Geometry-Based Optimal Rate Coordination for Robot Manipulators With Redundancy

1992 ◽  
Author(s):  
K. R. Hareendra Varma ◽  
Ming Z. Huang
Keyword(s):  
Objective Function ◽  
Closed Form ◽  
Optimal Solution ◽  
Minimum Norm ◽  
Redundancy Resolution ◽  
Minimum Norm Solution ◽  
Serial Chain ◽  
Gradient Solution ◽  
Resolution Problem ◽  
The Common

Abstract The redundancy resolution problem for kinematically redundant serial chain manipulators is addressed. In this paper, we present a generalization of the geometry based rate allocation algorithm, developed initially in [12] for only minimum norm solution, to obtain the optimal joint rate solution for any specified objective function, with or without weightage. This generalization is made possible through a geometrical interpretation of the common pseudoinverse-based gradient solution scheme, and by developing a modified formulation for the objective function as a minimum criterion not with respect to the origin of the joint rate space, but with respect to another point in the joint rate space represented by the gradient of the specified objective. Application examples of the algorithm including procedures of solution are demonstrated using 7R manipulators with two generic types of geometry. A closed form optimal solution for the 7R anthropomorphic arm considered is also presented.

A More Effective Formulation of the Path Generation Mechanism Synthesis Problem

1994 ◽  
Author(s):  
Irfan Ullah ◽  
Sridhar Kota
Keyword(s):  
Objective Function ◽  
Error Function ◽  
Mathematical Optimization ◽  
Optimization Methods ◽  
Complex Nature ◽  
Mechanism Synthesis ◽  
Structural Error ◽  
Crank Angle ◽  
The Common ◽  
Selection Of

Abstract Use of mathematical optimization methods for synthesis of path-generating mechanisms has had only limited success due to the very complex nature of the commonly used Structural Error objective function. The complexity arises, in part, because the objective function represents not only the error in the shape of the coupler curve, but also the error in location, orientation and size of the curve. Furthermore, the common introduction of timing (or crank angle), done generally to facilitate selection of corresponding points on the curve for calculating structural error, has little practical value and unnecessarily limits possible solutions. This paper proposes a new objective function, based on Fourier Descriptors, which allows search for coupler curve of the desired shape without reference to location, orientation, or size. The proposed objective function compares overall shape properties of curves rather than making point-by-point comparison and therefore does not requires prescription of timing. Experimental evidence is provided to show that it is much easier to search the space of the proposed objective function compared to the structural error function.

Failure recovery for wrench capability of wire-actuated parallel manipulators

Robotica ◽  
2011 ◽  
Vol 30 (6) ◽  
pp. 941-950 ◽  
Author(s):  
Leila Notash
Keyword(s):  
Failure Modes ◽  
Parallel Manipulators ◽  
Failure Recovery ◽  
Partial Recovery ◽  
Minimum Norm ◽  
Minimum Norm Solution ◽  
Actuator Failures ◽  
Force Moment ◽  
Hybrid Actuation

SUMMARYWire-actuated parallel manipulators and their failures are studied in this paper taking into consideration their failure modes. A methodology for investigating the effect of wire/actuator failures on the force/moment capability of manipulators is presented, and the criteria for full and partial recovery from these failures are established. The methodology is also applicable for the cases that the minimum norm solution for the vector of wire tensions gives a negative value for tension by treating the corresponding wire as failed. The proposed criteria are also valid for the manipulators that utilize hybrid actuation of wires and joints. Three planar wire-actuated parallel manipulators are used as the case study to illustrate the proposed methodology and criteria.

scholarly journals An evolutionary-based optimization algorithm for truss sizing design

2016 ◽  
Vol 38 (4) ◽  
pp. 307-317
Author(s):  
Pham Hoang Anh
Keyword(s):  
Local Search ◽  
Objective Function ◽  
Optimization Algorithm ◽  
Optimization Problems ◽  
Optimal Solution ◽  
The Other ◽  
Truss Structures ◽  
Benchmark Problems ◽  
Discrete Variables ◽  
Objective Functions

In this paper, the optimal sizing of truss structures is solved using a novel evolutionary-based optimization algorithm. The efficiency of the proposed method lies in the combination of global search and local search, in which the global move is applied for a set of random solutions whereas the local move is performed on the other solutions in the search population. Three truss sizing benchmark problems with discrete variables are used to examine the performance of the proposed algorithm. Objective functions of the optimization problems are minimum weights of the whole truss structures and constraints are stress in members and displacement at nodes. Here, the constraints and objective function are treated separately so that both function and constraint evaluations can be saved. The results show that the new algorithm can find optimal solution effectively and it is competitive with some recent metaheuristic algorithms in terms of number of structural analyses required.

