The form-closure and force-closure properties of robotic grasping can be loosely defined as the capability of the robot to inhibit motions of the workpiece in spite of externally applied forces. In this paper, the for...
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The form-closure and force-closure properties of robotic grasping can be loosely defined as the capability of the robot to inhibit motions of the workpiece in spite of externally applied forces. In this paper, the form-closure property of robotic grasping is considered as a purely geometric property of a set of unilateral (contact) constraints, such as those applied on a workpiece by a mechanical fixture. The concept of partial form-closure is introduced and discussed in relation with other concepts appeared in literature, such as accessibility and detachability. An algorithm is proposed to obtain a synthetic geometric description of partial form-closure constraints.
In this paper, we outline the design of linear controllers by convex programming and demonstrate its merits for an example which has been treated with purely analytic methods before. It is shown that the choice of the...
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In this paper, we outline the design of linear controllers by convex programming and demonstrate its merits for an example which has been treated with purely analytic methods before. It is shown that the choice of the base functions for the series expansion of the Youla parameter is crucial for the success. A modified procedure which reduces this problem is described.
We study a special universal “conic” formulation of a convex program where the problem is in minimizing a linear objective over the intersection of a convex cone and an affine plane. We focus on the duality relation...
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Formulas for computing the directional derivative of the optimal value function or of lower or upper bounds of it are well-known from literature. Because they have as a rule a minmax structure, methods from nondiffere...
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The central cutting plane algorithm for linear semi-infinite programming (SIP) is extended to nonlinear convex SIP of the form min {f(x)vertical bar x is an element of H, g(x, t) <= 0 all t is an element of S}. Und...
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The central cutting plane algorithm for linear semi-infinite programming (SIP) is extended to nonlinear convex SIP of the form min {f(x)vertical bar x is an element of H, g(x, t) <= 0 all t is an element of S}. Under differentiability assumptions that are weaker than those employed in superlinearly convergent algorithms, a linear convergence rate is established that has additional important features. These features are the ability to (i) generate a cut from any violated constraint;(ii) invoke efficient constraint-dropping rules for management of linear programming (LP) subproblem size;(iii) provide an efficient grid management scheme to generate cuts and ultimately to test feasibility to a high degree of accuracy, as well as to provide an automatic grid refinement for use in obtaining admissible starting solutions for the nonlinear system of first-order conditions;and, (iv) provide primal and dual (Lagrangian) SIP feasible solutions in a finite number of iterations.
This paper deals with the H(infinity) guaranteed cost control problem for continuous-time uncertain systems. It consists of the determination of a stabilizing state feedback gain which imposes on all possible closed-l...
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This paper deals with the H(infinity) guaranteed cost control problem for continuous-time uncertain systems. It consists of the determination of a stabilizing state feedback gain which imposes on all possible closed-loop models an H(infinity)-norm upper bound gamma > 0. Assuming that the uncertain domain is convex-bounded and the uncertain system is quadratic-stabilizable with gamma disturbance attenuation, it is shown how to determine, by means of a convex programming problem, the global minimum of gamma. As a particular and important case, for precisely known linear systems, the last problem reduces to the classical H(infinity) optimal control problem. The results follow from the definition of a special parameter space on which the above-mentioned problems are convex.
A mixed H2/H(infinity) control problem for discrete-time systems is considered, where an upper bound on the H2 norm of a closed loop transfer matrix is minimized subject to an H(infinity) constraint on another closed ...
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A mixed H2/H(infinity) control problem for discrete-time systems is considered, where an upper bound on the H2 norm of a closed loop transfer matrix is minimized subject to an H(infinity) constraint on another closed loop transfer matrix. Both state-feedback and output-feedback cases are considered. It is shown that these problems are equivalent to finite-dimensional convex programming problems. In the state-feedback case, nearly optimal controllers can be chosen to be static gains. In the output feedback case, nearly optimal controllers can be chosen to have a structure similar to that of the central single objective H(infinity) controller. In particular, the state dimension of nearly optimal output-feedback controllers need not exceed the plant dimension.
In this paper, we present a general scheme for bundle-type algorithms which includes a nonmonotone line search procedure and for which global convergence can be proved. Some numerical examples are reported, showing th...
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In this paper, we present a general scheme for bundle-type algorithms which includes a nonmonotone line search procedure and for which global convergence can be proved. Some numerical examples are reported, showing that the nonmonotonicity can be beneficial from a computational point of view.
Let T be a maximal monotone operator defined on R(N). In this paper we consider the associated variational inequality 0 is-an-element-of T(x*) and stationary sequences {x(k)*} for this operator, i.e., satisfying T(x(k...
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Let T be a maximal monotone operator defined on R(N). In this paper we consider the associated variational inequality 0 is-an-element-of T(x*) and stationary sequences {x(k)*} for this operator, i.e., satisfying T(x(k)*) --> 0. The aim of this paper is to give sufficient conditions ensuring that these sequences converge to the solution set T - 1(0) especially when they are unbounded. For this we generalize and improve the directionally local boundedness theorem of Rockafellar to maximal monotone operators T defined on R(N).
This paper proposes a new approach to determine H2 optimal control for discrete-time linear systems, based on convex programming. It is shown that all stabilizing state feedback control gains belong to a certain conve...
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This paper proposes a new approach to determine H2 optimal control for discrete-time linear systems, based on convex programming. It is shown that all stabilizing state feedback control gains belong to a certain convex set, well-defined in a special parameter space. The Linear Quadratic Problem can be then formulated as the minimization of a linear objective over a convex set. The optimal solution of this convex problem furnishes, under certain conditions, the same feedback control gain which is obtained from the classical discrete-time Riccati equation solution. Furthermore, the method proposed can also handle additional constraints, for instance, the ones needed to assure asymptotical stability of discrete-time systems under actuators failure. Some examples illustrate the theory.
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