Optimum Trajectory Planning for Redundant and Hyper-Redundant Manipulators Through Inverse Dynamics

2011 ◽  
Author(s):  
Kagan K. Ayten ◽  
M. Necip Sahinkaya ◽  
P. Iravani
Keyword(s):  
Cost Function ◽  
Trajectory Planning ◽  
Inverse Dynamics ◽  
Minimum Energy ◽  
Redundant Manipulators ◽  
Inverse Dynamic ◽  
Dynamic Constraints ◽  
Function Calculation ◽  
The Cost ◽  
Fifth Order

This paper presents a method to develop minimum energy trajectories for redundant/hyper-redundant manipulators with pre-defined kinematic and dynamic constraints. The optimal trajectory planning uses fifth order B-spline functions to represent the Cartesian coordinates of the end-effector and angles of the redundant links. The actuator torques are considered for the formulation of the cost function. Calculation of the cost function is carried out by using an inverse dynamic analysis. The system constraints are handled within the cost function to avoid running the inverse dynamics when the constraints are not satisfied. A novel virtual link concept is introduced to replace all the redundant links to eliminate physicaly impossible configurations before running the inverse dynamic model. The process is applicable to hyper redundant manipulators with large number of links. The proposed scheme is verified with computer simulations based on a 5-link planar redundant manipulator.

Modeling on Inverse Dynamic Process of Cut Tobacco Dryer

2013 ◽  
Vol 655-657 ◽  
pp. 1378-1382
Author(s):  
Li Zhang ◽  
Li Lei ◽  
Peng Xu
Keyword(s):  
Process Model ◽  
Inverse Dynamics ◽  
Process Efficiency ◽  
Process Equipment ◽  
Inverse Dynamic ◽  
Coupling Time ◽  
Increasing Process ◽  
Cut Tobacco ◽  
The Cost ◽  
Typical Process

The cut tobacco dryer is one of the most important process equipment in the cigarette production ,which is a typical process involving many factors such as multivariablity, strong coupling, time-varying and large time delay .Based on the identification of inverse dynamics, this paper establishes a process model related to some important parameters of the cut tobacco dryer which lays a foundation for optimizing the control parameters, increasing process efficiency and reducing the cost in the tobacco drying process.

The Effect of Pedal Platform Height on Cycling Biomechanics

1990 ◽  
Vol 6 (1) ◽  
pp. 1-17 ◽  
Author(s):  
Maury L. Hull ◽  
Hiroko K. Gonzalez
Keyword(s):  
Cost Function ◽  
Inverse Dynamics ◽  
Problem Solution ◽  
Pedal Force ◽  
Upper Limits ◽  
Inverse Dynamics Problem ◽  
The Cost ◽  
Force Data ◽  
Linkage Model ◽  
Pedaling Rate

Using a five-bar linkage model of the leg/bicycle system in conjunction with experimental kinematic and pedal force data, the inverse dynamics problem is solved to yield the intersegmental moments. Among the input data that affect the problem solution is the height of the pedal platform. This variable is isolated and its effects on the total joint moments are studied as it assumes values over a ±4-cm range. Platform height variation affects the total joint moment peak values by up to 13%. Relying on a cost function derived from the hip and knee moments, it is found that the platform height that minimizes the cost function is +2 cm. The sensitivity of the cost function to the platform height variable is low; over the variable range the cost function increases 2% above the minimum. These results hold for a pedaling rate of 90 rpm. As pedaling rate is varied above and below 90 rpm, the sensitivity of the cost function increases. The platform heights that minimize the cost function are the lower and upper limits for 60 and 120 rpm, respectively. Thus the platform height variable interacts with pedaling rate, requiring a compromise in platform height adjustment. The compromise height depends on the individual’s preferred pedaling rate range.

scholarly journals Two-Dimensional Symmetric Box Delivery Motion Prediction and Validation: Subtask-Based Optimization Method

2020 ◽  
Vol 10 (24) ◽  
pp. 8798
Author(s):  
Yujiang Xiang ◽  
Shadman Tahmid ◽  
Paul Owens ◽  
James Yang
Keyword(s):  
Cost Function ◽  
Material Handling ◽  
Optimization Method ◽  
Joint Torque ◽  
Two Dimensional ◽  
Computationally Efficient ◽  
Inverse Dynamic ◽  
Manual Material Handling ◽  
Research Outcome ◽  
The Cost

Box delivery is a complicated manual material handling task which needs to consider the box weight, delivering speed, stability, and location. This paper presents a subtask-based inverse dynamic optimization formulation for determining the two-dimensional (2D) symmetric optimal box delivery motion. For the subtask-based formulation, the delivery task is divided into five subtasks: lifting, the first transition step, carrying, the second transition step, and unloading. To render a complete delivering task, each subtask is formulated as a separate optimization problem with appropriate boundary conditions. For carrying and lifting subtasks, the cost function is the sum of joint torque squared. In contrast, for transition subtasks, the cost function is the combination of joint discomfort and joint torque squared. Joint angle profiles are validated through experimental results using Pearson’s correlation coefficient (r) and root-mean-square-error (RMSE). Results show that the subtask-based approach is computationally efficient for complex box delivery motion simulation. This research outcome provides a practical guidance to prevent injury risks in joint torque space for workers who deliver heavy objects in their daily jobs.

