The convex hull of a set of points is the smallest convex set that contains the points. This article presents a practical convex hull algorithm that combines the two-dimensional Quickhull algorithm with the general-dimension Beneath-Beyond Algorithm. It is similar to the randomized, incremental algorithms for convex hull and delaunay triangulation. We provide empirical evidence that the algorithm runs faster when the input contains nonextreme points and that it used less memory. computational geometry algorithms have traditionally assumed that input sets are well behaved. When an algorithm is implemented with floating-point arithmetic, this assumption can lead to serous errors. We briefly describe a solution to this problem when computing the convex hull in two, three, or four dimensions. The output is a set of “thick” facets that contain all possible exact convex hulls of the input. A variation is effective in five or more dimensions.

/pdf/the-quickhull-algorithm-for-convex-hulls-ug134bwaff.pdf

The quickhull algorithm for convex hulls

https://users.encs.concordia.ca/~ymzhang/publications/ARC32-2-98Zhang_pp.229-252.pdf

Bibliographical review on reconfigurable fault-tolerant control systems

Traditional engineering instruction is deductive, beginning with theories and progressing to the applications of those theories Alternative teaching approaches are more inductive Topics are introduced by presenting specific observations, case studies or problems, and theories are taught or the students are helped to discover them only after the need to know them has been established This study reviews several of the most commonly used inductive teaching methods, including inquiry learning, problem-based learning, project-based learning, case-based teaching, discovery learning, and just-in-time teaching The paper defines each method, highlights commonalities and specific differences, and reviews research on the effectiveness of the methods While the strength of the evidence varies from one method to another, inductive methods are consistently found to be at least equal to, and in general more effective than, traditional deductive methods for achieving a broad range of learning outcomes

Inductive Teaching and Learning Methods: Definitions, Comparisons, and Research Bases

The technology of hydrodynamic modeling and marine craft motion control systems has progressed greatly in recent years. This timely survey includes the latest tools for analysis and design of advanced guidance, navigation and control systems and presents new material on underwater vehicles and surface vessels. Each section presents numerous case studies and applications, providing a practical understanding of how model-based motion control systems are designed.

/pdf/handbook-of-marine-craft-hydrodynamics-and-motion-control-2qu7epb0pt.pdf

Handbook of Marine Craft Hydrodynamics and Motion Control: Fossen/Handbook of Marine Craft Hydrodynamics and Motion Control

https://www.fossen.biz/home/papers/JohansenFossen%20Automatica%202013.pdf

Control allocation—A survey

This paper addresses the problem of the allocation of several airplane flight controls to the generation of specified body-axis moments. The number of controls is greater than the number of moments being controlled, and the ranges of the controls are constrained to certain limits. They are assumed to be individually linear in their effect throughout their ranges of motion and independent of one another in their effects. The geometries of the subset of the constrained controls and of its image in moment space are examined. A direct method of allocating these several controls is presented that guarantees the maximum possible moment can be generated within the constraints of the controls. It is shown that no single generalized inverse can yield these maximum moments everywhere without violating some control constraint. A method is presented for the determination of a generalized inverse that satisfies given specifications which are arbitrary but restricted in number. We then pose and solve a minimization problem that yields the generalized inverse that best approximates the exact solutions. The results are illustrated at each step by an example problem involving three controls and two moments.

Constrained Control Allocation

This paper presents a method for the solution of the constrained control allocation problem for the case of three moments. The control allocation problem is to find the "best" combination of several flight control effectors for the generation of specified body-axis moments. The number of controls is greater than the number of moments being controlled, and the ranges of the controls are constrained to certain limits. The controls are assumed to be individually linear in their effect throughout their ranges of motion and complete in the sense that they generate moments in arbitrary combinations. The best combination of controls is taken to be an apportioning of the controls that yields the greatest total moment in a specified ratio of moments without exceeding any control constraint. The method of solving the allocation problem is presented as an algorithm and is demonstrated for a problem of seven aerodynamic controls on an F-18 airplane.

Constrained control allocation - Three-moment problem

This paper describes the results of recent research into the problem of allocating several flight control effectors to generate moments acting on a flight vehicle. The results focus on the use of various generalized inverse solutions and a hybrid solution utilizing daisy chaining. In this analysis, the number of controls is greater than the number of moments being controlled, and the ranges of the controls are constrained to certain limits. The control effectors are assumed to be individually linear in their effects throughout their ranges of motion and independent of one another in their effects. A standard of comparison is developed based on the volume of moments or moment coefficients a given method can yield using admissible control deflections. Details of the calculation of the various volumes are presented. Results are presented for a sample problem involving 10 flight control effectors. The effectivenesses of the various allocation schemes are contrasted during an aggressive roll about the velocity vector at low dynamic pressure. The performance of three specially derived generalized inverses, a daisy-chaining solution, and direct control allocation are compared.

Closed-form solutions to constrained control allocation problem

Attainable moments for the constrained control allocation problem

A computationally efficient method for calculating near-optimal solutions to the three-objective, linear control allocation problem is disclosed. The control allocation problem is that of distributing the effort of redundant control effectors to achieve some desired set of objectives. The problem is deemed linear if control effectiveness is affine with respect to the individual control effectors. The optimal solution is that which exploits the collective maximum capability of the effectors within their individual physical limits. Computational efficiency is measured by the number of floating-point operations required for solution. The method presented returned optimal solutions in more than 90% of the cases examined; non-optimal solutions returned by the method were typically much less than 1% different from optimal and the errors tended to become smaller than 0.01% as the number of controls was increased. The magnitude of the errors returned by the present method was much smaller than those that resulted from either pseudo inverse or cascaded generalized inverse solutions. The computational complexity of the method presented varied linearly with increasing numbers of controls; the number of required floating point operations increased from 5.5 i, to seven times faster than did the minimum-norm solution (the pseudoinverse), and at about the same rate as did the cascaded generalized inverse solution. The computational requirements of the method presented were much better than that of previously described facet-searching methods which increase in proportion to the square of the number of controls.

/pdf/computationally-efficient-control-allocation-o2c1zidchd.pdf

Wayne Durham

Papers

Constrained Control Allocation

Constrained control allocation - Three-moment problem

Closed-form solutions to constrained control allocation problem

Attainable moments for the constrained control allocation problem

Computationally efficient control allocation