Design and robustness analysis of fuzzy PID controller for automatic voltage regulator system using genetic algorithm

2022 ◽  
pp. 014233122110667
Author(s):  
Tufan Dogruer ◽  
Mehmet Serhat Can
Keyword(s):  
Genetic Algorithm ◽  
Objective Function ◽  
Pid Controller ◽  
Robustness Analysis ◽  
Optimal Solution ◽  
Voltage Regulator ◽  
Fuzzy Pid ◽  
Multi Objective ◽  
Fuzzy Pid Controller ◽  
Automatic Voltage Regulator

In this paper, a Fuzzy proportional–integral–derivative (Fuzzy PID) controller design is presented to improve the automatic voltage regulator (AVR) transient characteristics and increase the robustness of the AVR. Fuzzy PID controller parameters are determined by a genetic algorithm (GA)-based optimization method using a novel multi-objective function. The multi-objective function, which is important for tuning the controller parameters, obtains the optimal solution using the Integrated Time multiplied Absolute Error (ITAE) criterion and the peak value of the output response. The proposed method is tested on two AVR models with different parameters and compared with studies in the literature. It is observed that the proposed method improves the AVR transient response properties and is also robust to parameter changes.

An Exact Algorithm for Large-Scale Continuous Nonlinear Resource Allocation Problems with Minimax Regret Objectives

2021 ◽  
Author(s):  
Jungho Park ◽  
Hadi El-Amine ◽  
Nevin Mutlu
Keyword(s):  
Resource Allocation ◽  
Objective Function ◽  
Large Scale ◽  
Computational Study ◽  
Optimal Solution ◽  
Exact Algorithm ◽  
Minimax Regret ◽  
Optimal Solutions ◽  
Heuristic Approaches ◽  
Exact Approach

We study a large-scale resource allocation problem with a convex, separable, not necessarily differentiable objective function that includes uncertain parameters falling under an interval uncertainty set, considering a set of deterministic constraints. We devise an exact algorithm to solve the minimax regret formulation of this problem, which is NP-hard, and we show that the proposed Benders-type decomposition algorithm converges to an [Formula: see text]-optimal solution in finite time. We evaluate the performance of the proposed algorithm via an extensive computational study, and our results show that the proposed algorithm provides efficient solutions to large-scale problems, especially when the objective function is differentiable. Although the computation time takes longer for problems with nondifferentiable objective functions as expected, we show that good quality, near-optimal solutions can be achieved in shorter runtimes by using our exact approach. We also develop two heuristic approaches, which are partially based on our exact algorithm, and show that the merit of the proposed exact approach lies in both providing an [Formula: see text]-optimal solution and providing good quality near-optimal solutions by laying the foundation for efficient heuristic approaches.

Optimizing Series Repairable Systems with Imperfect Repair

2013 ◽  
pp. 83-93
Author(s):  
Mohammed Hajeeh
Keyword(s):  
Mathematical Model ◽  
Closed Form ◽  
Optimal Solution ◽  
Closed Form Expression ◽  
Repairable Systems ◽  
Nonlinear Mathematical Model ◽  
Repair Rate ◽  
Imperfect Repair ◽  
Repair Models ◽  
Minimum Costs

Repairable systems are either repaired perfectly to a state of as good as new or imperfectly. In this work, a system which undergoes imperfect repair is investigated. A nonlinear mathematical model is formulated for a system with the objective of finding the optimum failure and repair rate with the minimum costs subject to attaining a pre-specified performance level. Two imperfect repair models are examined. In the first model, the system is replaced by a new one after several failures. In the second model, the system is either replaced with a specific probability (1-p) or is imperfectly repaired after each failure with probability p. The optimal solution is presented in a closed form expression.

Solving Solid Transportation Problems With Multi-Choice Cost and Stochastic Supply and Demand

2018 ◽  
pp. 137-170 ◽  
Author(s):  
Sankar Kumar Roy ◽  
Deshabrata Roy Mahapatra
Keyword(s):  
Stochastic Programming ◽  
Objective Function ◽  
Transportation Problem ◽  
Supply And Demand ◽  
Optimal Solution ◽  
Programming Approach ◽  
Solid Transportation Problem ◽  
New Approach ◽  
Non Linear Programming ◽  
The Cost

In this chapter, the authors propose a new approach to analyze the Solid Transportation Problem (STP). This new approach considers the multi-choice programming into the cost coefficients of objective function and stochastic programming, which is incorporated in three constraints, namely sources, destinations, and capacities constraints, followed by Cauchy's distribution for solid transportation problem. The multi-choice programming and stochastic programming are combined into a solid transportation problem, and this new problem is called Multi-Choice Stochastic Solid Transportation Problem (MCSSTP). The solution concepts behind the MCSSTP are based on a new transformation technique that will select an appropriate choice from a set of multi-choice, which optimize the objective function. The stochastic constraints of STP converts into deterministic constraints by stochastic programming approach. Finally, the authors construct a non-linear programming problem for MCSSTP, and by solving it, they derive an optimal solution of the specified problem. A realistic example on STP is considered to illustrate the methodology.

Sign in / Sign up

Export Citation Format

Share Document