robust to outliers simultaneously present in the measurements {\it and} in the state dynamics. Outliers are handled through auxiliary unknown variables that are jointly estimated along with the state based on the least-squares criterion that is regularized with the $\ell_1$-norm of the outliers in order to effect sparsity control. The resultant iterative estimators rely on coordinate descent and the alternating direction method of multipliers, are expressed in closed form per iteration, and are provably convergent. Additional attractive features of the novel doubly robust smoother include: i) ability to handle both types of outliers; ii) universality to unknown nominal noise and outlier distributions; iii) flexibility to encompass maximum a posteriori optimal estimators with reliable performance under nominal conditions; and iv) improved performance relative to competing alternatives at comparable complexity, as corroborated via simulated tests.Comment: Submitted to IEEE Trans. on Signal Processin

Trajectory generation for lane-change maneuver of autonomous vehicles

Lane-change maneuver is one of the most thoroughly investigated automatic driving operations that can be used by an autonomous self-driving vehicle as a primitive for performing more complex operations like merging, entering/exiting highways or overtaking another vehicle. This thesis focuses on two coherent problems that are associated with the trajectory generation for lane-change maneuvers of autonomous vehicles in a highway scenario: (i) an effective velocity estimation of neighboring vehicles under different road scenarios involving linear and curvilinear motion of the vehicles, and (ii) trajectory generation based on the estimated velocities of neighboring vehicles for safe operation of self-driving cars during lane-change maneuvers. ^ We first propose a two-stage, interactive-multiple-model-based estimator to perform multi-target tracking of neighboring vehicles in a lane-changing scenario. The first stage deals with an adaptive window based turn-rate estimation for tracking maneuvering target vehicles using Kalman filter. In the second stage, variable-structure models with updated estimated turn-rate are utilized to perform data association followed by velocity estimation. Based on the estimated velocities of neighboring vehicles, piecewise Bezier-curve-based methods that minimize the safety/collision risk involved and maximize the comfort ride have been developed for the generation of desired trajectory for lane-change maneuvers. The proposed velocity-estimation and trajectory-generation algorithms have been validated experimentally using Pioneer3- DX mobile robots in a simulated lane-change environment as well as validated by computer simulations

Fast Gravitational Approach for Rigid Point Set Registration with Ordinary Differential Equations

This article introduces a new physics-based method for rigid point set alignment called Fast Gravitational Approach (FGA). In FGA, the source and target point sets are interpreted as rigid particle swarms with masses interacting in a globally multiply-linked manner while moving in a simulated gravitational force field. The optimal alignment is obtained by explicit modeling of forces acting on the particles as well as their velocities and displacements with second-order ordinary differential equations of motion. Additional alignment cues (point-based or geometric features, and other boundary conditions) can be integrated into FGA through particle masses. We propose a smooth-particle mass function for point mass initialization, which improves robustness to noise and structural discontinuities. To avoid prohibitive quadratic complexity of all-to-all point interactions, we adapt a Barnes-Hut tree for accelerated force computation and achieve quasilinear computational complexity. We show that the new method class has characteristics not found in previous alignment methods such as efficient handling of partial overlaps, inhomogeneous point sampling densities, and coping with large point clouds with reduced runtime compared to the state of the art. Experiments show that our method performs on par with or outperforms all compared competing non-deep-learning-based and general-purpose techniques (which do not assume the availability of training data and a scene prior) in resolving transformations for LiDAR data and gains state-of-the-art accuracy and speed when coping with different types of data disturbances.Comment: 18 pages, 18 figures and two table

Automated Top View Registration of Broadcast Football Videos

In this paper, we propose a novel method to register football broadcast video frames on the static top view model of the playing surface. The proposed method is fully automatic in contrast to the current state of the art which requires manual initialization of point correspondences between the image and the static model. Automatic registration using existing approaches has been difficult due to the lack of sufficient point correspondences. We investigate an alternate approach exploiting the edge information from the line markings on the field. We formulate the registration problem as a nearest neighbour search over a synthetically generated dictionary of edge map and homography pairs. The synthetic dictionary generation allows us to exhaustively cover a wide variety of camera angles and positions and reduce this problem to a minimal per-frame edge map matching procedure. We show that the per-frame results can be improved in videos using an optimization framework for temporal camera stabilization. We demonstrate the efficacy of our approach by presenting extensive results on a dataset collected from matches of football World Cup 2014