scholarly journals Optimal Trajectory Planning for Wheeled Mobile Robots under Localization Uncertainty and Energy Efficiency Constraints

Sensors ◽  
2021 ◽  
Vol 21 (2) ◽  
pp. 335
Author(s):  
Xiaolong Zhang ◽  
Yu Huang ◽  
Youmin Rong ◽  
Gen Li ◽  
Hui Wang ◽  
...  
Keyword(s):  
Energy Efficiency ◽  
Mobile Robots ◽  
Cost Function ◽  
Trajectory Planning ◽  
Optimal Trajectory ◽  
Planning Method ◽  
Wheeled Mobile Robots ◽  
The Cost ◽  
Localization Uncertainty ◽  
Optimal Trajectory Planning

With the rapid development of robotics, wheeled mobile robots are widely used in smart factories to perform navigation tasks. In this paper, an optimal trajectory planning method based on an improved dolphin swarm algorithm is proposed to balance localization uncertainty and energy efficiency, such that a minimum total cost trajectory is obtained for wheeled mobile robots. Since environmental information has different effects on the robot localization process at different positions, a novel localizability measure method based on the likelihood function is presented to explicitly quantify the localization ability of the robot over a prior map. To generate the robot trajectory, we incorporate localizability and energy efficiency criteria into the parameterized trajectory as the cost function. In terms of trajectory optimization issues, an improved dolphin swarm algorithm is then proposed to generate better localization performance and more energy efficiency trajectories. It utilizes the proposed adaptive step strategy and learning strategy to minimize the cost function during the robot motions. Simulations are carried out in various autonomous navigation scenarios to validate the efficiency of the proposed trajectory planning method. Experiments are performed on the prototype “Forbot” four-wheel independently driven-steered mobile robot; the results demonstrate that the proposed method effectively improves energy efficiency while reducing localization errors along the generated trajectory.

scholarly journals An Adaptive Optimization Method Based on Learning Rate Schedule for Neural Networks

2021 ◽  
Vol 11 (2) ◽  
pp. 850
Author(s):  
Dokkyun Yi ◽  
Sangmin Ji ◽  
Jieun Park
Keyword(s):  
Artificial Intelligence ◽  
Cost Function ◽  
Numerical Experiments ◽  
Global Minimum ◽  
Optimization Method ◽  
Learning Method ◽  
Adaptive Optimization ◽  
The Cost ◽  
Proof Of Convergence ◽  
Learning Data

Artificial intelligence (AI) is achieved by optimizing the cost function constructed from learning data. Changing the parameters in the cost function is an AI learning process (or AI learning for convenience). If AI learning is well performed, then the value of the cost function is the global minimum. In order to obtain the well-learned AI learning, the parameter should be no change in the value of the cost function at the global minimum. One useful optimization method is the momentum method; however, the momentum method has difficulty stopping the parameter when the value of the cost function satisfies the global minimum (non-stop problem). The proposed method is based on the momentum method. In order to solve the non-stop problem of the momentum method, we use the value of the cost function to our method. Therefore, as the learning method processes, the mechanism in our method reduces the amount of change in the parameter by the effect of the value of the cost function. We verified the method through proof of convergence and numerical experiments with existing methods to ensure that the learning works well.

Sorting permutations by fragmentation-weighted operations

2020 ◽  
Vol 18 (02) ◽  
pp. 2050006 ◽  
Author(s):  
Alexsandro Oliveira Alexandrino ◽  
Carla Negri Lintzmayer ◽  
Zanoni Dias
Keyword(s):  
Approximation Algorithms ◽  
Computational Biology ◽  
Cost Function ◽  
Traditional Approach ◽  
Upper Bounds ◽  
Evolutionary Distance ◽  
Lower And Upper Bounds ◽  
Approximation Factor ◽  
New Type ◽  
The Cost

One of the main problems in Computational Biology is to find the evolutionary distance among species. In most approaches, such distance only involves rearrangements, which are mutations that alter large pieces of the species’ genome. When we represent genomes as permutations, the problem of transforming one genome into another is equivalent to the problem of Sorting Permutations by Rearrangement Operations. The traditional approach is to consider that any rearrangement has the same probability to happen, and so, the goal is to find a minimum sequence of operations which sorts the permutation. However, studies have shown that some rearrangements are more likely to happen than others, and so a weighted approach is more realistic. In a weighted approach, the goal is to find a sequence which sorts the permutations, such that the cost of that sequence is minimum. This work introduces a new type of cost function, which is related to the amount of fragmentation caused by a rearrangement. We present some results about the lower and upper bounds for the fragmentation-weighted problems and the relation between the unweighted and the fragmentation-weighted approach. Our main results are 2-approximation algorithms for five versions of this problem involving reversals and transpositions. We also give bounds for the diameters concerning these problems and provide an improved approximation factor for simple permutations considering transpositions.

