Accelerated Reduced Gradient Algorithm with Constraint Relaxation in Differential Inverse Kinematics

2021 ◽  
Vol 1 (2) ◽  
pp. 21-32
Author(s):  
Bence Varga ◽  
Hazem Issa ◽  
Richárd Horváth ◽  
József Tar
Keyword(s):  
Kinematic Chain ◽  
Auxiliary Function ◽  
Inverse Kinematic ◽  
Quadratic Functions ◽  
Gradient Algorithm ◽  
Constraint Relaxation ◽  
Hard Constraints ◽  
Reduced Gradient ◽  
Constraint Structure ◽  
The Cost

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

Optimal Design of Semisubmersible’s Form Based on Systems Analysis

1984 ◽  
Vol 106 (4) ◽  
pp. 524-530 ◽  
Author(s):  
S. Akagi ◽  
R. Yokoyama ◽  
K. Ito
Keyword(s):  
Optimal Design ◽  
Computer Aided Design ◽  
Optimization Problem ◽  
Design Method ◽  
Gradient Algorithm ◽  
Interpretive Structural Modeling ◽  
Reduced Gradient ◽  
Optimal Design Method ◽  
Generalized Reduced Gradient ◽  
Aided Design

With the objective of developing a computer-aided design method to seek the optimal semisubmersible’s form, hierarchical relationships among many design objectives and conditions are investigated first based on the interpretive structural modeling method. Then, an optimal design method is formulated as a nonlinear multiobjective optimization problem by adopting three mutually conflicting design objectives. A set of Pareto optimal solutions is derived numerically by adopting the generalized reduced gradient algorithm, and it is ascertained that the designer can determine the optimal form more rationally by investigating the trade-off relationships among design objectives.

A model for fi nding the optimal routes for a combined route container train

Innotrans ◽  
2021 ◽  
pp. 15-21
Author(s):  
Chang Hao ◽  
◽  
Daria Ivanovna Kochneva ◽  
Keyword(s):  
Software Implementation ◽  
Gradient Algorithm ◽  
Rolling Stock ◽  
Optimal Route ◽  
Delivery Time ◽  
Container Transportation ◽  
Cargo Handling ◽  
Reduced Gradient ◽  
Generalized Reduced Gradient ◽  
Train Loading

The article is devoted to the development of the model for finding an optimal route for a combined route container train (CRCT), i.e. a train with a designated route and schedule, en route from the initial to the final station without reforming of a rolling stock, but carrying out cargo handling operations for loading/unloading containers at intermediate stops of the route. It is proposed to call the optimal route of a CRCT, which provides the minimum delivery time while ensuring the targeted train loading on each section and with a set value of demand for container transportation at each point of the route. A software implementation of the model in the MS Excel environment is proposed using the built-in generalized reduced gradient algorithm.

scholarly journals Study on the Optimum Design of a Ground Heat Pump System Using Optimization Algorithms

Energies ◽  
2019 ◽  
Vol 12 (21) ◽  
pp. 4033 ◽  
Author(s):  
Moon ◽  
Kim ◽  
Nam
Keyword(s):  
Heat Pump ◽  
High Efficiency ◽  
Optimization Algorithms ◽  
Peak Load ◽  
Gradient Algorithm ◽  
System Capacity ◽  
Pump System ◽  
Partial Load ◽  
Investment Cost ◽  
The Cost

Geothermal energy has attracted attention as a high-efficiency energy source that can be used year-round, but it has a relatively higher initial investment cost. For the design of ground source heat pump (GSHP) systems, a calculation method to determine the capacity of a system to meet the peak load of the target building is usually used. However, this method requires excessive system capacity design, especially regarding buildings with partial load operations. In this study, the optimization of a system design was performed in the view of the cost of the lifecycle cost. Several optimization algorithms were considered, such as the discrete Armijo gradient algorithm, a particle swarm optimization (PSO) algorithm, and a coordinate search method algorithm. The results of the optimization described the system capacity (heat pump, ground heat exchanger, thermal storage tank, etc.) and the cost performance, showing that the total investment cost was reduced compared to the existing design.

Optimization of a Novel Combined Power/Refrigeration Thermodynamic Cycle

2003 ◽  
Vol 125 (2) ◽  
pp. 212-217 ◽  
Author(s):  
Shaoguang Lu ◽  
D. Yogi Goswami
Keyword(s):  
Waste Heat ◽  
Thermodynamic Cycle ◽  
Gradient Algorithm ◽  
Cycle Performance ◽  
Working Fluid ◽  
Heat Sources ◽  
Objective Functions ◽  
Ambient Temperatures ◽  
Reduced Gradient ◽  
Generalized Reduced Gradient

A novel combined power/refrigeration thermodynamic cycle is optimized for thermal performance in this paper. The cycle uses ammonia-water binary mixture as a working fluid and can be driven by various heat sources, such as solar, geothermal, and low temperature waste heat. The optimization program, which is based on the Generalized Reduced Gradient algorithm, can be used to optimize for different objective functions. In addition, cycle performance over a range of ambient temperatures was investigated.

scholarly journals Second-Order SCA Security with almost no Fresh Randomness

2021 ◽  
pp. 708-755
Author(s):  
Aein Rezaei Shahmirzadi ◽  
Amir Moradi
Keyword(s):  
Nonlinear Function ◽  
Target Function ◽  
Second Order ◽  
Quadratic Functions ◽  
Security Level ◽  
Cryptographic Primitives ◽  
Minimum Number ◽  
Implementation Costs ◽  
Channel Analysis ◽  
The Cost

Masking schemes are among the most popular countermeasures against Side-Channel Analysis (SCA) attacks. Realization of masked implementations on hardware faces several difficulties including dealing with glitches. Threshold Implementation (TI) is known as the first strategy with provable security in presence of glitches. In addition to the desired security order d, TI defines the minimum number of shares to also depend on the algebraic degree of the target function. This may lead to unaffordable implementation costs for higher orders.For example, at least five shares are required to protect the smallest nonlinear function against second-order attacks. By cuttingsuch a dependency, the successor schemes are able to achieve the same security level by just d + 1 shares, at the cost of high demand for fresh randomness, particularly at higher orders. In this work, we provide a methodology to realize the second-order glitch-extended probing-secure implementation of a group of quadratic functions with three shares and no fresh randomness. This allows us to construct second-order secure implementations of several cryptographic primitives with very limited number of fresh masks, including Keccak, SKINNY, Midori, PRESENT, and PRINCE.

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