Solving a generalized constrained optimization problem with both logic AND and OR relationships by a mathematical transformation and its application to robot motion planning

2000 ◽  
Vol 30 (4) ◽  
pp. 525-536 ◽  
Author(s):  
Yongji Wang ◽  
D.M. Lane
Keyword(s):  
Motion Planning ◽  
Constrained Optimization ◽  
Optimization Problem ◽  
Robot Motion ◽  
Robot Motion Planning ◽  
Constrained Optimization Problem ◽  
Mathematical Transformation

Application of Evolutionary Algorithms for Humanoid Robot Motion Planning

2010 ◽  
Vol 3 (4) ◽  
pp. 21-33
Author(s):  
G. Capi ◽  
K. Mitobe
Keyword(s):  
Motion Planning ◽  
Humanoid Robot ◽  
Optimization Problem ◽  
Walking Speed ◽  
Fitness Function ◽  
Minimum Energy ◽  
Multiple Objectives ◽  
Robot Motion ◽  
Robot Motion Planning ◽  
Minimum Energy Consumption

In this article, the authors present a new method for humanoid robot motion planning, satisfying multiple objectives. In this method, the multiple objectives humanoid robot motion is formulated as a multiobjective optimization problem, considering each objective as a separate fitness function. Three different objectives are considered: (1) minimum energy consumption; (2) stability; and (3) walking speed. The advantage of the proposed method is that, in a single run of multiobjective evolution, generated humanoid robot motions satisfy each objective separately or multiple objectives simultaneously. Therefore, the humanoid robot can switch between different gaits based on environmental conditions. The results show that humanoid robot gaits generated by multiobjective evolution are similar to that of humans. To further verify the performance of optimal motions, they are transferred to the “Bonten-Maru” humanoid robot.

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 Learning Interaction-Aware Trajectory Predictions for Decentralized Multi-Robot Motion Planning in Dynamic Environments

2021 ◽  
Vol 6 (2) ◽  
pp. 2256-2263
Author(s):  
Hai Zhu ◽  
Francisco Martinez Claramunt ◽  
Bruno Brito ◽  
Javier Alonso-Mora
Keyword(s):  
Motion Planning ◽  
Dynamic Environments ◽  
Robot Motion ◽  
Robot Motion Planning ◽  
Multi Robot

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.

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