Experimental and Novel Analytical Trajectory Optimization of a 7-DOF Baxter Robot: Global Design Sensitivity and Step Size Analyses

2017 ◽  
Author(s):  
Mostafa Bagheri ◽  
Peiman Naseradinmousavi ◽  
Rasha Morsi
Keyword(s):  
Global Optimization ◽  
Cost Function ◽  
Trajectory Optimization ◽  
Computational Cost ◽  
Joint Space ◽  
Design Sensitivity ◽  
Target Object ◽  
Size Analysis ◽  
Step Size ◽  
Novel Approach

In this paper, we present a novel nonlinear analytical coupled trajectory optimization of a 7-DOF Baxter manipulator validated through experimental work utilizing global optimization tools. The robotic manipulators used in network-based applications of industrial units and even homes, for disabled patients, spend significant lumped amount of energy and therefore, optimal trajectories need to be generated to address efficiency issues. We here examine both heuristic (Genetics) and gradient based (GlobalSearch) algorithms for a novel approach of “S-Shaped” trajectory (unlike conventional polynomials), to avoid being trapped in several possible local minima along with yielding minimal computational cost, enforcing operational time and torque saturation constraints. The global schemes are utilized in minimizing the lumped amount of energy consumed in a nominal path given in the collision-free joint space except an impact between the robot’s end effector and a target object for the nominal operation. Note that such robots are typically operated for thousands of cycles resulting in a considerable cost of operation. Due to the expected computational cost of such global optimization algorithms, step size analysis is carried out to minimize both the computational cost (iteration) and possibly cost function by finding an optimal step size. Global design sensitivity analysis is also performed to examine the effects of changes of optimization variables on the cost function defined.

Multivariable Extremum Seeking for Joint-Space Trajectory Optimization of a High-Degrees-of-Freedom Robot

2018 ◽  
Vol 140 (11) ◽  
Author(s):  
Mostafa Bagheri ◽  
Miroslav Krstić ◽  
Peiman Naseradinmousavi
Keyword(s):  
Trajectory Optimization ◽  
Degrees Of Freedom ◽  
Research Effort ◽  
Minimum Energy ◽  
Joint Space ◽  
Design Sensitivity ◽  
Extremum Seeking ◽  
Minimum Energy Consumption ◽  
Gradient Based ◽  
The Cost

In this paper, a novel analytical coupled trajectory optimization of a seven degrees-of-freedom (7DOF) Baxter manipulator utilizing extremum seeking (ES) approach is presented. The robotic manipulators are used in network-based industrial units, and even homes, by expending a significant lumped amount of energy, and therefore, optimal trajectories need to be generated to address efficiency issues. These robots are typically operated for thousands of cycles resulting in a considerable cost of operation. First, coupled dynamic equations are derived using the Lagrangian method and experimentally validated to examine the accuracy of the model. Then, global design sensitivity analysis is performed to investigate the effects of changes of optimization variables on the cost function leading to select the most effective ones. We examine a discrete-time multivariable gradient-based ES scheme enforcing operational time and torque saturation constraints in order to minimize the lumped amount of energy consumed in a path given; therefore, time-energy optimization would not be the immediate focus of this research effort. The results are compared with those of a global heuristic genetic algorithm (GA) to discuss the locality/globality of optimal solutions. Finally, the optimal trajectory is experimentally implemented to be thoroughly compared with the inefficient one. The results reveal that the proposed scheme yields the minimum energy consumption in addition to overcoming the robot's jerky motion observed in an inefficient path.

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.

scholarly journals A NOTE ON PHASING LONG GENOMIC REGIONS USING LOCAL HAPLOTYPE PREDICTIONS

2006 ◽  
Vol 04 (03) ◽  
pp. 639-647 ◽  
Author(s):  
ELEAZAR ESKIN ◽  
RODED SHARAN ◽  
ERAN HALPERIN
Keyword(s):  
Large Scale ◽  
Computational Cost ◽  
Nucleotide Polymorphisms ◽  
Single Nucleotide ◽  
Novel Approach ◽  
Maximum Likelihood Criterion ◽  
The Common ◽  
Genomic Regions ◽  
High Computational Cost ◽  
Combining Information

The common approaches for haplotype inference from genotype data are targeted toward phasing short genomic regions. Longer regions are often tackled in a heuristic manner, due to the high computational cost. Here, we describe a novel approach for phasing genotypes over long regions, which is based on combining information from local predictions on short, overlapping regions. The phasing is done in a way, which maximizes a natural maximum likelihood criterion. Among other things, this criterion takes into account the physical length between neighboring single nucleotide polymorphisms. The approach is very efficient and is applied to several large scale datasets and is shown to be successful in two recent benchmarking studies (Zaitlen et al., in press; Marchini et al., in preparation). Our method is publicly available via a webserver at .

