Parallel Monte Carlo approach for integration of the rendering equation

This paper is addressed to the numerical solving of the rendering equation in realistic image creation. The rendering equation is integral equation describing the light propagation in a scene accordingly to a given illumination model. The used illumination model determines the kernel of the equation under consideration. Nowadays, widely used are the Monte Carlo methods for solving the rendering equation in order to create photorealistic images. In this work we consider the Monte Carlo solving of the rendering equation in the context of the parallel sampling scheme for hemisphere. Our aim is to apply this sampling scheme to stratified Monte Carlo integration method for parallel solving of the rendering equation. The domain for integration of the rendering equation is a hemisphere. We divide the hemispherical domain into a number of equal sub-domains of orthogonal spherical triangles. This domain partitioning allows to solve the rendering equation in parallel. It is known that the Neumann series represent the solution of the integral equation as a infinity sum of integrals. We approximate this sum with a desired truncation error (systematic error) receiving the fixed number of iteration. Then the rendering equation is solved iteratively using Monte Carlo approach. At each iteration we solve multi-dimensional integrals using uniform hemisphere partitioning scheme. An estimate of the rate of convergence is obtained using the stratified Monte Carlo method. This domain partitioning allows easy parallel realization and leads to convergence improvement of the Monte Carlo method. The high performance and Grid computing of the corresponding Monte Carlo scheme are discussed.

Parallel Monte Carlo sampling scheme for sphere and hemisphere

The sampling of certain solid angle is a fundamental operation in realistic image synthesis, where the rendering equation describing the light propagation in closed domains is solved. Monte Carlo methods for solving the rendering equation use sampling of the solid angle subtended by unit hemisphere or unit sphere in order to perform the numerical integration of the rendering equation. In this work we consider the problem for generation of uniformly distributed random samples over hemisphere and sphere. Our aim is to construct and study the parallel sampling scheme for hemisphere and sphere. First we apply the symmetry property for partitioning of hemisphere and sphere. The domain of solid angle subtended by a hemisphere is divided into a number of equal sub-domains. Each sub-domain represents solid angle subtended by orthogonal spherical triangle with fixed vertices and computable parameters. Then we introduce two new algorithms for sampling of orthogonal spherical triangles. Both algorithms are based on a transformation of the unit square. Similarly to the Arvo's algorithm for sampling of arbitrary spherical triangle the suggested algorithms accommodate the stratified sampling. We derive the necessary transformations for the algorithms. The first sampling algorithm generates a sample by mapping of the unit square onto orthogonal spherical triangle. The second algorithm directly compute the unit radius vector of a sampling point inside to the orthogonal spherical triangle. The sampling of total hemisphere and sphere is performed in parallel for all sub-domains simultaneously by using the symmetry property of partitioning. The applicability of the corresponding parallel sampling scheme for Monte Carlo and Quasi-D/lonte Carlo solving of rendering equation is discussed.

Museum robots: multi-robot systems for public exhibition

Mobile robots provide a versatile platform for research, however they can also provide an interesting educational platform for public exhibition at museums. In general museums require exhibits that are both eye catching and exciting to the public whilst requiring a minimum of maintenance time from museum technicians. In many cases it is simply not possible to continuously change batteries and some method of supplying continous power is required. A powered flooring system is described that is capable of providing power continuously to a group of robots. Three different museum exhibit applications are described. All three robot exhibits are of a similar basic design although the exhibits are very different in appearance and behaviour. The durability and versatility of the robots also makes them extremely good candidates for long duration experiments such as those required by evolutionary robotics.

Structural design of an escort type rehabilitation robot for post-stroke therapies of upper-limb

This paper describes a structural design technique for rehabilitation robot intended for upper-limb post-stroke therapy. First, a novel approach to a rehabilitation robot is proposed and the features of the robot are explained. Second, the direct kinematics and the inverse kinematics of the proposed robot structure are derived. Finally, a mechanical design procedure is explained that achieves a compromise between the required motion range and assuring the workspace safety. The suitability of a portable escort type structure for upper limb rehabilitation of both acute and chronic stroke is discussed

Parallel performance and scalability experiments with the Danish Eulerian Model on the EPCC supercomputers

The Danish Eulerian Model (DEM) is a powerful air pollution model, designed to calculate the concentrations of various dangerous species over a large geographical region (e.g. Europe). It takes into account the main physical and chemical processes between these species, the actual meteorological conditions, emissions, etc.. This is a huge computational task and requires significant resources of storage and CPU time. Parallel computing is essential for the efficient practical use of the model. Some efficient parallel versions of the model were created over the past several years. A suitable parallel version of DEM by using the Message Passing Interface library (AIPI) was implemented on two powerful supercomputers of the EPCC - Edinburgh, available via the HPC-Europa programme for transnational access to research infrastructures in EC: a Sun Fire E15K and an IBM HPCx cluster. Although the implementation is in principal, the same for both supercomputers, few modifications had to be done for successful porting of the code on the IBM HPCx cluster. Performance analysis and parallel optimization was done next. Results from bench marking experiments will be presented in this paper. Another set of experiments was carried out in order to investigate the sensitivity of the model to variation of some chemical rate constants in the chemical submodel. Certain modifications of the code were necessary to be done in accordance with this task. The obtained results will be used for further sensitivity analysis Studies by using Monte Carlo simulation.

3D path planning with novel multiple 2D layered approach for complex human-robot interaction

Navigating cluttered indoor environments is a difficult problem in indoor service robotics. The Acroboter concept, a novel approach to indoor locomotion, represents unique opportunity to avoid obstacles in indoor environments by navigating the ceiling plane. This mode of locomotion requires the ability to accurately detect obstacles, and plan 3D trajectories through the environment. This paper presents the development of a resilient object tracking system, as well as a novel approach to generating 3D paths suitable for such robot configurations. Distributed human-machine interfacing allowing simulation previewing of actions is also considered in the developed system architecture.

Modeling and simulating a mathematical tool for multi-robot pattern transformation

The work reported in this paper is motivated by the need to investigate general methods for pattern transformation. A formal definition for pattern transformation is provided and four special cases namely, elementary and geometric transformation based on repositioning all and some agents in the pattern are introduced. The need for a mathematical tool and simulations for visualizing the behavior of a transformation method is highlighted. A mathematical method based on the Moebius transformation is proposed. The transformation method involves discretization of events for planning paths of individual robots in a pattern. Simulations on a particle physics simulator are used to validate the feasibility of the proposed method.