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The Quickhull algorithm for convex hulls
 ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE
, 1996
"... 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 twodimensional Quickhull Algorithm with the generaldimension BeneathBeyond Algorithm. It is similar to the randomized, incremental algo ..."
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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 twodimensional Quickhull Algorithm with the generaldimension BeneathBeyond 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 uses less memory. Computational geometry algorithms have traditionally assumed that input sets are well behaved. When an algorithm is implemented with floatingpoint arithmetic, this assumption can lead to serious 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.
2006 “A Survey of Control Allocation Methods for Ships and Underwater
 Vehicles,” Invited paper at the 14th IEEE Mediterranean Conference on Control and Automation
"... Abstract — Control allocation problems for marine vessels can be formulated as optimization problems, where the objective typically is to minimize the use of control effort (or power) subject to actuator rate and position constraints, power constraints as well as other operational constraints. In ad ..."
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Cited by 6 (3 self)
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Abstract — Control allocation problems for marine vessels can be formulated as optimization problems, where the objective typically is to minimize the use of control effort (or power) subject to actuator rate and position constraints, power constraints as well as other operational constraints. In addition, singularity avoidance for vessels with azimuthing thrusters represent a challenging problem since a nonconvex nonlinear program must be solved. This is useful to avoid temporarily loss of controllability in some cases. In this paper, a survey of control allocation methods for overactuated vessels are presented. I.
Fault Tolerant Control Allocation for a ThrusterControlled Floating Platform using Parametric Programming
"... Abstract — The task in control allocation is to determine how to generate a specified generalized force from a redundant set of control effectors where the associated actuator control inputs are constrained, and other physical and operational constraints and objective should be met. In this paper we ..."
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Cited by 2 (1 self)
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Abstract — The task in control allocation is to determine how to generate a specified generalized force from a redundant set of control effectors where the associated actuator control inputs are constrained, and other physical and operational constraints and objective should be met. In this paper we consider a convex approximation to a control allocation problem for a thrustercontrolled floating platform. The platform has eight rotatable azimuth thrusters and the high level controller is assumed to specify three generalized forces; surge, sway and yaw. The control allocation problem is formulated as a convex quadraticor linear program, where the constraints are dependent on the specified generalized force. The problem is solved explicitly by viewing the generalized forces as a vector of parameters and utilizing parametric programming techniques. For convex parametric quadratic programs (pQP) or parametric linear programs (pLP) with a linear parametrization of the constraints, there always exists a continuous piecewise affine (PWA) minimizer function. Consequently, the conventional online optimization can be replaced by a simple evaluation of a PWA function. Experimental results for a scale model of a platform are presented. It is shown how thruster failure scenarios can be handled by automatic reconfiguration of the control allocation, exploiting symmetry of the thruster configuration.
Control Allocation A Survey
"... The control algorithm hierarchy of motion control for overactuated mechanical systems with a redundant set of effectors and actuators commonly includes three levels. First, a highlevel motion control algorithm commands a vector of virtual control efforts (i.e. forces and moments) in order to meet ..."
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The control algorithm hierarchy of motion control for overactuated mechanical systems with a redundant set of effectors and actuators commonly includes three levels. First, a highlevel motion control algorithm commands a vector of virtual control efforts (i.e. forces and moments) in order to meet the overall motion control objectives. Second, a control allocation algorithm coordinates the different effectors such that they together produce the desired virtual control efforts, if possible. Third, lowlevel control algorithms may be used to control each individual effector via its actuators. Control allocation offers the advantage of a modular design where the highlevel motion control algorithm can be designed without detailed knowledge about the effectors and actuators. Important issues such as input saturation and rate constraints, actuator and effector fault tolerance, and meeting secondary objectives such as power efficiency and tearandwear minimization are handled within the control allocation algorithm. The objective of the present paper is to survey control allocation algorithms, motivated by the rapidly growing range of applications that have expanded from the aerospace and maritime industries, where control allocation has its roots, to automotive, mechatronics, and other industries. The survey classifies the different algorithms according to two main classes based on the use of linear or nonlinear models, respectively. The presence of physical constraints (e.g input saturation and rate constraints), operational constraints and secondary objectives makes optimizationbased design a powerful approach. The simplest formulations allow explicit solutions to be computed using numerical linear algebra in combination with some logic and engineering solutions, while the more challenging formulations with nonlinear models or complex constraints and objectives call for iterative numerical optimization procedures.