Convergence analysis of online learning algorithm with two-stage step size

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Weilin Nie ◽  
Cheng Wang
Keyword(s):  
Online Learning ◽  
Optimization Problems ◽  
Learning Algorithm ◽  
Computational Cost ◽  
Reproducing Kernels ◽  
Step Size ◽  
Two Stage ◽  
Logarithmic Term ◽  
Convergence Performance ◽  
Online Learning Algorithm

Abstract Online learning is a classical algorithm for optimization problems. Due to its low computational cost, it has been widely used in many aspects of machine learning and statistical learning. Its convergence performance depends heavily on the step size. In this paper, a two-stage step size is proposed for the unregularized online learning algorithm, based on reproducing Kernels. Theoretically, we prove that, such an algorithm can achieve a nearly min–max convergence rate, up to some logarithmic term, without any capacity condition.

Multi-Objective Trajectory Optimization of Free-Floating Space Manipulator Using NSGA-II

2015 ◽  
Vol 713-715 ◽  
pp. 800-804 ◽  
Author(s):  
Gang Chen ◽  
Cong Wei ◽  
Qing Xuan Jia ◽  
Han Xu Sun ◽  
Bo Yang Yu
Keyword(s):  
Trajectory Optimization ◽  
Interpolation Method ◽  
Optimal Solution ◽  
Optimization Method ◽  
Joint Space ◽  
Motion Path ◽  
Objective Functions ◽  
Nsga Ii ◽  
Space Manipulator ◽  
Multi Objective

In this paper, a kind of multi-objective trajectory optimization method based on non-dominated sorting genetic algorithm II (NSGA-II) is proposed for free-floating space manipulator. The aim is to optimize the motion path of the space manipulator with joint angle constraints and joint velocity constraints. Firstly, the kinematics and dynamics model are built. Secondly, the 3-5-3 piecewise polynomial is selected as interpolation method for trajectory planning of joint space. Thirdly, three objective functions are established to simultaneously minimize execution time, energy consumption and jerk of the joints. At last, the objective functions are combined with the NSGA-II algorithm to get the Pareto optimal solution set. The effectiveness of the mentioned method is verified by simulations.

scholarly journals divand-1.0: <i>n</i>-dimensional variational data analysis for ocean observations

2014 ◽  
Vol 7 (1) ◽  
pp. 225-241 ◽  
Author(s):  
A. Barth ◽  
J.-M. Beckers ◽  
C. Troupin ◽  
A. Alvera-Azcárate ◽  
L. Vandenbulcke
Keyword(s):  
Cost Function ◽  
Dimensional Analysis ◽  
Computational Cost ◽  
Posteriori Error ◽  
Cholesky Factorization ◽  
Ocean Current ◽  
Posteriori Error Estimate ◽  
Two Dimensional ◽  
A Posteriori ◽  
A Posteriori Error

Abstract. A tool for multidimensional variational analysis (divand) is presented. It allows the interpolation and analysis of observations on curvilinear orthogonal grids in an arbitrary high dimensional space by minimizing a cost function. This cost function penalizes the deviation from the observations, the deviation from a first guess and abruptly varying fields based on a given correlation length (potentially varying in space and time). Additional constraints can be added to this cost function such as an advection constraint which forces the analysed field to align with the ocean current. The method decouples naturally disconnected areas based on topography and topology. This is useful in oceanography where disconnected water masses often have different physical properties. Individual elements of the a priori and a posteriori error covariance matrix can also be computed, in particular expected error variances of the analysis. A multidimensional approach (as opposed to stacking two-dimensional analysis) has the benefit of providing a smooth analysis in all dimensions, although the computational cost is increased. Primal (problem solved in the grid space) and dual formulations (problem solved in the observational space) are implemented using either direct solvers (based on Cholesky factorization) or iterative solvers (conjugate gradient method). In most applications the primal formulation with the direct solver is the fastest, especially if an a posteriori error estimate is needed. However, for correlated observation errors the dual formulation with an iterative solver is more efficient. The method is tested by using pseudo-observations from a global model. The distribution of the observations is based on the position of the Argo floats. The benefit of the three-dimensional analysis (longitude, latitude and time) compared to two-dimensional analysis (longitude and latitude) and the role of the advection constraint are highlighted. The tool divand is free software, and is distributed under the terms of the General Public Licence (GPL) (http://modb.oce.ulg.ac.be/mediawiki/index.php/divand).

scholarly journals Novel Approach to Estimate Osteoarthritis Progression: Use of the Reliable Change Index in the Evaluation of Joint Space Loss

2019 ◽  
Vol 71 (2) ◽  
pp. 300-307 ◽  
Author(s):  
Camille M. Parsons ◽  
Andrew Judge ◽  
Kirsten Leyland ◽  
Olivier Bruyère ◽  
Florence Petit Dop ◽  
...  
Keyword(s):  
Joint Space ◽  
Reliable Change Index ◽  
Reliable Change ◽  
Novel Approach ◽  
Osteoarthritis Progression ◽  
Joint Space Loss

Comparing Online Robot Joint Space Trajectory Optimization for Task Space Applications

2021 ◽  
Author(s):  
Maximilian Kramer ◽  
Rodrigo J. Velasco-Guillen ◽  
Philipp Beckerle ◽  
Torsten Bertram
Keyword(s):  
Trajectory Optimization ◽  
Joint Space ◽  
Task Space ◽  
Space Applications
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