Repeatable Joint Displacement Generation for Redundant Robotic Systems

1994 ◽  
Vol 116 (1) ◽  
pp. 11-16 ◽  
Author(s):  
Y. S. Chung ◽  
M. Griffis ◽  
J. Duffy
Keyword(s):  
Joint Space ◽  
Inverse Kinematic ◽  
Torsional Stiffness ◽  
Numerical Verification ◽  
Redundant Manipulators ◽  
Redundant Manipulator ◽  
Kinematic Equation ◽  
End Effector ◽  
Prismatic Joints ◽  
Cyclic Type

This paper presents a novel, practical, and theoretically sound kinematic control strategy for serial redundant manipulators. This strategy yields repeatability in the joint space of a serial redundant manipulator whose end effector undergoes some general cyclic type motion. This is accomplished by deriving a new inverse kinematic equation that is based on springs being theoretically or conceptually located in the joints of the manipulator (torsional springs for revolute joints, translational springs for prismatic joints). Previous researchers have also derived an inverse kinematic equation for serial redundant manipulators. However, to the authors’ knowledge, the new strategy is the first to include the free angles of torsional springs and the free lengths of translational springs. This is important because it ensures the repeatability in the joint space of a serial redundant manipulator whose end effector undergoes a cyclic type motion. Numerical verification for repeatability is done in terms of Lie bracket condition. Choices for the free angle and torsional stiffness of a joint (or the free length and translational stiffness) are made based upon the mechanical limits of the joint.

Motion Planning for a Redundant Manipulator Using Genetic Algorithm

2011 ◽  
Vol 467-469 ◽  
pp. 782-787 ◽  
Author(s):  
S. Parasuraman ◽  
Chiew Mun Hou ◽  
V. Ganapathy
Keyword(s):  
Genetic Algorithm ◽  
Trajectory Planning ◽  
Collision Detection ◽  
Angular Displacement ◽  
Joint Space ◽  
Redundant Manipulators ◽  
Evaluation Function ◽  
Redundant Manipulator ◽  
End Effector ◽  
Total Displacement

The trajectory planning of redundant manipulator is key areas of research, which require efficient optimization algorithms. This paper presents a new method that combines multiple objectives for trajectory planning and generation for redundant manipulators. The algorithm combines collision detection, finding target and optimizing trajectory using Genetic algorithm. In order to optimize the path, an evaluation function is defined based on multiple criteria, including the total displacement of the end-effector, the total angular displacement of all the joints, as well as the uniformity of Cartesian and joint space velocities. These criteria result in minimized, smooth end-effector motions. These algorithm yields solutions instantaneously and generate the path. The proposed algorithm is analyzed and its performance is demonstrated through simulation and the results are compared with the other methods.

Unique Joint Displacement Generation for Redundant Robotic Systems

1992 ◽  
Author(s):  
Y. S. Chung ◽  
M. Griffis ◽  
Joseph Duffy
Keyword(s):  
Potential Energy ◽  
Potential Energy Function ◽  
Joint Space ◽  
Torsional Stiffness ◽  
Inverse Kinematic Problem ◽  
End Effector ◽  
Serial Manipulators ◽  
Cyclic Type ◽  
Zero Potential ◽  
Joint Limits

Abstract This paper presents a novel, practical, and theoretically sound kinematic control strategy for redundant serial manipulators. This strategy yields repeatability in the joint space of a redundant serial manipulator whose end effector undergoes some general cyclic type motion. This is accomplish by defining a potential energy function that is based on springs being theoretically or conceptually located in the joints of the manipulator (torsional springs for revolute joints, translational springs for prismatic joints). Previous researchers have also minimized potential energy functions to solve the inverse kinematic problem for redundant serial manipulators. However, to the authors’ knowledge, the new strategy is the first to include the free angles of torsional springs and the free lengths of translational springs. This is important because it provides a meaningful reference for zero potential energy i.e. when all joints are at their free angles or free lengths. This reference for zero potential energy ensures the repeatability in the joint space of a redundant serial manipulator whose end effector undergoes a cyclic-type motion. Choices for the free angle and torsional stiffness of a joint (or the free length and translational stiffness) are made based upon the mechanical limits of the joint. For instance, the free angle of a joint is that angle which is midway between joint limits. Joint stiffnesses are chosen so that the most dexterous joint is the most pliable, and so that the least dexterous joint is the stiffest. This strategy ensures that joints of the manipulator are kept away from their respective joint limits.

Inverse Kinematics of Serial Redundant Manipulators With Locked Articulations

1995 ◽  
Author(s):  
Louis Perreault ◽  
Clément M. Gosselin
Keyword(s):  
Inverse Kinematics ◽  
General Procedure ◽  
Inverse Kinematic ◽  
Redundant Manipulators ◽  
Redundant Manipulator ◽  
Inverse Kinematic Problem

Abstract This paper presents an algorithm for the solution of the inverse kinematics of a serial redundant manipulator with one (or more) locked joint(s). To this end, a general procedure is developed for the determination of the equivalent Denavit-Hartenberg parameters of a serial manipulator with locked joints. This procedure can be applied to any serial architecture. The solution of the inverse kinematic problem for the three cases which can arise is then addressed. An example of the application of the method to a SARCOS 7-DOF manipulator is also given.

