Simultaneous Optimal Robot Base Placement and Motion Planning Using Expanded Lagrangian Homotopy

2016 ◽  
Author(s):  
Audelia Gumarus Dharmawan ◽  
Shaohui Foong ◽  
Gim Song Soh
Keyword(s):  
Motion Planning ◽  
Constrained Optimization ◽  
Optimization Problem ◽  
Planning Process ◽  
Inequality Constraints ◽  
Future Research ◽  
Lagrangian System ◽  
Constrained Optimization Problem ◽  
Continuation Problem ◽  
Joint Limits

This paper presents a new approach to simultaneously determine the optimal robot base placement and motion plan for a prescribed set of tasks using expanded Lagrangian homotopy. First, the optimal base placement is formulated as a constrained optimization problem based on manipulability and kinematics of the robot. Then, the constrained optimization problem is expressed into the expanded Lagrangian system and subsequently converted into a homotopy map. Finally, the Newton-Raphson method is used to solve the constrained optimization problem as a continuation problem. The complete formulation for the case of a 6-DOF manipulator is presented and a planar optimal mobile platform motion planning approach is proposed. Numerical simulations confirm that the proposed approach is able to achieve the desired results. The approach also shows the potential for incorporating factors such as joint limits or collision avoidance into the motion planning process as inequality constraints and will be part of future research.

scholarly journals Nonconvex constrained optimization by a filtering branch and bound

2020 ◽  
Author(s):  
Gabriele Eichfelder ◽  
Kathrin Klamroth ◽  
Julia Niebling
Keyword(s):  
Constrained Optimization ◽  
Optimization Problem ◽  
Feasible Solution ◽  
Constrained Optimization Problem ◽  
Numerical Tests ◽  
Nonconvex Constrained Optimization ◽  
Objective Value ◽  
Feasible Solutions ◽  
Quality Guarantee ◽  
Single Objective

AbstractA major difficulty in optimization with nonconvex constraints is to find feasible solutions. As simple examples show, the $$\alpha $$ α BB-algorithm for single-objective optimization may fail to compute feasible solutions even though this algorithm is a popular method in global optimization. In this work, we introduce a filtering approach motivated by a multiobjective reformulation of the constrained optimization problem. Moreover, the multiobjective reformulation enables to identify the trade-off between constraint satisfaction and objective value which is also reflected in the quality guarantee. Numerical tests validate that we indeed can find feasible and often optimal solutions where the classical single-objective $$\alpha $$ α BB method fails, i.e., it terminates without ever finding a feasible solution.

scholarly journals Optimal P-Q Control of Grid-Connected Inverters in a Microgrid Based on Adaptive Population Extremal Optimization

Energies ◽  
2018 ◽  
Vol 11 (8) ◽  
pp. 2107 ◽  
Author(s):  
Min-Rong Chen ◽  
Huan Wang ◽  
Guo-Qiang Zeng ◽  
Yu-Xing Dai ◽  
Da-Qiang Bi
Keyword(s):  
Constrained Optimization ◽  
Optimization Problem ◽  
Reactive Power ◽  
Active Power ◽  
Adaptive Genetic Algorithm ◽  
Constrained Optimization Problem ◽  
Extremal Optimization ◽  
Active And Reactive Power ◽  
Three Phase ◽  
Grid Connected Inverter

The optimal P-Q control issue of the active and reactive power for a microgrid in the grid-connected mode has attracted increasing interests recently. In this paper, an optimal active and reactive power control is developed for a three-phase grid-connected inverter in a microgrid by using an adaptive population-based extremal optimization algorithm (APEO). Firstly, the optimal P-Q control issue of grid-connected inverters in a microgrid is formulated as a constrained optimization problem, where six parameters of three decoupled PI controllers are real-coded as the decision variables, and the integral time absolute error (ITAE) between the output and referenced active power and the ITAE between the output and referenced reactive power are weighted as the objective function. Then, an effective and efficient APEO algorithm with an adaptive mutation operation is proposed for solving this constrained optimization problem. The simulation and experiments for a 3kW three-phase grid-connected inverter under both nominal and variable reference active power values have shown that the proposed APEO-based P-Q control method outperforms the traditional Z-N empirical method, the adaptive genetic algorithm-based, and particle swarm optimization-based P-Q control methods.

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