Iterative Learning Based Trajectory Optimization Using Fourier Series Basis Functions

2022 ◽  
pp. 1-1
Author(s):  
Joseph A. Drallmeier ◽  
Jason B. Siegel ◽  
Anna G. Stefanopoulou
Keyword(s):  
Fourier Series ◽  
Trajectory Optimization ◽  
Iterative Learning ◽  
Basis Functions

The Surface Variational Principle: A Different Perspective for Structural Acoustic Modeling

1997 ◽  
Author(s):  
J. H. Ginsberg
Keyword(s):  
Fourier Series ◽  
Variational Principle ◽  
Vibration Analysis ◽  
Basis Functions ◽  
Acoustic Modeling ◽  
Normal Velocity ◽  
Convergence Properties ◽  
Variational Functional ◽  
Acoustic Interaction ◽  
System Equations

Abstract This paper surveys the development and application of the surface variational principle (SVP) governing the acoustic interaction between surface pressure and normal velocity. SVP is analogous to the method of assumed modes for vibration analysis, in that it represents the response in terms of a sequence of basis functions that are globally defined. The system equations governing the series coefficients are obtained by requiring that the value of the variational functional be stationary. In the wavenumber-based version of SVP, the pressure and velocity are represented by dual range Fourier series. A brief description of the steps entailed in formulating the SVP equations and coupling them to the equations for an elastic structure is provided. Then the computational requirements of an SVP analysis relative to conventional boundary element and finite element techniques are discussed. This is followed by an example illustrating the convergence properties of SVP. Another example is used to highlight the physical interpretation of the SVP representation of surface response. The evolution of the present version of SVP is surveyed, along with some of its applications. The paper closes with a brief discussion of possible future applications of the method.

scholarly journals Minimum Energy Trajectory Optimization for Driving Systems of Palletizing Robot Joints

2018 ◽  
Vol 2018 ◽  
pp. 1-26
Author(s):  
Ying He ◽  
Jiangping Mei ◽  
Zhiwei Fang ◽  
Fan Zhang ◽  
Yanqin Zhao
Keyword(s):  
Fourier Series ◽  
Energy Consumption ◽  
Total Energy ◽  
Dynamic Model ◽  
Trajectory Optimization ◽  
Joint Torque ◽  
Total Energy Consumption ◽  
Energy Consumption Model ◽  
Energy Consumption Optimization ◽  
Consumption Model

Palletizing robot is widely used in logistics operation. At present, people pay attention to not only the loading capacity and working efficiency of palletizing robots, but also the energy consumption in their working process. This paper takes MD1200-YJ palletizing robot as the research object and studies the problem of low energy consumption optimization of joint driving system from the perspective of trajectory optimization. Firstly, a multifactor dynamic model of palletizing robot is established based on the conventional inverse rigid body dynamic model of the robot, the Stribeck friction model and the spring balance torque model. And then based on joint torque, friction torque, motion parameter, and joule’s law, the useful work model, thermal loss model of joint motor, friction energy consumption model of joint system, and total energy consumption model of palletizing robot are established, and through simulation and experiment, the correctness of the multifactor dynamic model and energy consumption model is verified. Secondly, based on the Fourier series approximation method to construct the joint trajectory expression, the minimum total energy consumption as the optimization objective, with coefficients of Fourier series as optimization variables, the motion parameters of initial and final position, and running time constant as constraint conditions, the genetic algorithm is used to solve the optimization problem. Finally, through the simulation analysis the optimized Fourier series motion law and the 3-4-5 polynomial motion law are comprehensively evaluated to verify the effectiveness of the optimization method. Moreover, it provides the theoretical basis for the follow-up research and points out the direction of improvement.

Transient Conduction From Parallel Isothermal Cylinders

2012 ◽  
Vol 134 (12) ◽  
Author(s):  
Rajai S. Alassar
Keyword(s):  
Heat Transfer ◽  
Fourier Series ◽  
Heat Conduction ◽  
Energy Equation ◽  
Transient Heat Conduction ◽  
Infinite Medium ◽  
Basis Functions ◽  
Cylindrical Coordinates ◽  
Transient Conduction ◽  
Isothermal Cylinders

The transient heat conduction from two parallel isothermal cylinders is studied using the naturally fit bipolar cylindrical coordinates system. The energy equation is expanded in a Fourier series using appropriate basis functions to eliminate one of the physical coordinates. The resulting modes of the expansion are solved using a finite difference scheme. It is shown that, as is the case with a single isothermal cylinder in an infinite medium, steady states for two isothermal cylinders are not possible and heat transfer changes indefinitely with time.

Nonparametric Identification of Hammerstein Systems Using Orthogonal Basis Functions as Ersatz Nonlinearities

2013 ◽  
Author(s):  
Khaled F. Aljanaideh ◽  
Dennis S. Bernstein
Keyword(s):  
Fourier Series ◽  
Theoretical Analysis ◽  
Orthogonal Basis ◽  
Basis Functions ◽  
Inner Product ◽  
Fourier Series Expansion ◽  
Unknown Input ◽  
Hammerstein System ◽  
Basis Expansion ◽  
Input Nonlinearity

In this paper, we present a technique for estimating the input nonlinearity of a Hammerstein system by using multiple orthogonal ersatz nonlinearities. Theoretical analysis shows that by replacing the unknown input nonlinearity by an ersatz nonlinearity, the estimates of the Markov parameters of the plant are correct up to a scalar factor, which is related to the inner product of the true input nonlinearity and the ersatz nonlinearity. These coefficients are used to construct and estimate the true nonlinearity represented as an orthogonal basis expansion. We demonstrate this technique by using a Fourier series expansion as well as orthogonal polynomials. We show that the kernel of the inner product associated with the orthogonal basis functions must be chosen to be the density function of the input signal.

Reentry Trajectory Optimization Based on Time-Domain Improved Particle Swarm Optimization

2015 ◽  
Vol 734 ◽  
pp. 482-486
Author(s):  
Bo Yang ◽  
Hai Xiao Wang
Keyword(s):  
Time Domain ◽  
Trajectory Optimization ◽  
Pso Algorithm ◽  
Basis Functions ◽  
Final Time ◽  
Swarm Optimization ◽  
Reentry Vehicle ◽  
Time Optimal ◽  
Reentry Trajectory ◽  
Reentry Trajectory Optimization

A new time-domain improved PSO algorithm is proposed to solve the problem of reentry trajectory optimization. The approach uses time-domain basis functions fitting the control variables, solves free final time optimal control directly, and sets parameters by using vehicle's dynamic characteristics. Simulation of a reentry vehicle with no-fly zone constraints is used to demonstrate the effectiveness and veracity of algorithm in reentry trajectory optimization. The final condition error is less than 1%.

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