Type Parametric Compilation of Algebraic Constraints

2009 ◽  
pp. 201-212 ◽  
Author(s):  
Marco Correia ◽  
Pedro Barahona
Keyword(s):  
Algebraic Constraints

Formation of Geometric Tolerance Zones for Polyhedral Objects

1997 ◽  
Author(s):  
Utpal Roy ◽  
Bing Li
Keyword(s):  
Variational Model ◽  
Tolerance Zone ◽  
Geometric Tolerance ◽  
Geometric Tolerances ◽  
Polyhedral Objects ◽  
Different Types ◽  
Tolerance Zones ◽  
Algebraic Constraints ◽  
Size Tolerance ◽  
Part Model

Abstract This paper presents a scheme for establishing geometric tolerance zones for polyhedral objects in solid modelers. The proposed scheme is based on a surface-based variational model. Variations are applied to a part model by varying each surface’s model variables. Those model variables are constrained by some algebraic relations derived from the specified geometric tolerances. For size tolerance, two types of tolerance zones are considered in order to reflect two different types of size tolerances. For any other geometric tolerance (form, orientation or positional), the resultant tolerance zone is defined by the combination of size tolerance and that particular geometric tolerance specifications. Appropriate algebraic constraints (on the model variables) are finally used to establish the tolerance zone boundaries in the surface-based variational model.

Positive fractional continuous-time linear systems with singular pencils

2012 ◽  
Vol 60 (1) ◽  
pp. 9-12 ◽  
Author(s):  
T. Kaczorek
Keyword(s):  
Linear Systems ◽  
Continuous Time ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Descriptor Systems ◽  
State Variables ◽  
Algebraic Constraints ◽  
Necessary And Sufficient ◽  
Time Linear

Positive fractional continuous-time linear systems with singular pencils A method for checking the positivity and finding the solution to the positive fractional descriptor continuous-time linear systems with singular pencils is proposed. The method is based on elementary row and column operations of the fractional descriptor systems to equivalent standard systems with some algebraic constraints on state variables and inputs. Necessary and sufficient conditions for the positivity of the fractional descriptor systems are established.

Constraint Manifold Synthesis of Planar Linkages

1996 ◽  
Author(s):  
A. P. Murray ◽  
J. M. McCarthy
Keyword(s):  
Design Theory ◽  
Geometric Constraints ◽  
Design Parameters ◽  
Design Problems ◽  
Constraint Manifold ◽  
Linkage Design ◽  
Versatile Tool ◽  
Algebraic Constraints ◽  
Planar Linkages

Abstract This paper formulates the design theory of planar four-bar linkages using the planar form of dual quaternions known as planar quaternions. The set of positions reachable by the floating link of a dyad is a quadratic algebraic surface called a constraint manifold. Determining the coefficients of the quadratic form defining this manifold is equivalent to setting the design parameters of the linkage. If the task of the linkage is specified as geometric constraints on the location of the floating link, then algebraic constraints are obtained on the quaternion components. We seek the coefficients of the constraint manifold that satisfies these constraints. The result is an algebraic formulation that is symmetric in its characterization of the linkage and task, and provides a versatile tool for the formulation and solution of linkage design problems.

Optimal Control Strategies for Wheeled Mobile Robot With Bounded Inputs

2010 ◽  
Author(s):  
Ilan Zohar ◽  
Amit Ailon
Keyword(s):  
Optimal Control ◽  
Mobile Robot ◽  
Control Strategies ◽  
Equations Of Motion ◽  
Wheeled Mobile Robots ◽  
Optimal Control Strategy ◽  
Input Signals ◽  
Control Objective ◽  
Quadratic Index ◽  
Algebraic Constraints

This paper presents a simple approach for solving optimal control problems in wheeled mobile robots with bounded inputs. The control objective is to minimize a quadratic index of performance subject to differential constraints (the mobile robot equations of motion). The solution to the problem is obtained by utilizing an explicit trajectory parametrization method, which allows us to establish a sub-optimal control strategy by minimizing a multivariable function subject to a set of algebraic constraints. The approach is based on the flatness property, which allows us to represent the flat output by a polynomial. The bounds on the input signals are taken into consideration in the current analysis.

Second Order Sliding Mode Neural Network-Based Visual Servoing of Robot Hands With Fast Manipulation, Including Transition

2005 ◽  
Author(s):  
Rodolfo Garci´a-Rodri´guez ◽  
V. Parra-Vega ◽  
Francisco Rui´z-Sa´nchez
Keyword(s):  
Neural Network ◽  
Visual Servoing ◽  
Sliding Mode ◽  
Second Order ◽  
Constrained Motion ◽  
Unilateral Constraints ◽  
Robot Hands ◽  
Commuting Time ◽  
Algebraic Constraints ◽  
The Impact

Strictly speaking, transition tasks such as those executed by robot hands involve free, impact, and constrained motion regimes, with changing dynamics. Impulsive, unilateral constraints arises in the impact regime, which makes very difficult to design a control system. Moreover, algebraic constraints arise in the constrained regime. The trivial approach would be to avoid impact, and to commute consistently ODE- and DAE-based controller, or to impose virtual constraints to model as a DAE system all regimes. In any case, it is required to know exactly the commuting time. In this paper, a very simple control scheme is proposed based on avoiding impact regime, through zero transition velocity from free to constrained motion, therefore impulsive dynamics does not appear. This is possible because we guarantee exactly the time to commute with a novel well-posed finite time convergence scheme, to produce convergence toward any desired trajectory at any given arbitrarily time and for any initial condition. In this way, ODE and DAE dynamics/controllers commute stably. Inertial and gravitational forces are compensated by a recurrent neural network driven by image-based position and force tracking errors, with a decentralized structure for each robot. The network is tuned on line with a second order force-position sliding modes to finally guarantee exponential tracking.

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