On the integration of singularity-free representations of SO(3) for direct optimal control

In this paper we analyze the performance of different combinations of: (1) parameterization of the rotational degrees of freedom (DOF) of multibody systems, and (2) choice of the integration scheme, in the context of direct optimal control discretized according to the direct multiple-shooting method. The considered representations include quaternions and Direction Cosine Matrices, both having the peculiarity of being non-singular and requiring more than three parameters to describe an element of the Special Orthogonal group SO(3). These representations yield invariants in the dynamics of the system, i.e., algebraic conditions which have to be satisfied in order for the model to be representative of physical reality. The investigated integration schemes include the classical explicit Rungeâ\u80\u93Kutta method, its stabilized version based on Baumgarteâ\u80\u99s technique, which tends to reduce the drift from the underlying manifold, and a structure-preserving alternative, namely the Rungeâ\u80\u93Kutta Munthe-Kaas method, which preserves the invariants by construction. The performances of the combined choice of representation and integrator are assessed by solving thousands of planning tasks for a nonholonomic, underactuated cart-pendulum system, where the pendulum can experience arbitrarily large 3D rotations. The aspects analyzed include success rate, average number of iterations and CPU time to convergence, and quality of the solution. The results reveal how structure-preserving integrators are the only choice for lower accuracies, whereas higher-order, non-stabilized standard integrators seem to be the computationally most competitive solution when higher levels of accuracy are pursued. Overall, the quaternion-based representation is the most efficient in terms of both iterations and CPU time to convergence, albeit at the cost of lower success rates and increased probability of being trapped by higher local minima

Non-iterative, fast SE(3) path smoothing

In this paper, we present a fast, non-iterative approach to smooth a noisy input on the Special Euclidean Group, SE(3) manifold. The translational part can be smoothed by a simple Gaussian convolution.We then proposed a novel approach to rotation smoothing. Unlike existing rotation smoothing methods using either iterative optimization methods or stochastic filtering methods, our method allows direct computation of the smoothing result and allows parallelization of the computation. Furthermore, we have done a comparative study on Jia and Evans’s method published in 2014 [1], and shown that our method can better smooth an input rotation sequence, with shorter computational time. The smoothed camera path is then used for video stabilisation, which shows fluid and smooth camera motion.Australian ARC Centre of Excellence for Robotic Vision (CE140100016

Towards High-Frequency Tracking and Fast Edge-Aware Optimization

This dissertation advances the state of the art for AR/VR tracking systems by increasing the tracking frequency by orders of magnitude and proposes an efficient algorithm for the problem of edge-aware optimization. AR/VR is a natural way of interacting with computers, where the physical and digital worlds coexist. We are on the cusp of a radical change in how humans perform and interact with computing. Humans are sensitive to small misalignments between the real and the virtual world, and tracking at kilo-Hertz frequencies becomes essential. Current vision-based systems fall short, as their tracking frequency is implicitly limited by the frame-rate of the camera. This thesis presents a prototype system which can track at orders of magnitude higher than the state-of-the-art methods using multiple commodity cameras. The proposed system exploits characteristics of the camera traditionally considered as flaws, namely rolling shutter and radial distortion. The experimental evaluation shows the effectiveness of the method for various degrees of motion. Furthermore, edge-aware optimization is an indispensable tool in the computer vision arsenal for accurate filtering of depth-data and image-based rendering, which is increasingly being used for content creation and geometry processing for AR/VR. As applications increasingly demand higher resolution and speed, there exists a need to develop methods that scale accordingly. This dissertation proposes such an edge-aware optimization framework which is efficient, accurate, and algorithmically scales well, all of which are much desirable traits not found jointly in the state of the art. The experiments show the effectiveness of the framework in a multitude of computer vision tasks such as computational photography and stereo.Comment: PhD thesi

Embedded video stabilization system on field programmable gate array for unmanned aerial vehicle

Unmanned Aerial Vehicles (UAVs) equipped with lightweight and low-cost cameras have grown in popularity and enable new applications of UAV technology. However, the video retrieved from small size UAVs is normally in low-quality due to high frequency jitter. This thesis presents the development of video stabilization algorithm implemented on Field Programmable Gate Array (FPGA). The video stabilization algorithm consists of three main processes, which are motion estimation, motion stabilization and motion compensation to minimize the jitter. Motion estimation involves block matching and Random Sample Consensus (RANSAC) to estimate the affine matrix that defines the motion perspective between two consecutive frames. Then, parameter extraction, motion smoothing and motion vector correction, which are parts of the motion stabilization, are tasked in removing unwanted camera movement. Finally, motion compensation stabilizes two consecutive frames based on filtered motion vectors. In order to facilitate the ground station mobility, this algorithm needs to be processed onboard the UAV in real-time. The nature of parallelization of video stabilization processing is suitable to be utilized by using FPGA in order to achieve real-time capability. The implementation of this system is on Altera DE2-115 FPGA board. Full hardware dedicated cores without Nios II processor are designed in stream-oriented architecture to accelerate the computation. Furthermore, a parallelized architecture consisting of block matching and highly parameterizable RANSAC processor modules show that the proposed system is able to achieve up to 30 frames per second processing and a good stabilization improvement up to 1.78 Interframe Transformation Fidelity value. Hence, it is concluded that the proposed system is suitable for real-time video stabilization for UAV application