Stabilized minimum infinity-norm torque solution for redundant manipulators

Robotica ◽  
1998 ◽  
Vol 16 (2) ◽  
pp. 193-205 ◽  
Author(s):  
Ick-Chan Shim ◽  
Yong-San Yoon
Keyword(s):  
Dynamic Control ◽  
Inequality Constraint ◽  
Redundant Manipulators ◽  
Redundant Manipulator ◽  
End Effector ◽  
Joint Torques ◽  
Infinity Norm ◽  
Instability Problem ◽  
Geometrical Relation ◽  
Feasibility Constraint

The minimization of the joint torques based on the ∞-norm is proposed for the dynamic control of a kinematically redundant manipulator. The ∞-norm is preferred to the 2-norm in the minimization of the joint torques since the maximum torques of the actuators are limited. To obtain the minimum ∞-norm torque solution, we devised a new algorithm that uses the acceleration polyhedron representing the end-effector's acceleration capability. Usually the minimization of the joint torques has an instability problem for the long trajectories of the end-effector. To suppress this instability problem, an inequality constraint, named the feasibility constraint, is developed from the geometrical relation between the required end-effector acceleration and the acceleration polyhedron. The minimization of the °-norm of the joint torques subject to the feasibility constraint is shown to improve the performances through the simulations of a 3-link planar redundant manipulator.

A new motion planning method for discretely actuated hyper-redundant manipulators

Robotica ◽  
2015 ◽  
Vol 35 (1) ◽  
pp. 101-118 ◽  
Author(s):  
Alireza Motahari ◽  
Hassan Zohoor ◽  
Moharam Habibnejad Korayem
Keyword(s):  
Genetic Algorithm ◽  
Motion Planning ◽  
Trajectory Tracking ◽  
Inverse Kinematic ◽  
Planning Problem ◽  
Redundant Manipulators ◽  
Tracking Problem ◽  
Parallel Mechanisms ◽  
Redundant Manipulator ◽  
The Common

SUMMARYA hyper-redundant manipulator is made by mounting the serial and/or parallel mechanisms on top of each other as modules. In discrete actuation, the actuation amounts are a limited number of certain values. It is not feasible to solve the kinematic analysis problems of discretely actuated hyper-redundant manipulators (DAHMs) by using the common methods, which are used for continuous actuated manipulators. In this paper, a new method is proposed to solve the trajectory tracking problem in a static prescribed obstacle field. To date, this problem has not been considered in the literature. Theremoving first collision(RFC) method, which is originally proposed for solving the inverse kinematic problems in the obstacle fields was modified and used to solve the motion planning problem. For verification, the numerical results of the proposed method were compared with the results of thegenetic algorithm(GA) method. Furthermore, a novel DAHM designed and implemented by the authors is introduced.

Dynamic Performance and Modular Design of Redundant Macro-/Minimanipulators

2008 ◽  
Vol 130 (9) ◽  
Author(s):  
Alan P. Bowling ◽  
Oussama Khatib
Keyword(s):  
Task Performance ◽  
Modular Design ◽  
Dynamic Performance ◽  
Dynamic Capability ◽  
Redundant Manipulators ◽  
Redundant Manipulator ◽  
End Effector ◽  
Analysis And Design ◽  
Inertia Ellipsoid ◽  
Six Degree Of Freedom

This paper presents methodologies for the analysis and design of redundant manipulators, especially macro-/ministructures, for improved dynamic performance. Herein, the dynamic performance of a redundant manipulator is characterized by the end-effector inertial and acceleration properties. The belted inertia ellipsoid is used to characterize inertial properties, and the recently developed dynamic capability equations are used to analyze acceleration capability. The approach followed here is to design the ministructure to achieve the task performance and then to design the macrostructure to support and complement the ministructure, referred to here as modular design. The methodology is illustrated in the design of a six-degree-of-freedom planar manipulator.

