scholarly journals Multimodal trajectory optimization for motion planning

2020 ◽  
Vol 39 (8) ◽  
pp. 983-1001
Author(s):  
Takayuki Osa
Keyword(s):  
Motion Planning ◽  
Cost Function ◽  
Trajectory Optimization ◽  
Multiple Solutions ◽  
3D Space ◽  
Single Solution ◽  
Planning Methods ◽  
The Cost ◽  
2D And 3D

Existing motion planning methods often have two drawbacks: (1) goal configurations need to be specified by a user, and (2) only a single solution is generated under a given condition. In practice, multiple possible goal configurations exist to achieve a task. Although the choice of the goal configuration significantly affects the quality of the resulting trajectory, it is not trivial for a user to specify the optimal goal configuration. In addition, the objective function used in the trajectory optimization is often non-convex, and it can have multiple solutions that achieve comparable costs. In this study, we propose a framework that determines multiple trajectories that correspond to the different modes of the cost function. We reduce the problem of identifying the modes of the cost function to that of estimating the density induced by a distribution based on the cost function. The proposed framework enables users to select a preferable solution from multiple candidate trajectories, thereby making it easier to tune the cost function and obtain a satisfactory solution. We evaluated our proposed method with motion planning tasks in 2D and 3D space. Our experiments show that the proposed algorithm is capable of determining multiple solutions for those tasks.

scholarly journals Mathematical modeling for a multiproduct manufacturing system featuring postponement, external suppliers, overtime, and scrap

2022 ◽  
Vol 13 (1) ◽  
pp. 1-12
Author(s):  
Yuan-Shyi P. Chiu ◽  
Jian-Hua Lian ◽  
Victoria Chiu ◽  
Yunsen Wang ◽  
Hsiao-Chun Wu
Keyword(s):  
Decision Making ◽  
Cost Function ◽  
Due Dates ◽  
Numerical Illustration ◽  
Screening Process ◽  
Multiproduct Manufacturing ◽  
The Cost ◽  
Decision Making Model ◽  
Mathematical Derivation

Manufacturing firms operating in today’s competitive global markets must continuously find the appropriate manufacturing scheme and strategies to effectively meet customer needs for various types of quality of merchandise under the constraints of short order lead-time and limited in-house capacity. Inspired by the offering of a decision-making model to aid smooth manufacturers’ operations, this study builds an analytical model to expose the influence of the outsourcing of common parts, postponement policies, overtime options, and random scrapped items on the optimal replenishment decision and various crucial system performance indices of the multiproduct problem. A two-stage fabrication scheme is presented to handle the products’ commonality and the uptime-reduced strategies to satisfy the short amount of time before the due dates of customers’ orders. A screening process helps identify and remove faulty items to ensure the finished lot’s anticipated quality. Mathematical derivation assists us in finding the manufacturing relevant total cost function. The differential calculus helps optimize the cost function and determine the optimal stock-replenishing rotation cycle policy. Lastly, a simulated numerical illustration helps validate our research result’s applicability and demonstrate the model’s capability to disclose the crucial managerial insights and facilitate manufacturing-relevant decision making.

scholarly journals The cost function of the data fusion process and its application

2019 ◽  
Vol 12 (5) ◽  
pp. 2967-2977 ◽  
Author(s):  
Simone Ceccherini ◽  
Nicola Zoppetti ◽  
Bruno Carli ◽  
Ugo Cortesi ◽  
Samuele Del Bianco ◽  
...  
Keyword(s):  
Data Fusion ◽  
Cost Function ◽  
Covariance Matrix ◽  
Expected Value ◽  
Covariance Matrices ◽  
Complete Data ◽  
Sufficient Statistics ◽  
The Cost ◽  
Analytical Expressions

Abstract. When the complete data fusion method is used to fuse inconsistent measurements, it is necessary to add to the measurement covariance matrix of each fusing profile a covariance matrix that takes into account the inconsistencies. A realistic estimate of these inconsistency covariance matrices is required for effectual fused products. We evaluate the possibility of assisting the estimate of the inconsistency covariance matrices using the value of the cost function minimized in the complete data fusion. The analytical expressions of expected value and variance of the cost function are derived. Modelling the inconsistency covariance matrix with one parameter, we determine the value of the parameter that makes the reduced cost function equal to its expected value and use the variance to assign an error to this determination. The quality of the inconsistency covariance matrix determined in this way is tested for simulated measurements of ozone profiles obtained in the thermal infrared in the framework of the Sentinel-4 mission of the Copernicus programme. As expected, the method requires sufficient statistics and poor results are obtained when a small number of profiles are being fused together, but very good results are obtained when the fusion involves a large number of profiles.

