Control of Redundant Joint Structures Using Image Information During the Tracking of Non-Smooth Trajectories

Visual information is increasingly being used in a great number of applications in order to perform the guidance of joint structures. This paper proposes an image-based controller which allows the joint structure guidance when its number of degrees of freedom is greater than the required for the developed task. In this case, the controller solves the redundancy combining two different tasks: the primary task allows the correct guidance using image information, and the secondary task determines the most adequate joint structure posture solving the possible joint redundancy regarding the performed task in the image space. The method proposed to guide the joint structure also employs a smoothing Kalman filter not only to determine the moment when abrupt changes occur in the tracked trajectory, but also to estimate and compensate these changes using the proposed filter. Furthermore, a direct visual control approach is proposed which integrates the visual information provided by this smoothing Kalman filter. This last aspect permits the correct tracking when noisy measurements are obtained. All the contributions are integrated in an application which requires the tracking of the faces of Asperger children.

Mathematical approach for predicting non-negative tristimulus values using the CAT02 chromatic adaptation transform

It has been reported that for certain colour samples, the chromatic adaptation transform CAT02 imbedded in the CIECAM02 colour appearance model predicts corresponding colours with negative tristimulus values (TSVs), which can cause problems in certain applications. To overcome this problem, a mathematical approach is proposed for modifying CAT02. This approach combines a non-negativity constraint for the TSVs of corresponding colours with the minimization of the colour differences between those values for the corresponding colours obtained by visual observations and the TSVs of the corresponding colours predicted by the model, which is a constrained non-linear optimization problem. By solving the non-linear optimization problem, a new matrix is found. The performance of the CAT02 transform with various matrices including the original CAT02 matrix, and the new matrix are tested using visual datasets and the optimum colours. Test results show that the CAT02 with the new matrix predicted corresponding colours without negative TSVs for all optimum colours and the colour matching functions of the two CIE standard observers under the test illuminants considered. However, the accuracy with the new matrix for predicting the visual data is approximately 1 CIELAB colour difference unit worse compared with the original CAT02. This indicates that accuracy has to be sacrificed to achieve the non-negativity constraint for the TSVs of the corresponding colours.

Comparative study of RPSALG algorithm for convex semi-infinite programming

The Remez penalty and smoothing algorithm (RPSALG) is a unified framework for penalty and smoothing methods for solving min-max convex semi-infinite programing problems, whose convergence was analyzed in a previous paper of three of the authors. In this paper we consider a partial implementation of RPSALG for solving ordinary convex semi-infinite programming problems. Each iteration of RPSALG involves two types of auxiliary optimization problems: the first one consists of obtaining an approximate solution of some discretized convex problem, while the second one requires to solve a non-convex optimization problem involving the parametric constraints as objective function with the parameter as variable. In this paper we tackle the latter problem with a variant of the cutting angle method called ECAM, a global optimization procedure for solving Lipschitz programming problems. We implement different variants of RPSALG which are compared with the unique publicly available SIP solver, NSIPS, on a battery of test problems.

Curtin-Hammett versus non-Curtin-Hammett frameworks is optimizing the enantioselective binolam/titanium(IV)-catalyzed cyanobenzoylation of aldehydes: Part 2