Kinematic control of planar redundant manipulators by extended motion distribution scheme

Robotica ◽  
1992 ◽  
Vol 10 (3) ◽  
pp. 255-262 ◽  
Author(s):  
W. J. Chung ◽  
W. K. Chung ◽  
Y. Youm
Keyword(s):  
Difficult Problem ◽  
Redundant Manipulators ◽  
Redundant Manipulator ◽  
End Effector ◽  
Kinematic Control ◽  
Internal Joint ◽  
Distribution Scheme ◽  
Joint Velocity ◽  
Self Motion ◽  
Velocity Level

SUMMARYThe kinematic control of a planar manipulator with several-degrees of redundancy has been a difficult problem because of the heavy computational burden and/or lack of appropriate techniques. The extended motion distribution scheme, which is based on decomposing a planar redundant manipulator into a series of nonredundant/redundant local arms (referred to as subarms) and distributing the motion of an end-effector to subarms at the joint velocity level, is proposed in this paper. The configuration index, which is defined as the product of minors corresponding to subarms in the Jacobian matrix, is used to globally guide the redundant manipulators. To enhance the performance of the proposed scheme, a self-motion control, which handles the internal joint motion that does not contribute to the end-effector motion, can be used optionally to guarantee globally optimal manipulation. The repeatability problem for the redundant manipulators is discussed using the proposed scheme. The results of computer simulations are shown and analyzed in detail for planar 8-DOF and 9-DOF manipulators, as examples.

scholarly journals Computing Robust Inverse Kinematics Under Uncertainty

2019 ◽  
Author(s):  
Anirban Sinha ◽  
Nilanjan Chakraborty
Keyword(s):  
Inverse Kinematics ◽  
Joint Space ◽  
Redundant Manipulators ◽  
Task Space ◽  
Success Rates ◽  
Redundant Manipulator ◽  
Space Error ◽  
Inverse Kinematics Problem ◽  
Robotic Tasks ◽  
Present Simulation

Abstract Robotic tasks, like reaching a pre-grasp configuration, are specified in the end effector space or task space, whereas, robot motion is controlled in joint space. Because of inherent actuation errors in joint space, robots cannot achieve desired configurations in task space exactly. Furthermore, different inverse kinematics (IK) solutions map joint space error set to task space differently. Thus for a given task with a prescribed error tolerance, all IK solutions will not be guaranteed to successfully execute the task. Any IK solution that is guaranteed to execute a task (possibly with high probability) irrespective of the realization of the joint space error is called a robust IK solution. In this paper we formulate and solve the robust inverse kinematics problem for redundant manipulators with actuation uncertainties (errors). We also present simulation and experimental results on a 7-DoF redundant manipulator for two applications, namely, a pre-grasp positioning and a pre-insertion positioning scenario. Our results show that the robust IK solutions result in higher success rates and also allows the robot to self-evaluate how successful it might be in any application scenario.

scholarly journals Optimal Point-to-Point Trajectory Tracking of Redundant Manipulators using Generalized Pattern Search

10.5772/5781 ◽  
2005 ◽  
Vol 2 (3) ◽  
pp. 24 ◽  
Author(s):  
Atef A. Ata ◽  
Thi Rein Myo
Keyword(s):  
Genetic Algorithm ◽  
Optimal Trajectory ◽  
Pattern Search ◽  
Redundant Manipulators ◽  
Redundant Manipulator ◽  
Optimal Point ◽  
Intermediate Point ◽  
End Effector ◽  
Generalized Pattern Search ◽  
Point To Point

Optimal point-to-point trajectory planning for planar redundant manipulator is considered in this study. The main objective is to minimize the sum of the position error of the end-effector at each intermediate point along the trajectory so that the end-effector can track the prescribed trajectory accurately. An algorithm combining Genetic Algorithm and Pattern Search as a Generalized Pattern Search GPS is introduced to design the optimal trajectory. To verify the proposed algorithm, simulations for a 3-D-O-F planar manipulator with different end-effector trajectories have been carried out. A comparison between the Genetic Algorithm and the Generalized Pattern Search shows that The GPS gives excellent tracking performance.

scholarly journals Solving the Inverse Kinematic Equations of Elastic Robot Arm Utilizing Neural Network

2017 ◽  
Vol 13 (1) ◽  
pp. 13-25 ◽  
Author(s):  
Hussein M. Al-Khafaji ◽  
Muhsin J. Jweeg
Keyword(s):  
Neural Network ◽  
Inverse Kinematic ◽  
Robot Arm ◽  
Joint Angles ◽  
Kinematic Equation ◽  
End Effector ◽  
Joint Configuration ◽  
Network Training ◽  
The Neural Network ◽  
Forward Kinematic

The inverse kinematic equation for a robot is very important to the control robot’s motion and position. The solving of this equation is complex for the rigid robot due to the dependency of this equation on the joint configuration and structure of robot link. In light robot arms, where the flexibility exists, the solving of this problem is more complicated than the rigid link robot because the deformation variables (elongation and bending) are present in the forward kinematic equation. The finding of an inverse kinematic equation needs to obtain the relation between the joint angles and both of the end-effector position and deformations variables. In this work, a neural network has been proposed to solve the problem of inverse kinematic equation. To feed the neural network, experimental data were taken from an elastic robot arm for training the network, these data presented by joint angles, deformation variables and end-effector positions. The results of network training showed a good fit between the output results of the neural network and the targets data. In addition, this method for finding the inverse of kinematic equation proved its effectiveness and validation when applying the results of neural network practically in the robot’s operating software for controlling the real light robot’s position.

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