Accelerated Reduced Gradient Algorithm with Constraint Relaxation in Differential Inverse Kinematics

The Moore-Penrose pseudoinverse-based solution of the differential inverse kinematic task of redundant robots corresponds to the result of a particular optimization underconstraints in which the implementation of Lagrange’s ReducedGradient Algorithm can be evaded simply by considering the zero partial derivatives of the ”Auxiliary Function” associated with this problem. This possibility arises because of the fact that the cost term is built up of quadratic functions of the variable of optimization while the constraint term is linear function of the same variables. Any modification in the cost and/or constraint structure makes it necessary the use of the numerical algorithm. Anyway, the penalty effect of the cost terms is always overridden by the hard constraints that makes practical problems in the vicinity of kinematic singularities where the possible solution stillexists but needs huge joint coordinate time-derivatives. While in the special case the pseudoinverse simply can be deformed, inthe more general one more sophisticated constraint relaxation can be applied. In this paper a formerly proposed acceleratedtreatment of the constraint terms is further developed by the introduction of a simple constraint relaxation. Furthermore, thenumerical results of the algorithm are smoothed by a third order tracking strategy to obtain dynamically implementable solution.The improved method’s operation is exemplified by computation results for a 7 degree of freedom open kinematic chain

A New Augmented Lagrangian Method for MPCCs—Theoretical and Numerical Comparison with Existing Augmented Lagrangian Methods

We propose a new augmented Lagrangian (AL) method for solving the mathematical program with complementarity constraints (MPCC), where the complementarity constraints are left out of the AL function and treated directly. Two observations motivate us to propose this method: The AL subproblems are closer to the original problem in terms of the constraint structure; and the AL subproblems can be solved efficiently by a nonmonotone projected gradient method, in which we have closed-form solutions at each iteration. The former property helps us show that the proposed method converges globally to an M-stationary (better than C-stationary) point under MPCC relaxed constant positive linear dependence condition. Theoretical comparison with existing AL methods demonstrates that the proposed method is superior in terms of the quality of accumulation points and the strength of assumptions. Numerical comparison, based on problems in MacMPEC, validates the theoretical results.

Optimal solutions of multiplier DEA models

Conventional models of data envelopment analysis (DEA) are based on the constant and variable returns-to-scale production technologies. Any optimal input and output weights of the multiplier DEA models based on these technologies are interpreted as being the most favorable for the decision making unit (DMU) under the assessment when the latter is benchmarked against the set of all observed DMUs. In this paper we consider a very large class of DEA models based on arbitrary polyhedral technologies, which includes almost all known convex DEA models. We highlight the fact that the conventional interpretation of the optimal input and output weights in such models is generally incorrect, which raises a question about the meaning of multiplier models. We address this question and prove that the optimal solutions of such models show the DMU under the assessment in the best light in comparison to the entire technology, but not necessarily in comparison to the set of observed DMUs. This result allows a clear and meaningful interpretation of the optimal solutions of multiplier models, including known models with a complex constraint structure whose interpretation has been problematic and left unaddressed in the existing literature.

An Electrostatic Self-Excited Resonator with Pre-Tension/Pre-Compression Constraint for Active Rotation Control

We report a novel electrostatic self-excited resonator driven by DC voltage that achieves variable velocity-position characteristics via applying the pre-tension/pre-compression constraint. The resonator consists of a simply supported micro-beam, two plate electrodes, and two adjustable constraint bases, and it can be under pre-compression or pre-tension constraint by adjusting the distance L between two constraint bases (when beam length l > L, the resonator is under pre-compression and when l < L, it is under pre-tension). The oscillating velocity of the beam reaches the maximum value in the position around electrodes under the pre-compression constraint and reaches the maximum value in the middle position between two electrodes under the pre-tension condition. By changing the constraint of the microbeam, the position of the maximum velocity output of the oscillating beam can be controlled. The electrostatic self-excited resonator with a simple constraint structure under DC voltage has great potential in the field of propulsion of micro-robots, such as active rotation control of flapping wings.

Propositional Constraint Graphs: An Intuitive, Domain-General Tool for Diagramming Knowledge, Assumptions, and Uncertainties

A diagramming method called Propositional Constraint (PC) graphing was developed as an aid for tasks involving argumentation, planning, and design. Motivated by several AI models of defeasible (or non- monotonic) reasoning, PC graphs were designed to represent knowledge according to an analogical framework in which constraints (e.g., evidence, goals, system constraints) may elicit or deny possibilities (e.g., explanations, decisions, behaviors). In cases of underspecification, an absence of constraints yields uncertainty and competition among plausible outcomes. In cases of overspecification, no plausible outcome is yielded until one of the constraints is amended or forfeited. This framework shares features with theoretical models of reasoning and argumentation, but despite its intuitiveness and applicability, we know of no modeling language or graphical aid that explicitly depicts this defeasible constraint structure. We describe the syntax and semantics for PC graphing and then illustrate potential uses for it.

Gossip and Reputation in Social Networks

This contribution suggests and defends two propositions. First, gossip and reputation are coevolving relational phenomena, which conceptually overlap and empirically reinforce one another. Second, this coevolution is shaped by the opportunity and constraint structure of the social networks (e.g., organizations) in which these phenomena are typically embedded. The chapter presents theorizing, measures, and empirical findings on information sharing along three analytical levels. At the macro level, global structures describe overall network characteristics, such as density; at the meso level, local structures concern triadic configurations, like transitivity and clustering; at the micro level, individual structures cover ego-centric measures, including actor centrality and betweenness. The overview closes with three major suggestions for future research avenues on the study of gossip and reputation from a social network perspective.

Comparative social policy analysis of parental leave policies through the lens of the capability approach

This chapter analyses public parental leave in five pairs of European countries and assesses its opportunity potential to facilitate equal parental involvement and employment, focusing on gender and income opportunity gaps. It draws on Sen's capability approach and Weber's ideal-types to comparative policy analysis. It offers the ideal parental leave design, one which minimizes the policy-generated gender and class inequality in parents' opportunities to share parenting while working, thus providing real opportunities for different groups of individuals to achieve valued functionings as parents. Five policy indicators are created using benchmarking and graphical analysis and two sources of opportunity inequality are considered: the leave system as the opportunity and constraint structure and the socio-economic contexts as the conversion factors. The chapter produces a comprehensive overview of national leave policies, visually presenting leave policy across ten European countries. It demonstrates that leave systems in countries from the same welfare regime can diverge in the degree to which they create real opportunities for parents and children as well as in key policy dimensions through which these opportunities are created.

Hamiltonian analysis of a topological theory in the presence of boundaries

We perform the canonical Hamiltonian analysis of a topological gauge theory, that can be seen both as a theory defined on a four-dimensional spacetime region with boundaries — the bulk theory —, or as a theory defined on the boundary of the region — the boundary theory —. In our case, the bulk theory is given by the 4-dimensional [Formula: see text] Pontryagin action and the boundary one is defined by the [Formula: see text] Chern–Simons action. We analyze the conditions that need to be imposed on the bulk theory so that the total Hamiltonian, smeared constraints and generators of gauge transformations be well defined (differentiable) for generic boundary conditions. We pay special attention to the interplay between the constraints and boundary conditions in the bulk theory on the one side, and the constraints in the boundary theory, on the other side. We illustrate how both theories are equivalent, despite the different canonical variables and constraint structure, by explicitly showing that they both have the same symmetries, degrees of freedom and observables.