About the Algebraic Solutions of Smallest Enclosing Cylinders Problems

Given n points in Euclidean space E^d, we propose an algebraic algorithm to compute the best fitting (d-1)-cylinder. This algorithm computes the unknown direction of the axis of the cylinder. The location of the axis and the radius of the cylinder are deduced analytically from this direction. Special attention is paid to the case d=3 when n=4 and n=5. For the former, the minimal radius enclosing cylinder is computed algebrically from constrained minimization of a quartic form of the unknown direction of the axis. For the latter, an analytical condition of existence of the circumscribed cylinder is given, and the algorithm reduces to find the zeroes of an one unknown polynomial of degree at most 6. In both cases, the other parameters of the cylinder are deduced analytically. The minimal radius enclosing cylinder is computed analytically for the regular tetrahedron and for a trigonal bipyramids family with a symmetry axis of order 3.Comment: 13 pages, 0 figure; revised version submitted to publication (previous version is a copy of the original one of 2010

Space station integrated wall design and penetration damage control. Task 3: Theoretical analysis of penetration mechanics

The efforts to provide a penetration code called PEN4 version 10 is documented for calculation of projectile and target states for the impact of 2024-T3 aluminum, R sub B 90 1018 steel projectiles and icy meteoroids onto 2024-T3 aluminum plates at impact velocities from 0 to 16 km/s. PEN4 determines whether a plate is perforated by calculating the state of fragmentation of projectile and first plate. Depth of penetration into the second to n sup th plate by fragments resulting from first plate perforation is determined by multiple cratering. The results from applications are given

Dynamic Control Barrier Function-based Model Predictive Control to Safety-Critical Obstacle-Avoidance of Mobile Robot

This paper presents an efficient and safe method to avoid static and dynamic obstacles based on LiDAR. First, point cloud is used to generate a real-time local grid map for obstacle detection. Then, obstacles are clustered by DBSCAN algorithm and enclosed with minimum bounding ellipses (MBEs). In addition, data association is conducted to match each MBE with the obstacle in the current frame. Considering MBE as an observation, Kalman filter (KF) is used to estimate and predict the motion state of the obstacle. In this way, the trajectory of each obstacle in the forward time domain can be parameterized as a set of ellipses. Due to the uncertainty of the MBE, the semi-major and semi-minor axes of the parameterized ellipse are extended to ensure safety. We extend the traditional Control Barrier Function (CBF) and propose Dynamic Control Barrier Function (D-CBF). We combine D-CBF with Model Predictive Control (MPC) to implement safety-critical dynamic obstacle avoidance. Experiments in simulated and real scenarios are conducted to verify the effectiveness of our algorithm. The source code is released for the reference of the community.Comment: Submitted to IEEE International Conference on Robotics and Automation (ICRA) 202

Vorosweep: a fast generalized crystal growing Voronoi diagram generation algorithm

We propose a new algorithm for generating quickly approximate generalized Voronoi diagrams of point sites associated to arbitrary convex distance metric in the Euclidian plane. This algorithm produces connected cells by emulating the growth of crystals starting at the point sites, in order to reduce the complexity of the diagram. The main practical contribution is the Vorosweep package which is the reference implementation of the algorithm. Experimental results and benchmarks are given to demonstrate the versatility of this approach.WIST 3 grant 1017074 DOMHEX (Dominant Hexahedral Mesh Generation

Flow through and around fish farming nets

Computational fluid dynamics (CFD) modeling, tow tank and field measurements were used to investigate current flow through and around net panels and cages. For the numerical computations a porous media model was used to represent the net allowing efficient computation of both exterior and interior flow fields. The model was calibrated using tow tank measurements on a net panel at different velocities and angles of attack. The CFD method was able to reproduce the drag- and lift coefficients of the net panel and the velocity reduction behind the net panel with satisfactory accuracy. The approach was validated for a small size gravity cage by comparing CFD predictions with tow tank measurements of drag force on the cage and velocity reduction inside the cage and in the wake region. The modeled drag force was higher than the measured drag force. The modeled current compared well with the measured current inside the cage, but the reduction was underpredicted in the wake of the cage. Full scale simulations were performed for a cage with a clean net and a biofouled net and compared with field measurements of a cage fouled with jellyfish. The measured data compared well with model predictions for the biofouled net. Flushing rates were calculated for both the clean and the biofouled net cases. When the net was changed from clean to biofouled, flushing time increased by up to 44% and drag force increased by up to 80%