Extensive experimental and computational studies have been carried out on the enantioselective titanium(IV)-catalyzed cyanobenzoylation of aldehydes using 1:n Binolam:Ti(OiPr)4 mixtures as precatalysts, with the purpose of identifying the key mechanistic aspects governing enantioselectivity. HCN and isopropyl benzoate were detected in the reacting mixtures. This, as well as the reaction’s response to the presence of an exogenous base, and the failure to react in the presence of Binol:Ti(OiPr)4 mixtures, led us to propose not a direct cyanobenzoylation but an indirect process involving enantioselective hydrocyanation followed by O-benzoylation. Computational work provided positive evidence for the intervention of both indirect and direct cyanobenzoylation routes, the former being faster. However, the standard Curtin–Hammett-based optimization search ended with unsatisfactory results. Experimental and computational DFT studies (B3LYP/6-31G*) led us to conclude that: (1) the overall cyanobenzoylation of aldehydes catalyzed by 1:n Binolam:Ti(OiPr)4 mixtures involves an enantioselective hydrocyanation followed by an stereochemically inert O-benzoylation; (2) the initial complexes prevailing in a 1:1 Binolam:Ti(OiPr)4 mixture are the solvated mononuclear monomer 5·2(iPrOH) and solvated dinuclear dimer 9·2(iPrOH), whereas 9·2(iPrOH) is the major component in a 1:2 or higher 1:n mixture; (3) since the slowest step is that of benzoylation of ligated iPrOH which yields the actual catalysts 5–9, the catalytic system fits into a non-Curtin–Hammett framework, the final products deriving from a kinetic quench of the competing routes; and (4) accordingly, catalysis by 1:1 Binolam:Ti(OiPr)4 mixtures should involve cyanobenzoylations promoted by mononuclear 5, contaminated with those promoted by some dinuclear open dimer 9, whereas cyanobenzoylations catalyzed by a 1:2 and higher 1:n mixtures should be the result of catalysis promoted by the large amounts of dinuclear open dimer 9.

An alternative disjunctive optimization model for heat integration with variable temperatures

This paper presents an alternative model to deal with the problem of optimal energy consumption minimization of non-isothermal systems with variable inlet and outlet temperatures. The model is based on an implicit temperature ordering and the “transshipment model” proposed by Papoulias and Grossmann (1983). It is supplemented with a set of logical relationships related to the relative position of the inlet temperatures of process streams and the dynamic temperature intervals. In the extreme situation of fixed inlet and outlet temperatures, the model reduces to the “transshipment model”. Several examples with fixed and variable temperatures are presented to illustrate the model's performance.

Mathematical programming model for heat exchanger design through optimization of partial objectives

Mathematical programming can be used for the optimal design of shell-and-tube heat exchangers (STHEs). This paper proposes a mixed integer non-linear programming (MINLP) model for the design of STHEs, following rigorously the standards of the Tubular Exchanger Manufacturers Association (TEMA). Bell–Delaware Method is used for the shell-side calculations. This approach produces a large and non-convex model that cannot be solved to global optimality with the current state of the art solvers. Notwithstanding, it is proposed to perform a sequential optimization approach of partial objective targets through the division of the problem into sets of related equations that are easier to solve. For each one of these problems a heuristic objective function is selected based on the physical behavior of the problem. The global optimal solution of the original problem cannot be ensured even in the case in which each of the sub-problems is solved to global optimality, but at least a very good solution is always guaranteed. Three cases extracted from the literature were studied. The results showed that in all cases the values obtained using the proposed MINLP model containing multiple objective functions improved the values presented in the literature.

Isobutane Alkylation Process Synthesis by means of Hybrid Simulation-Multiobjective Optimization

Multiobjective Generalized Disjunctive Programming (MO-GDP) optimization has been used for the synthesis of an important industrial process, isobutane alkylation. The two objective functions to be simultaneously optimized are the environmental impact, determined by means of LCA (Life Cycle Assessment), and the economic potential of the process. The main reason for including the minimization of the environmental impact in the optimization process is the widespread environmental concern by the general public. For the resolution of the problem we employed a hybrid simulation- optimization methodology, i.e., the superstructure of the process was developed directly in a chemical process simulator connected to a state of the art optimizer. The model was formulated as a GDP and solved using a logic algorithm that avoids the reformulation as MINLP -Mixed Integer Non Linear Programming-. Our research gave us Pareto curves compounded by three different configurations where the LCA has been assessed by two different parameters: global warming potential and ecoindicator-99.

Optimization of Chemical Processes Using Surrogate Models Based on a Kriging Interpolation

Superstructure approaches are the solution to the difficult problem which involves the rigorous economic design of a distillation column. These methods require complex initialization procedures and they are hard to solve. For this reason, these methods have not been extensively used. In this work, we present a methodology for the rigorous optimization of chemical processes implemented on a commercial simulator using surrogate models based on a kriging interpolation. Several examples were studied, but in this paper, we perform the optimization of a superstructure for a non-sharp separation to show the efficiency and effectiveness of the method. Noteworthy that it is possible to get surrogate models accurate enough with up to seven degrees of freedom.