Enhancing 3D Autonomous Navigation Through Obstacle Fields: Homogeneous Localisation and Mapping, with Obstacle-Aware Trajectory Optimisation

Small flying robots have numerous potential applications, from quadrotors for search and rescue, infrastructure inspection and package delivery to free-flying satellites for assistance activities inside a space station. To enable these applications, a key challenge is autonomous navigation in 3D, near obstacles on a power, mass and computation constrained platform. This challenge requires a robot to perform localisation, mapping, dynamics-aware trajectory planning and control. The current state-of-the-art uses separate algorithms for each component. Here, the aim is for a more homogeneous approach in the search for improved efficiencies and capabilities. First, an algorithm is described to perform Simultaneous Localisation And Mapping (SLAM) with physical, 3D map representation that can also be used to represent obstacles for trajectory planning: Non-Uniform Rational B-Spline (NURBS) surfaces. Termed NURBSLAM, this algorithm is shown to combine the typically separate tasks of localisation and obstacle mapping. Second, a trajectory optimisation algorithm is presented that produces dynamically-optimal trajectories with direct consideration of obstacles, providing a middle ground between path planners and trajectory smoothers. Called the Admissible Subspace TRajectory Optimiser (ASTRO), the algorithm can produce trajectories that are easier to track than the state-of-the-art for flight near obstacles, as shown in flight tests with quadrotors. For quadrotors to track trajectories, a critical component is the differential flatness transformation that links position and attitude controllers. Existing singularities in this transformation are analysed, solutions are proposed and are then demonstrated in flight tests. Finally, a combined system of NURBSLAM and ASTRO are brought together and tested against the state-of-the-art in a novel simulation environment to prove the concept that a single 3D representation can be used for localisation, mapping, and planning

Automatic Detection of Circular Objects by Ellipse Growing

We present a new method for automatically detecting circular objects in images: we detect an osculating circle to an elliptic arc using a Hough transform, iteratively deforming it into an ellipse, removing outlier pixels, and searching for a separate edge. The voting space is restricted to one and two dimensions for efficiency, and special weighting schemes are introduced to enhance the accuracy. We demonstrate the effectiveness of our method using real images. Finally, we apply our method to the calibration of a turntable for 3-D object shape reconstruction

Image-Based Modeling of Bridges and Its Applications to Evaluating Resiliency of Transportation Networks

Modern urban areas are heavily dependent on transportation networks to sustain their economic life. Hence, when vital components of a regional network are disrupted, economic losses are inevitable. As evidenced by 1989, Loma Prieta and 1994, Northridge earthquakes, the seismic damages experienced by bridges alone result in extensive traffic delays and rerouting, not only hindering emergency response but also causing indirect economic losses that far surpass the direct cost of damage to infrastructure. Nevertheless, in many areas of the U.S., transportation networks lack the resilience required to sustain the potential demands of natural hazards. Traditional hazard assessment methods, in theory, provide the tools required for predicting the vulnerabilities associated with natural hazards. Nonetheless, due to their abstractions of the complex infrastructure and the coupled regional behavior, they often fall short of that expectation. This study proposes a semi-automated image-based model generation framework for producing structure-specific models and fragility functions of bridges. The framework effectively fuses geometric and semantic information extracted from Google Street View images with centerline curve geometry, surface topology, and various relevant metadata to construct extremely accurate geometric representations of bridges. Then, using class statistics available in the literature for bridge structural properties, the framework generates structural models. Both the performance of the geometry extraction procedure and the structural modeling method proposed here are validated by comparison against the structural model of a real-life bridge developed based on as-built drawings.In principle, these models can be utilized to assess physical damage for any type of hazard, but in this study, the focus is limited to seismic applications. Thus to relate the damage resulting from seismic demands from ground shaking, bridge-specific fragility functions are developed for 100 bridge structures in the immediate surroundings of Ports of Los Angeles and Long Beach. Using these fragility curves, the physical damage resulting from a magnitude 7.3 scenario earthquake on Palos Verdes fault is predicted. Subsequently, the effects of the bridge infrastructure damage to the transportation patterns in the Los Angeles metropolitan area are investigated in terms of various resilience metrics