scholarly journals Automatic Registration and Error Detection of Multiple Slices Using Landmarks

2001 ◽  
Vol 23 (3-4) ◽  
pp. 159-165
Author(s):  
Hans Frimmel ◽  
Lars Egevad ◽  
Christer Busch ◽  
Ewert Bengtsson
Keyword(s):  
Cost Function ◽  
Error Detection ◽  
3D Structure ◽  
Automatic Registration ◽  
Registration Method ◽  
Automated Method ◽  
Current State ◽  
Manual Registration ◽  
The Cost

Objectives. When analysing the 3D structure of tissue, serial sectioning and staining of the resulting slices is sometimes the preferred option. This leads to severe registration problems. In this paper, a method for automatic registration and error detection of slices using landmark needles has been developed. A cost function takes some parameters from the current state of the problem to be solved as input and gives a quality of the current solution as output. The cost function used in this paper, is based on a model of the slices and the landmark needles. The method has been used to register slices of prostates in order to create 3D computer models. Manual registration of the same prostates has been undertaken and compared with the results from the algorithm. Methods. Prostates from sixteen men who underwent radical prostatectomy were formalin fixed with landmark needles, sliced and the slices were computer reconstructed. The cost function takes rotation and translation for each prostate slice, as well as slope and offset for each landmark needle as input. The current quality of fit of the model, using the input parameters given, is returned. The function takes the built‐in instability of the model into account. The method uses a standard algorithm to optimize the prostate slice positions. To verify the result, s standard method in statistics was used. Results. The methods were evaluated for 16 prostates. When testing blindly, a physician could not determine whether the registration shown to him were created by the automated method described in this paper, or manually by an expert, except in one out of 16 cases. Visual inspection and analysis of the outlier confirmed that the input data had been deformed. The automatic detection of erroneous slices marked a few slices, including the outlier, as suspicious. Conclusions. The model based registration performs better than traditional simple slice‐wise registration. In the case of prostate slice registration, other aspects, such as the physical slicing method used, may be more important to the final result than the selection of registration method to use.

scholarly journals The cost function of the data fusion process and its application

2019 ◽  
Author(s):  
Simone Ceccherini ◽  
Nicola Zoppetti ◽  
Bruno Carli ◽  
Ugo Cortesi ◽  
Samuele Del Bianco ◽  
...  
Keyword(s):  
Data Fusion ◽  
Cost Function ◽  
Covariance Matrix ◽  
Expected Value ◽  
Covariance Matrices ◽  
Complete Data ◽  
Sufficient Statistics ◽  
The Cost ◽  
Analytical Expressions

Abstract. When the complete data fusion method is used to fuse inconsistent measurements, it is necessary to add to the measurement covariance matrix of each fusing profile a covariance matrix that takes into account the inconsistencies. A realistic estimate of these inconsistency covariance matrices is required for effectual fused products. We evaluate the possibility of assisting the estimate of the inconsistency covariance matrices using the value of the cost function minimized in the complete data fusion. The analytical expressions of expected value and variance of the cost function are derived. Modelling the inconsistency covariance matrix with one parameter, we determine the value of the parameter that makes the reduced cost function equal to its expected value and use the variance to assign an error to this determination. The quality of the inconsistency covariance matrix determined in this way is tested for simulated measurements of ozone profiles obtained in the thermal infrared in the framework of the Sentinel 4 mission of the Copernicus programme. As expected, the method requires a sufficient statistics and poor results are obtained when a small numbers of profiles are being fused together, but very good results are obtained when the fusion involves a large number of profiles.

IMAGE COMPOSITION WITH COLOR HARMONIZATION

2012 ◽  
Vol 26 (03) ◽  
pp. 1254001
Author(s):  
YANLI WAN ◽  
ZHEN TANG ◽  
ZHENJIANG MIAO ◽  
BO LI
Keyword(s):  
Cost Function ◽  
Optimization Method ◽  
Image Composition ◽  
Local Smoothness ◽  
Color Harmony ◽  
Matching Cost ◽  
Computer Generated Imagery ◽  
The Cost ◽  
Previous Image

Image composition is a very important technique in computer generated imagery. Besides some factors such as contrast, texture and noise that affect the quality of the composition, color harmony between fore- and background is also an important factor that would affect the quality of the composition. However, in the previous image composition techniques, color harmony between fore- and background is seldom considered. In this paper, an optimization method is proposed to deal with the color harmonization problem that used in image composition. A cost function is derived from the local smoothness of the hue values, and the image is harmonized by minimizing the cost function. A new matching cost function is proposed to select the best matching harmonic schemes. Our approach overcomes several shortcomings of the existing color harmonization methods. We validate the performance of our method and demonstrate its effectiveness with a variety of experiments.

