Augmented reality-based block piling game with superimposed collapse prediction

Although the classical LQR design method has been very successful in real world engineering designs, in some cases, the classical design method needs modifications because of the saturation in actuators. This modified problem is sometimes called the constrained LQR design. For discrete systems, the constrained LQR design problem is equivalent to a convex quadratic programming problem with box constraints. We will show that the interior-point method is very efficient for this problem because an initial interior point is available, a condition which is not true for general convex quadratic programming problem. We will devise an effective and efficient algorithm for the constrained LQR design problem using the special structure of the box constraints and a recently introduced arc-search technique for the interior-point algorithm. We will prove that the algorithm is polynomial and has the best-known complexity bound for the convex quadratic programming. The proposed algorithm is implemented in MATLAB. An example for the constrained LQR design is provided to show the effectiveness and efficiency of the design method. The proposed algorithm can easily be used for model predictive control.

In this paper, we present a long-step infeasible primal-dual path-following algorithm for convex quadratic programming (CQP) whose search directions are computed by means of a preconditioned iterative linear solver. In contrast to the authors’ previous paper [Z. Lu, R.D.C. Monteiro, and J.W. O'Neal. An iterative solver-based infeasible primal-dual path-following algorithm for convex quadratic programming, SIAM J. Optim. 17(1) (2006), pp. 287–310], we propose a new linear system, which we refer to as the hybrid augmented normal equation (HANE), to determine the primal-dual search directions. Since the iterative linear solver can only generate an approximate solution to the HANE, this solution does not yield a primal-dual search direction satisfying all equations of the primal-dual Newton system. We propose a recipe to compute an inexact primal-dual search direction, based on a suitable approximate solution to the HANE. The second difference between this paper and [Z. Lu, R.D.C. Monteiro, and J.W. O'Neal. An iterative solver-based infeasible primal-dual path-following algorithm for convex quadratic programming, SIAM J. Optim. 17(1)(2006), pp. 287–310] is that, instead of using the maximum weight basis (MWB) preconditioner in the aforesaid recipe for constructing the inexact search direction, this paper proposes the use of any member of a whole class of preconditioners, of which the MWB preconditioner is just a special case. The proposed recipe allows us to: (i) establish a polynomial bound on the number of iterations performed by our path-following algorithm and (ii) establish a uniform bound, depending on the quality of the preconditioner, on the number of iterations performed by the iterative solver.

Deep learning has become the main way of the object detection task for autonomous vehicles. Meanwhile, this method typically requires vast amounts of training data to reach their full potential. However, collecting the data from real world and labeling manually is an expensive, time-consuming and error-prone process. Synthetic image has the potential to replace real image for training neural networks, because image creation and labeling annotations are free in this way. For the network trained by synthetic images, the reality gap between real and synthetic images is the main obstacle to use it in the real world. And most previous works are only devoted to generate synthetic images with a good performance on model training, but lack of analysis of the domain gap that affects the performance. This work designs a method of generating the real and synthetic images to analyze and reduce the reality gap between synthetic and real images for car detection. Firstly, this work put one single car with no-background in a random background image to generate real single car and synthetic single car images. In order to further reduce the domain gap in content level, this method keeps the car distribution in synthetic images is similar with the distribution of car in real world. For the purpose of reducing the domain gap in appearance level, the parameters of camera model are same as the camera parameters of image collecting cars and the image is rendered by using the PBRT(Physically Based Ray Tracing) when we generated the synthetic images. Secondly, by training the neural network of instance segmentation with different datasets, the across validation result proves that the reality gap between synthetic and real images is no more than the domain gap between real images. Thirdly, the training results of datasets with different samples diversity show that the diversity of the samples yields better generalization between different datasets for car detection which can effectively reduce the domain gap.

Mixed reality is different from the virtual reality in that users can feel immersed in a space which is composed of not only virtual but also real objects. Thus, it is essential to realize seamless integration and interaction of the virtual and real worlds. We need depth information of the real scene to synthesize the real and virtual objects. We propose a two-stage algorithm to find smooth and precise disparity vector fields with sharp object boundaries in a stereo image pair for depth estimation. Hierarchical region-dividing disparity estimation increases the efficiency and the reliability of the estimation process, and a shape-adaptive window provides high reliability of the fields around the object boundary region. At the second stage, the vector fields are regularized with a energy model which produces smooth fields while preserving their discontinuities resulting from the object boundaries. The vector fields are used to reconstruct 3D surface of the real scene. Simulation results show that the proposed algorithm provides accurate and spatially correlated disparity vector fields in various kinds of images, and synthesized 3D models produce natural space where the virtual objects interact with the real world as if they are in the same world.

