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.

Resolution of redundant manipulators via distance optimization

2000 ◽  
Vol 214 (8) ◽  
pp. 1037-1047 ◽  
Author(s):  
M Z Ding ◽  
C J Ong ◽  
A N Poo
Keyword(s):  
Three Dimensional ◽  
Redundant Manipulators ◽  
Joint Position ◽  
Redundancy Resolution ◽  
End Effector ◽  
Numerical Examples ◽  
The Past ◽  
Shortest Distance ◽  
Joint Velocity ◽  
Velocity Level

Redundant manipulators are useful in practice as they have freedom in addition to that needed for a specific end-effector position. This additional freedom has to be properly resolved, and such redundancy resolution problems have been actively studied over the past decade. The most common scheme for redundancy resolution is achieved at the joint velocity level and does not take into account the presence of obstacles. This work presents a new scheme for redundancy resolution based on maximizing the shortest distance to obstacles. The aim is to resolve the redundancy by reconfiguring the robot to be at the safest pose or furthest from obstacles. The proposed scheme resolves the redundancy at the joint position level and, hence, has the advantage of ensuring collision-free motion. Several numerical examples in two- and three-dimensional spaces demonstrate the effectiveness of the proposed scheme.

Dual arm-angle parameterisation and its applications for analytical inverse kinematics of redundant manipulators

Robotica ◽  
2015 ◽  
Vol 34 (12) ◽  
pp. 2669-2688 ◽  
Author(s):  
Wenfu Xu ◽  
Lei Yan ◽  
Zonggao Mu ◽  
Zhiying Wang
Keyword(s):  
Inverse Kinematics ◽  
Reference Plane ◽  
Redundant Manipulators ◽  
Redundant Manipulator ◽  
Singularity Problem ◽  
Human Arm ◽  
Angle Method ◽  
Self Motion ◽  
Dual Arm ◽  
Configuration Control

SUMMARYAn S-R-S (Spherical-Revolute-Spherical) redundant manipulator is similar to a human arm and is often used to perform dexterous tasks. To solve the inverse kinematics analytically, the arm-angle was usually used to parameterise the self-motion. However, the previous studies have had shortcomings; some methods cannot avoid algorithm singularity and some are unsuitable for configuration control because they use a temporary reference plane. In this paper, we propose a method of analytical inverse kinematics resolution based on dual arm-angle parameterisation. By making use of two orthogonal vectors to define two absolute reference planes, we obtain two arm angles that satisfy a specific condition. The algorithm singularity problem is avoided because there is always at least one arm angle to represent the redundancy. The dual arm angle method overcomes the shortcomings of traditional methods and retains the advantages of the arm angle. Another contribution of this paper is the derivation of the absolute reference attitude matrix, which is the key to the resolution of analytical inverse kinematics but has not been previously addressed. The simulation results for typical cases that include the algorithm singularity condition verified our method.

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.

Redundancy Parameterization for Flexible Motion Control

2010 ◽  
Author(s):  
B. Moore ◽  
E. Oztop
Keyword(s):  
Finite Number ◽  
Inverse Kinematics ◽  
Infinitely Many Solutions ◽  
Redundant Manipulators ◽  
Real Time Control ◽  
End Effector ◽  
Human Control ◽  
Time Control ◽  
Swivel Angle ◽  
Self Motion

Our overall research interest is in synthesizing human like reaching and grasping using anthropomorphic robot hand-arm systems, as well as understanding the principles underlying human control of these actions. When one needs to define the control and task requirements in the Cartesian space, the problem of inverse kinematics needs to be solved. For non-redundant manipulators, a desired end-effector position and orientation can be achieved by a finite number of solutions. For redundant manipulators however, there are in general infinitely many solutions where the cardinality of the solution set must be made finite by imposing certain constraints. In this paper, we consider the Mitsubishi PA10 manipulator which is similar to the human arm, in the sense that both wrist and shoulder joints can be considered to emulate a 3DOF ball joint. We explicitly derive the analytic solution for the inverse kinematics using quaternions. Then, we derive a parameterization in terms of a pure quaternion called the swivel quaternion. The swivel quaternion is similar to the elbow swivel angle used in most approaches, but avoid the computation of inverse trigonometric functions. This parameterization of the self-motion manifold is continuous with any end-effector motion. Given the pose of the end-effector and the swivel quaternion (or swivel angle), the algorithm derives all solution of the inverse kinematics (finite number). We then show how the parameterization of the elbow self-motion can be used for the real-time control of the PA10 manipulator in the presence of obstacles.

A unified approach to the inverse kinematic solution for a redundant manipulator

Robotica ◽  
1993 ◽  
Vol 11 (2) ◽  
pp. 159-165 ◽  
Author(s):  
J. H. Won ◽  
B. W. Choi ◽  
M. J. Chung
Keyword(s):  
Differential Equations ◽  
Optimal Solution ◽  
Inverse Kinematic ◽  
Necessary Condition ◽  
Redundant Manipulator ◽  
Performance Indices ◽  
Unified Approach ◽  
Joint Velocity ◽  
Velocity Level ◽  
Kinematic Solution

SUMMARYFor a kinematically redundant manipulator, some performance indices can be optimized while carrying out a given task. So far, the redundancy resolution has been solved at the joint angle level, the joint velocity level, or joint acceleration level depending on the performance indices. According to the resolution level, the solution is represented by high-order differential equations or superfluous number of equations. We propose a unified approach to the inverse kinematic solution which optimizes it at the joint velocity level regardless of the types of the performance indices. A unified approach to obtain an optimal joint velocity is derived by using the necessary condition for optimality so that the proposed method provides an optimal solution for any performance indices and tasks. The optimal solution becomes a set of the minimum number of first-order differential equations which requires a minimum search dimension.To show the validity of the approach, it is applied to a three-link planar manipulator for various types of performance indices.

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.

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.

scholarly journals Redundancy, Self-Motion, and Motor Control

2009 ◽  
Vol 21 (5) ◽  
pp. 1371-1414 ◽  
Author(s):  
V. Martin ◽  
J. P. Scholz ◽  
G. Schöner
Keyword(s):  
Process Model ◽  
Inverse Dynamics ◽  
Human Movement ◽  
Neuronal Dynamics ◽  
End Effector ◽  
Dynamic Movement ◽  
Model Predictions ◽  
Joint Velocity ◽  
Virtual Trajectory ◽  
Self Motion

Outside the laboratory, human movement typically involves redundant effector systems. How the nervous system selects among the task-equivalent solutions may provide insights into how movement is controlled. We propose a process model of movement generation that accounts for the kinematics of goal-directed pointing movements performed with a redundant arm. The key element is a neuronal dynamics that generates a virtual joint trajectory. This dynamics receives input from a neuronal timer that paces end-effector motion along its path. Within this dynamics, virtual joint velocity vectors that move the end effector are dynamically decoupled from velocity vectors that do not. Moreover, the sensed real joint configuration is coupled back into this neuronal dynamics, updating the virtual trajectory so that it yields to task-equivalent deviations from the dynamic movement plan. Experimental data from participants who perform in the same task setting as the model are compared in detail to the model predictions. We discover that joint velocities contain a substantial amount of self-motion that does not move the end effector. This is caused by the low impedance of muscle joint systems and by coupling among muscle joint systems due to multiarticulatory muscles. Back-coupling amplifies the induced control errors. We establish a link between the amount of self-motion and how curved the end-effector path is. We show that models in which an inverse dynamics cancels interaction torques predict too little self-motion and too straight end-effector paths.

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