Path Planning and Control of Redundant Manipulators Using Bilevel Optimization

2020 ◽  
Vol 142 (4) ◽  
Author(s):  
Uriel Nusbaum ◽  
Miri Weiss Cohen ◽  
Yoram Halevi
Keyword(s):  
Optimal Control ◽  
Dynamic Systems ◽  
Bilevel Optimization ◽  
Complex Tasks ◽  
Planning And Control ◽  
Optimal Inputs ◽  
Saturation Constraints ◽  
Level Problem ◽  
Upper Level ◽  
And Control

Abstract Redundancy is a useful feature in dynamic systems which can be exploited to enhance performance in various tasks. In this work, redundancy will be utilized to minimize the energy consumption of a linear manipulator, while in some cases an additional task of end-effector tracking will also be required and achieved. Optimal control theory has been extensively used for the optimization of dynamic systems; however, complex tasks and redundancy make these problems computationally expensive, numerically difficult to solve, and in many cases, ill-defined. In this paper, evolutionary bilevel optimization for the problem is presented. This is done by setting up an upper level optimization problem for a set of decision variables and a lower level one that actually calculates the optimal inputs and trajectories. The upper level problem is solved by a genetic algorithm (GA), whereas the lower level problem uses classical optimal control. As a result, the proposed algorithm allows the optimization of complex tasks that usually cannot be solved in practice using standard optimal control tools. In addition, despite the use of penalty functions to enforce saturation constraints, the algorithm leads to global energy minimization. Illustrative examples of a redundant x-y robotic manipulator with complex overall tasks will be presented, solved, and discussed.

Reduction of the Dimension of the Upper Level Problem in a Bilevel Optimization Model

2015 ◽  
pp. 289-308
Author(s):  
Stephan Dempe ◽  
Vyacheslav Kalashnikov ◽  
Gerardo A. Pérez-Valdés ◽  
Nataliya Kalashnykova
Keyword(s):  
Optimization Model ◽  
Bilevel Optimization ◽  
Level Problem ◽  
Upper Level

Trade-Offs Between Identification and Control in Dynamic Systems

1988 ◽  
Vol 55 (4) ◽  
pp. 939-945 ◽  
Author(s):  
Firdaus E. Udwadia ◽  
Henryk Flashner
Keyword(s):  
Dynamic Systems ◽  
Trial And Error ◽  
Plant Identification ◽  
Single Degree Of Freedom ◽  
Energy Constraint ◽  
Linear Dynamic Systems ◽  
Trade Offs ◽  
Optimal Inputs ◽  
Augmented State ◽  
And Control

A quantitative study of the trade-offs between the tasks of control law design and plant identification for linear dynamic systems is presented. The problem is formulated in the context of optimal control and optimal identification through the intermediary concept of an optimal input. The duality between identification and control is quantified by optimal inputs, which have a specified amount of energy, and which minimizes the objective function. The optimization problem together with the energy constraint is formulated by using an augmented state vector. This results in a nonlinear two-point boundary value problem and eliminates the need for using a trial and error approach to satisfy the energy constraint. An example of a single-degree-of-freedom oscillator is used to illustrate the basic concepts underlying the proposed approach. Significant trade-offs between identification and control tasks are observed, the trade-offs becoming increasingly important for increasing levels of input energy.

scholarly journals Inexact Derivative-Free Optimization for Bilevel Learning

2021 ◽  
Author(s):  
Matthias J. Ehrhardt ◽  
Lindon Roberts
Keyword(s):  
Approximate Solutions ◽  
Bilevel Optimization ◽  
Worst Case ◽  
Lower Level Problem ◽  
Derivative Free Optimization ◽  
Derivative Free ◽  
Common Strategy ◽  
Regularization Techniques ◽  
Level Problem ◽  
Upper Level

AbstractVariational regularization techniques are dominant in the field of mathematical imaging. A drawback of these techniques is that they are dependent on a number of parameters which have to be set by the user. A by-now common strategy to resolve this issue is to learn these parameters from data. While mathematically appealing, this strategy leads to a nested optimization problem (known as bilevel optimization) which is computationally very difficult to handle. It is common when solving the upper-level problem to assume access to exact solutions of the lower-level problem, which is practically infeasible. In this work we propose to solve these problems using inexact derivative-free optimization algorithms which never require exact lower-level problem solutions, but instead assume access to approximate solutions with controllable accuracy, which is achievable in practice. We prove global convergence and a worst-case complexity bound for our approach. We test our proposed framework on ROF denoising and learning MRI sampling patterns. Dynamically adjusting the lower-level accuracy yields learned parameters with similar reconstruction quality as high-accuracy evaluations but with dramatic reductions in computational work (up to 100 times faster in some cases).