Maximum Likelihood Ensemble Filter: Theoretical Aspects

2005 ◽  
Vol 133 (6) ◽  
pp. 1710-1726 ◽  
Author(s):  
Milija Zupanski
Keyword(s):  
Maximum Likelihood ◽  
Data Assimilation ◽  
Cost Function ◽  
Ensemble Data Assimilation ◽  
Error Covariance ◽  
Ensemble Data ◽  
Analysis Error ◽  
Nonlinear Observation ◽  
The Cost ◽  
Maximum Likelihood Ensemble Filter

Abstract A new ensemble-based data assimilation method, named the maximum likelihood ensemble filter (MLEF), is presented. The analysis solution maximizes the likelihood of the posterior probability distribution, obtained by minimization of a cost function that depends on a general nonlinear observation operator. The MLEF belongs to the class of deterministic ensemble filters, since no perturbed observations are employed. As in variational and ensemble data assimilation methods, the cost function is derived using a Gaussian probability density function framework. Like other ensemble data assimilation algorithms, the MLEF produces an estimate of the analysis uncertainty (e.g., analysis error covariance). In addition to the common use of ensembles in calculation of the forecast error covariance, the ensembles in MLEF are exploited to efficiently calculate the Hessian preconditioning and the gradient of the cost function. A sufficient number of iterative minimization steps is 2–3, because of superior Hessian preconditioning. The MLEF method is well suited for use with highly nonlinear observation operators, for a small additional computational cost of minimization. The consistent treatment of nonlinear observation operators through optimization is an advantage of the MLEF over other ensemble data assimilation algorithms. The cost of MLEF is comparable to the cost of existing ensemble Kalman filter algorithms. The method is directly applicable to most complex forecast models and observation operators. In this paper, the MLEF method is applied to data assimilation with the one-dimensional Korteweg–de Vries–Burgers equation. The tested observation operator is quadratic, in order to make the assimilation problem more challenging. The results illustrate the stability of the MLEF performance, as well as the benefit of the cost function minimization. The improvement is noted in terms of the rms error, as well as the analysis error covariance. The statistics of innovation vectors (observation minus forecast) also indicate a stable performance of the MLEF algorithm. Additional experiments suggest the amplified benefit of targeted observations in ensemble data assimilation.

Research on trajectory planning of non-developable surface for automated tape placement processing of composite

2017 ◽  
Vol 24 (6) ◽  
pp. 929-936
Author(s):  
Lin Liu ◽  
Jun Xiao ◽  
Yong Li
Keyword(s):  
Trajectory Planning ◽  
Local Stress ◽  
Developable Surface ◽  
Software Environment ◽  
Quantitative Characterization ◽  
Large Size ◽  
Variable Step ◽  
The Cost ◽  
Wing Panel

AbstractTape placement manufacturing process, as one of the automated forming technologies for composite material, not only substantially improves the productivity of composite component and reduces the cost of production significantly but also raises the reliability and stability of composite structure. Automated tape placement technology is mainly applied for manufacturing the fuselage and wing panel of airplane characterized by small curvature and large size. For these kinds of structural components with a non-developable surface, trajectory planning by “natural path” method could reduce the internal stress and improve the quality of composite products to a certain extent but not be optimized by quantitative characterization. On the basis of preliminary work, the theoretical model of “unnatural degree” (UD) is introduced in the first step, which could characterize the tensile and shear strain of the laying tape quantitatively. Secondly, by adjusting the iterative step and laying direction to diminish the UD, local stress could be softened in order to optimize the laying track. Ultimately, the simulation model of the non-developable surface is established under the Matlab software environment, and the “variable step-angle” algorithm is adopted to verify the adjustment effect of the tape-laying track.

Scaling laws of vascular trees: of form and function

2006 ◽  
Vol 290 (2) ◽  
pp. H894-H903 ◽  
Author(s):  
Ghassan S. Kassab
Keyword(s):  
Flow Rate ◽  
Scaling Laws ◽  
Minimum Energy ◽  
Blood Flow Rate ◽  
Tree Structure ◽  
Conservation Of Energy ◽  
Form And Function ◽  
And Function ◽  
The Cost ◽  
Vascular Trees

The branching pattern and vascular geometry of biological tree structure are complex. Here we show that the design of all vascular trees for which there exist morphometric data in the literature (e.g., coronary, pulmonary; vessels of various skeletal muscles, mesentery, omentum, and conjunctiva) obeys a set of scaling laws that are based on the hypothesis that the cost of construction of the tree structure and operation of fluid conduction is minimized. The laws consist of scaling relationships between 1) length and vascular volume of the tree, 2) lumen diameter and blood flow rate in each branch, and 3) diameter and length of vessel branches. The exponent of the diameter-flow rate relation is not necessarily equal to 3.0 as required by Murray's law but depends on the ratio of metabolic to viscous power dissipation of the tree of interest. The major significance of the present analysis is to show that the design of various vascular trees of different organs and species can be deduced on the basis of the minimum energy hypothesis and conservation of energy under steady-state conditions. The present study reveals the similarity of nature's scaling laws that dictate the design of various vascular trees and the underlying physical and physiological principles.

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