scholarly journals Path Planning Methods in Chemical Engineering

2015 ◽  
Vol 3 ◽  
pp. 198
Author(s):  
Edvards Valbahs ◽  
Peter Grabusts ◽  
Ilo Dreyer
Keyword(s):  
Motion Planning ◽  
Shortest Path ◽  
Chemical Engineering ◽  
Practical Application ◽  
Simulation And Optimization ◽  
3D Space ◽  
Planning Methods ◽  
Almost All ◽  
Work Done ◽  
And Robotics

Usually, when the practical motion planning and the shortest path are discoursed, mainly the limited number of tasks is observed. Almost all the tasks associated with the path from one point in 2D or 3D space to another point can be attributed to the usual issue in the practical application. Motion planning and the shortest path have vivid and indisputable importance as human activity in such areas as logistics and robotics. In our work we would like to draw particular attention to the field of application seems to be unnoticeable for the task such as motion planning and the shortest path problem. Due to quite simple examples used, we would like to show that the task of motion planning can be used for simulation and optimization of multi-staged and restricted processes which are presented in chemical engineering accordingly. In the article the simulation and optimization of three important chemical-technological processes for the chemical industry are discussed. The work done gave us the possibility to work out software for simulation and optimization of processes that in some cases facilitates and simplifies the work of professionals engaged in the field of chemical engineering.

scholarly journals Cartesian Constrained Stochastic Trajectory Optimization for Motion Planning

2021 ◽  
Vol 11 (24) ◽  
pp. 11712
Author(s):  
Michal Dobiš ◽  
Martin Dekan ◽  
Adam Sojka ◽  
Peter Beňo ◽  
František Duchoň
Keyword(s):  
Stochastic Optimization ◽  
Motion Planning ◽  
Cost Function ◽  
Trajectory Optimization ◽  
Trajectory Generation ◽  
Joint Space ◽  
Noise Generator ◽  
Robotic Arms ◽  
Cartesian Space ◽  
Path Constraints

This paper presents novel extensions of the Stochastic Optimization Motion Planning (STOMP), which considers cartesian path constraints. It potentially has high usage in many autonomous applications with robotic arms, where preservation or minimization of tool-point rotation is required. The original STOMP algorithm is unable to use the cartesian path constraints in a trajectory generation because it works only in robot joint space. Therefore, the designed solution, described in this paper, extends the most important parts of the algorithm to take into account cartesian constraints. The new sampling noise generator generates trajectory samples in cartesian space, while the new cost function evaluates them and minimizes traversed distance and rotation change of the tool-point in the resulting trajectory. These improvements are verified with simple experiments and the solution is compared with the original STOMP. Results of the experiments show that the implementation satisfies the cartesian constraints requirements.

HEURISTIC OPTIMIZATION OF THE FOUNDATION OF A DYNAMICALLY STRESSED ROTATING MACHINE USING THE LATE ACCEPTANCE HILL CLIMBING (LAHC) ALGORITHM

10.6036/9762 ◽  
2021 ◽  
Vol 96 (5) ◽  
pp. 498-504
Author(s):  
JUAN LUIS TERRADEZ MARCO ◽  
ANTONIO HOSPITALER PEREZ ◽  
VICENTE ALBERO GABARDA
Keyword(s):  
Cost Function ◽  
Random Search ◽  
Optimal Solution ◽  
Hill Climbing ◽  
Dynamic Loads ◽  
Rotating Machine ◽  
Permanent Working ◽  
The Cost ◽  
Late Acceptance Hill Climbing

This paper proposal the optimization of a foundation for rotative machine under dynamic loads in transient and permanent working mode. The foundation depends on fix parameters and 37 variables. Functional constraints are defined for the foundation. A cost function depending on the variables is defined to be minimized to find the optimal. From all the possible solutions, only are selected the ones that validate the constrains and minimize the cost function. The search of the optimal solution is made with an algorithm of random search by “neighbouring of one point” called Last Acceptance Hill Climbing(LAHC). It is an algorithm of the type called “Adaptative Memory Programming” (AMP) that accepts worse solutions to get the local minimum and learns of the results of the search. The algorithm only depends on the length of the comparison vector and the stop criteria. 350 experiences were made with different length of the comparison vector. It was analysed the quality of the optimal solutions got it with each length of the vector. Quality of the set of solutions was compared fitting them to a 3 parameters Weibull distribution.

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