On Bilevel Optimization with Inexact Follower

2020 ◽  
Vol 17 (1) ◽  
pp. 74-95 ◽  
Author(s):  
M. Hosein Zare ◽  
Oleg A. Prokopyev ◽  
Denis Sauré
Keyword(s):  
Optimization Problems ◽  
Broad Class ◽  
Bilevel Optimization ◽  
Modeling Framework ◽  
Optimization Framework ◽  
Lower Level Problem ◽  
Level Problem ◽  
Potential Impact ◽  
Upper Level ◽  
Optimal Reaction

Traditionally, in the bilevel optimization framework, a leader chooses her actions by solving an upper-level problem, assuming that a follower chooses an optimal reaction by solving a lower-level problem. However, in many settings, the lower-level problems might be nontrivial, thus requiring the use of tailored algorithms for their solution. More importantly, in practice, such problems might be inexactly solved by heuristics and approximation algorithms. Motivated by this consideration, we study a broad class of bilevel optimization problems where the follower might not optimally react to the leader’s actions. In particular, we present a modeling framework in which the leader considers that the follower might use one of a number of known algorithms to solve the lower-level problem, either approximately or heuristically. Thus, the leader can hedge against the follower’s use of suboptimal solutions. We provide algorithmic implementations of the framework for a class of nonlinear bilevel knapsack problem (BKP), and we illustrate the potential impact of incorporating this realistic feature through numerical experiments in the context of defender-attacker problems.

scholarly journals Pick and Place Operations in Logistics Using a Mobile Manipulator Controlled with Deep Reinforcement Learning

2019 ◽  
Vol 9 (2) ◽  
pp. 348 ◽  
Author(s):  
Ander Iriondo ◽  
Elena Lazkano ◽  
Loreto Susperregi ◽  
Julen Urain ◽  
Ane Fernandez ◽  
...  
Keyword(s):  
Reinforcement Learning ◽  
Path Planning ◽  
Mobile Manipulator ◽  
Complex Tasks ◽  
Complex Control ◽  
Planning And Control ◽  
Pick And Place ◽  
Policy Gradient ◽  
Point To Point ◽  
And Control

Programming robots to perform complex tasks is a very expensive job. Traditional path planning and control are able to generate point to point collision free trajectories, but when the tasks to be performed are complex, traditional planning and control become complex tasks. This study focused on robotic operations in logistics, specifically, on picking objects in unstructured areas using a mobile manipulator configuration. The mobile manipulator has to be able to place its base in a correct place so the arm is able to plan a trajectory up to an object in a table. A deep reinforcement learning (DRL) approach was selected to solve this type of complex control tasks. Using the arm planner’s feedback, a controller for the robot base is learned, which guides the platform to such a place where the arm is able to plan a trajectory up to the object. In addition the performance of two DRL algorithms ((Deep Deterministic Policy Gradient (DDPG)) and (Proximal Policy Optimisation (PPO)) is compared within the context of a concrete robotic task.

scholarly journals Proximal Gradient Method for Solving Bilevel Optimization Problems

2020 ◽  
Vol 25 (4) ◽  
pp. 66
Author(s):  
Seifu Endris Yimer ◽  
Poom Kumam ◽  
Anteneh Getachew Gebrie
Keyword(s):  
Optimization Problem ◽  
Optimization Problems ◽  
Gradient Methods ◽  
Split Feasibility Problem ◽  
Bilevel Optimization ◽  
Feasibility Problem ◽  
Proximal Gradient Method ◽  
Level Problem ◽  
Upper Level ◽  
The Split Feasibility Problem

In this paper, we consider a bilevel optimization problem as a task of finding the optimum of the upper-level problem subject to the solution set of the split feasibility problem of fixed point problems and optimization problems. Based on proximal and gradient methods, we propose a strongly convergent iterative algorithm with an inertia effect solving the bilevel optimization problem under our consideration. Furthermore, we present a numerical example of our algorithm to illustrate its applicability.

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