This paper presents linear algebra techniques used in the implementation of an interior point method for solving linear programs and convex quadratic programs with linear constraints. New regularization techniques for Newton systems applicable to both symmetric positive definite and symmetric indefinite systems are described. They transform the latter to quasidef-inite systems known to be strongly factorizable to a form of Cholesky-like factorization.Two different regularization techniques,primal; and dual, are very well suited to the (infeasible) primal-dual interior point algorithm. This particular algorithm, with an extension of multiple centrality correctors, is implemented in our solver HOPDM. Computational results are given to illustrate the potential advantages of the approach when applied to the solution of very large linear and convex quadratic programs.

The main difficulty in realizing a motion simulator comes from the constraints on its workspace. The so-called washout filter prevents a simulator from being driven to go off its pre-determined boundaries and generate excessive torques. By noting that the existing washout filters are conservative and more aggressive motions may be accommodated, this paper presents a novel approach that fully exploits the simulator workspace and thereby reproduces the real-world sensations with high fidelity. The washout filter converts the real-world input trajectory as a realizable one that satisfies the spatial and dynamic constraints while minimizing the sensation error and fidelity between the motions experienced in the real world and on the motion simulator. The control objective is to reduce the computational burdens by using the QP algorithm. The proposed approach formulates the task of designing a washout filter as a quadratic programming (QP). The direct approach to the solution of the QP often results in a computational burden that amounts toO(N3) flops andO(N2) storage space (N=104 ∼ 105, typically). By judiciously exploiting the Toeplitz structures of the underlying matrices, an orders-of-magnitude faster algorithm is obtained to reduce the computational burdens toO(Nlog2N) flops andO(N) storage space. The extensive simulation studies on the Eclipse-II motion simulator at Seoul National University assure that the QP-based fast algorithm outperforms the existing ones in reproducing the real-world sensations.

When applying the sequential quadratic programming (SQP) algorithm to topology optimization, using the quasi-Newton methods or calculating the Hessian matrix directly will result in a considerable amount of calculation, making it computationally infeasible when the number of optimization variables is large. To solve the above problems, this paper creatively proposes a method for calculating the approximate Hessian matrix for structural topology optimization with minimum compliance problems. Then, the second-order Taylor expansion transforms the original problem into a series of separable and easy-to-solve convex quadratic programming (QP) subproblems. Finally, the quadratic programming optimality criteria (QPOC) method and the QP solver of MATLAB are used to solve the subproblems. Compared with other sequential quadratic programming methods, the advantage of the proposed method is that the Hessian matrix is diagonally positive definite and its calculation is simple. Numerical experiments on an MBB beam and cantilever beam verify the feasibility and efficiency of the proposed method.

We have discussed important Java 3D objects that are basically static in the last few chapters. Starting from this chapter, we will be looking at universe and objects that are dynamic in nature. Specifically, we will discuss issues on animation and interaction in this and the next chapter, respectively. As well demonstrated by popular interactive computer games, animation, and interaction are crucial in making a Java 3D world more interesting. Technically, animation is associated with changes in graphical objects and images as time passes without any direct user action, while interaction corresponds to any such change in response to an action or input from the user (Tso, Tharp, Zhang, & Tai, 1999). In any virtual reality or game application, animation and interaction are often crucial and critical. Through animation, the user is able to have a more realistic feel of the real 3D objects through looking at the object at different angles and perspectives. Through interaction with these objects, the user will become more integrated into the virtual 3D world in the same way as sensing our own reality in the real world. Under Java 3D, the “behavior” class is used to define and control both animation and interaction. However, note that the behavior class is an abstract class and cannot be directly used (Stromer, Quon, Gordon, Turinsky, & Sensen, 2005). Instead, there are three classes that extend the behavior class and that are commonly used. They are the “interpolator,” the “billboard,” and the “level of detail (LOD)” class. Furthermore, we can create a new behavior class by extending the behavior class to fit any special need. Briefly, in this chapter, we will discuss the important interpolator classes by using a number of illustrating examples, followed by some details discussions on the billboard and LOD classes.

