A Fast and Robust Algorithm for General Inequality/Equality Constrained Minimum-Time Problems

1999 ◽  
Vol 121 (3) ◽  
pp. 337-345 ◽  
Author(s):  
B. J. Driessen ◽  
N. Sadegh ◽  
G. G. Parker ◽  
G. R. Eisler
Keyword(s):  
Maximum Principle ◽  
Quadratic Programming ◽  
Sequential Quadratic Programming ◽  
Joint Angle ◽  
Minimum Time ◽  
Robotic Arm ◽  
General Inequality ◽  
Constrained Problems ◽  
Ill Conditioning ◽  
Minimum Time Problems

This work has developed a new robust and reliable O(N) algorithm for solving general inequality/equality constrained minimum-time problems. To our knowledge, no one has ever applied an O(N) algorithm for solving such minimum time problems. Moreover, the algorithm developed here is new and unique and does not suffer the inevitable ill-conditioning problems that pre-existing O(N) methods for inequality-constrained problems do. Herein we demonstrate the new algorithm by solving several cases of a tip path constrained three-link redundant robotic arm problem with torque bounds and joint angle bounds. Results are consistent with Pontryagin’s Maximum Principle. We include a speed/robustness/complexity comparison with a sequential quadratic programming (SQP) code. Here, the O(N) complexity and the significant speed, robustness, and complexity improvements over an SQP code are demonstrated. These numerical results are complemented with a rigorous theoretical convergence proof of the new O(N) algorithm.

Design of evolutionary cubic spline intelligent solver for nonlinear Painlevé-I transcendent

2021 ◽  
Author(s):  
Sharafat Ali ◽  
Iftikhar Ahmad ◽  
Muhammad Asif Zahoor Raja ◽  
Siraj ul Islam Ahmad ◽  
Muhammad Shoaib
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Genetic Algorithms ◽  
Statistical Analysis ◽  
Quadratic Programming ◽  
Sequential Quadratic Programming ◽  
Process Variation ◽  
Nonlinear Ordinary Differential Equation ◽  
Second Derivative ◽  
Search Technique

In this research paper, an innovative bio-inspired algorithm based on evolutionary cubic splines method (CSM) has been utilized to estimate the numerical results of nonlinear ordinary differential equation Painlevé-I. The computational mechanism is used to support the proposed technique CSM and optimize the obtained results with global search technique genetic algorithms (GAs) hybridized with sequential quadratic programming (SQP) for quick refinement. Painlevé-I is solved by the proposed technique CSM-GASQP. In this process, variation of splines is implemented for various scenarios. The CSM-GASQP produces an interpolated function that is continuous upto its second derivative. Also, splines proved to be stable than a single polynomial fitted to all points, and reduce wiggles between the tabulated points. This method provides a reliable and excellent procedure for adaptation of unknown coefficients of splines by searching globally exploiting the performance of GA-SQP algorithms. The convergence, exactness and accuracy of the proposed scheme are examined through the statistical analysis for the several independent runs.

Design Human-Robot Collaborative Lifting Task Using Optimization

2021 ◽  
Author(s):  
Asif Arefeen ◽  
Yujiang Xiang
Keyword(s):  
Degrees Of Freedom ◽  
Joint Angle ◽  
Joint Torque ◽  
Robotic Arm ◽  
Inverse Dynamic ◽  
Floating Base ◽  
Grasping Forces ◽  
Design Variables ◽  
Human Arm ◽  
Lifting Task

Abstract In this paper, an optimization-based dynamic modeling method is used for human-robot lifting motion prediction. The three-dimensional (3D) human arm model has 13 degrees of freedom (DOFs) and the 3D robotic arm (Sawyer robotic arm) has 10 DOFs. The human arm and robotic arm are built in Denavit-Hartenberg (DH) representation. In addition, the 3D box is modeled as a floating-base rigid body with 6 global DOFs. The interactions between human arm and box, and robot and box are modeled as a set of grasping forces which are treated as unknowns (design variables) in the optimization formulation. The inverse dynamic optimization is used to simulate the lifting motion where the summation of joint torque squares of human arm is minimized subjected to physical and task constraints. The design variables are control points of cubic B-splines of joint angle profiles of the human arm, robotic arm, and box, and the box grasping forces at each time point. A numerical example is simulated for huma-robot lifting with a 10 Kg box. The human and robotic arms’ joint angle, joint torque, and grasping force profiles are reported. These optimal outputs can be used as references to control the human-robot collaborative lifting task.

Sign in / Sign up

Export Citation Format

Share Document