scholarly journals Crossable Surfaces of Robotic Manipulators With Joint Limits

2000 ◽  
Vol 122 (1) ◽  
pp. 52-60 ◽  
Author(s):  
Karim Abdel-Malek ◽  
Harn-Jou Yeh
Keyword(s):  
Inequality Constraints ◽  
Robotic Manipulators ◽  
Normal Curvature ◽  
Parametric Surface ◽  
Singular Surfaces ◽  
Active Joint ◽  
Complete Treatment ◽  
Acceleration Analysis ◽  
Joint Limits ◽  
Surface Curve

A broadly applicable formulation for determining the crossability of singular surfaces and curves in the workspace of serial robotic manipulators is presented. Singular surfaces and curves are analytically determined using nullspace rank-deficiency criteria of the mechanism’s constraint position Jacobian. Imposed joint limits in terms of inequality constraints are taken into account in the formulation. Directions of admissible normal movements on a surface or curve are established from the analysis of the normal curvature of singular surfaces. The normal curvature of a parametric surface used in this formulation, is determined from the first and second fundamental forms adapted from differential geometry. Definiteness properties of a quadratic form developed from the acceleration analysis determine admissible normal movements. For singular surfaces resulting from active joint constraints, definiteness properties are not enough and supplementary criteria are necessary. Two additional criteria are derived. This paper is a complete treatment of the problem of determining whether a singular surface/curve in the workspace is crossable. Planar and spatial numerical examples are presented to illustrate the formulation. [S1050-0472(00)01301-5]

Time-optimal motions of robotic manipulators

Robotica ◽  
2000 ◽  
Vol 18 (6) ◽  
pp. 659-667 ◽  
Author(s):  
Miroslaw Galicki ◽  
Dariusz Uciński
Keyword(s):  
Penalty Function ◽  
Function Method ◽  
Inequality Constraints ◽  
Admissible Solution ◽  
Robotic Manipulators ◽  
Penalty Function Method ◽  
Planning Time ◽  
Time Optimal ◽  
Joint Limits ◽  
State Inequality Constraints

An approach to planning time-optimal collision-free motions of robotic manipulators is presented. It is based on using a negative formulation of the Pontryagin Maximum Principle which handles efficiently various control and/or state constraints imposed on the manipulator motions, which arise naturally out of manipulator joint limits and obstacle avoidance. This approach becomes similar to that described by Weinreb and Bryson, as well as by Bryson and Ho if no state inequality constraints are imposed. In contrast to the penalty function method, the proposed algorithm does not require an initial admissible solution (i.e. an initial admissible trajectory) and finds manipulator trajectories with a smaller cost value than the penalty function approach. A computer example involving a planar redundant manipulator of three revolute kinematic pairs is included. The numerical results are compared with those obtained using an exterior penalty function method.

A modified firefly algorithm for the inverse kinematics solutions of robotic manipulators

2021 ◽  
Vol 28 (3) ◽  
pp. 257-275
Author(s):  
Jesus Hernandez-Barragan ◽  
Carlos Lopez-Franco ◽  
Nancy Arana-Daniel ◽  
Alma Y. Alanis ◽  
Adriana Lopez-Franco
Keyword(s):  
Inverse Kinematics ◽  
Degrees Of Freedom ◽  
Firefly Algorithm ◽  
Statistical Tests ◽  
Robotic Manipulators ◽  
Optimization Techniques ◽  
Multimodal Optimization ◽  
End Effector ◽  
Prismatic Joints ◽  
Joint Limits

The inverse kinematics of robotic manipulators consists of finding a joint configuration to reach a desired end-effector pose. Since inverse kinematics is a complex non-linear problem with redundant solutions, sophisticated optimization techniques are often required to solve this problem; a possible solution can be found in metaheuristic algorithms. In this work, a modified version of the firefly algorithm for multimodal optimization is proposed to solve the inverse kinematics. This modified version can provide multiple joint configurations leading to the same end-effector pose, improving the classic firefly algorithm performance. Moreover, the proposed approach avoids singularities because it does not require any Jacobian matrix inversion, which is the main problem of conventional approaches. The proposed approach can be implemented in robotic manipulators composed of revolute or prismatic joints of n degrees of freedom considering joint limits constrains. Simulations with different robotic manipulators show the accuracy and robustness of the proposed approach. Additionally, non-parametric statistical tests are included to show that the proposed method has a statistically significant improvement over other multimodal optimization algorithms. Finally, real-time experiments on five degrees of freedom robotic manipulator illustrate the applicability of this approach.

Simultaneous Optimal Robot Base Placement and Motion Planning Using Expanded Lagrangian Homotopy

2016 ◽  
Author(s):  
Audelia Gumarus Dharmawan ◽  
Shaohui Foong ◽  
Gim Song Soh
Keyword(s):  
Motion Planning ◽  
Constrained Optimization ◽  
Optimization Problem ◽  
Planning Process ◽  
Inequality Constraints ◽  
Future Research ◽  
Lagrangian System ◽  
Constrained Optimization Problem ◽  
Continuation Problem ◽  
Joint Limits

This paper presents a new approach to simultaneously determine the optimal robot base placement and motion plan for a prescribed set of tasks using expanded Lagrangian homotopy. First, the optimal base placement is formulated as a constrained optimization problem based on manipulability and kinematics of the robot. Then, the constrained optimization problem is expressed into the expanded Lagrangian system and subsequently converted into a homotopy map. Finally, the Newton-Raphson method is used to solve the constrained optimization problem as a continuation problem. The complete formulation for the case of a 6-DOF manipulator is presented and a planar optimal mobile platform motion planning approach is proposed. Numerical simulations confirm that the proposed approach is able to achieve the desired results. The approach also shows the potential for incorporating factors such as joint limits or collision avoidance into the motion planning process as inequality constraints and will be part of future research.

On the Determination of the Workspace of Complex Planar Robotic Manipulators

1998 ◽  
Vol 120 (2) ◽  
pp. 269-278 ◽  
Author(s):  
Re´mi Ricard ◽  
Cle´ment M. Gosselin
Keyword(s):  
Robotic Manipulators ◽  
Degree Of Freedom ◽  
New Method ◽  
Three Degree Of Freedom ◽  
Joint Limits

A new method for the determination of the workspace of complex planar robotic manipulators is described in this paper. The method is based on the use of joint limits to obtain equations describing limiting curves. These limiting curves are then segmented at their mutual intersections and validated. The resulting sets of portions of curves form the envelope of the workspace. The algorithm is completely general and can be applied to any three-degree-of-freedom planar manipulator—serial, parallel or hybrid—with or without joint limits. Examples of the application of the method to a serial three-degree-of-freedom manipulator, to a hybrid three-degree-of-freedom manipulator and to a parallel three-degree-of-freedom manipulator are given.

Which Sex Offenders Complete Treatment?

1999 ◽  
Author(s):  
D. L. Moore ◽  
B. A. Bergman ◽  
P. L. Knox
Keyword(s):  
Sex Offenders ◽  
Complete Treatment
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