The notion of a sharp, or strongly unique, minimum is extended to include the possibility of a nonunique solution set. These minima will be called weak sharp minima. Conditions necessary for the solution set of a minimization problem to be a set of weak sharp minima are developed in both the unconstrained and constrained cases. These conditions are also shown to be sufficient under the appropriate convexity hypotheses. The existence of weak sharp minima is characterized in the cases of linear and quadratic convex programming and for the linear complementarity problem. In particular, a result of Mangasarian and Meyer is reproduced that shows that the solution set of a linear program is always a set of weak sharp minima whenever it is nonempty. Consequences for the convergence theory of algorithms are also examined, especially conditions yielding finite termination.

Quadratic programming (QP) is a family of methods, techniques, and algorithms that can be used to minimize quadratic objective functions subject to linear constraints. QP shares many combinatorial features with linear programming (LP) and it is often used as the basis of constrained nonlinear programming. An important branch of QP is convex QP where the objective function is a convex quadratic function.

The next generation (NextGen) transport aircraft configurations being investigated as part of the NASA Aeronautics Subsonic Fixed Wing Project have more control surfaces, or control effectors, than existing transport aircraft configurations. Conventional flight control is achieved through two symmetric elevators, two antisymmetric ailerons, and a rudder. The five control surfaces, reduced to three command variables, produce moments along the three main axes of the aircraft and enable the pilot to control the attitude of the aircraft. Next generation aircraft will have additional redundant control effectors to control the three moments, creating a situation where the aircraft is over-actuated and where a simple relationship no longer exists between the required control surface deflections and the desired moments. NextGen flight controllers will incorporate control allocation algorithms to determine the optimal effector commands to attain the desired moments, taking into account the effector limits. Approaches to solving the problem using linear programming and quadratic programming algorithms have been proposed and tested. It is of great interest to understand their relative advantages and disadvantages and how design parameters may affect their properties. In this paper, we investigate the sensitivity of the effector commands with respect to the desired moments and show on some examples the sensitivity of the solutions provided by the linear programming and quadratic programming methods.

This paper proposes a Blended Reality Agent called "BReA" that can exist in both the real and virtual world and has communicative advantages that is more than simply the sum of those of a robotic agent and an on-screen agent. BReA can seamlessly transfer between the real world and virtual world and users can communicate with BReA without interruption during the transference. We conducted a field test and showed that users can recognize when it points from the virtual world to a real world object after it moves from the real world to virtual world. This result supports a hypothesis that communicating with BReA helps users recognize the link between real world and virtual world objects and virtual world information.

This paper presents new linear programming techniques for the design of optimal 1D IIR digital filters. the first method is based on a linear minimax criterion and leads to a linear programming approximation problem whose optimal solution is attained by a new fast algorithm. Next, the linear minimax approximation problem is extended and formulated as two linear integer programming problems which permit the design of 1D IIR digital filters with coefficients of finite word length. the first of these methods is formulated as a 0‐1 integer linear programming problem and its optimal solution is attained rapidly by a new algorithm. This method appears to be suitable for the design of high‐order digital filters. the second method is more general and is formulated as a mixed integer linear programming problem. to solve the design problem efficiently, a new integer tree search algorithm is introduced. the feasibility of the proposed algorithms is illustrated with detailed solutions or numerical examples.

In this paper we combine an infeasible Interior Point Method (IPM) with the Proximal Method of Multipliers (PMM). The resulting algorithm (IP-PMM) is interpreted as a primal-dual regularized IPM, suitable for solving linearly constrained convex quadratic programming problems. We apply few iterations of the interior point method to each sub-problem of the proximal method of multipliers. Once a satisfactory solution of the PMM sub-problem is found, we update the PMM parameters, form a new IPM neighbourhood and repeat this process. Given this framework, we prove polynomial complexity of the algorithm, under standard assumptions. To our knowledge, this is the first polynomial complexity result for a primal-dual regularized IPM. The algorithm is guided by the use of a single penalty parameter; that of the logarithmic barrier. In other words, we show that IP-PMM inherits the polynomial complexity of IPMs, as well as the strict convexity of the PMM sub-problems. The updates of the penalty parameter are controlled by IPM, and hence are well-tuned, and do not depend on the problem solved. Furthermore, we study the behavior of the method when it is applied to an infeasible problem, and identify a necessary condition for infeasibility. The latter is used to construct an infeasibility detection mechanism. Subsequently, we provide a robust implementation of the presented algorithm and test it over a set of small to large scale linear and convex quadratic programming problems. The numerical results demonstrate the benefits of using regularization in IPMs as well as the reliability of the method.

"Game Theory-Mathematical Models of Conflict." Journal of the Operational Research Society, 31(11), pp. 1050–1051