Null space velocity control with dynamically consistent pseudo-inverse

Robotica ◽  
2000 ◽  
Vol 18 (5) ◽  
pp. 513-518 ◽  
Author(s):  
Bojan Nemec ◽  
Leon Zlajpah
Keyword(s):  
Physical Meaning ◽  
Null Space ◽  
Space Velocity ◽  
Velocity Control ◽  
Redundant Manipulator ◽  
Projection Technique ◽  
Space Motion ◽  
Pseudo Inverse ◽  
Globally Stable ◽  
Good Behaviour

Null space velocity control is essential for achieving good behaviour of a redundant manipulator. Using the dynamically consistent pseudo-inverse, the task and null space motion and forces are decoupled. The paper presents a globally stable null space velocity controller and the gradient projection technique in conjunction with the dynamically consistent pseudo-inverse. The physical meaning and influence of the compensation terms in null the space velocity controller are explained. The performance of the proposed null space controller is tested on 4. d.o.f planar redundant manipulator interacting with the environment.

Comparison of null-space and minimal null-space control algorithms

Robotica ◽  
2007 ◽  
Vol 25 (5) ◽  
pp. 511-520 ◽  
Author(s):  
Bojan Nemec ◽  
Leon Žlajpah ◽  
Damir Omrčen
Keyword(s):  
Degrees Of Freedom ◽  
Null Space ◽  
Space Velocity ◽  
Control Algorithms ◽  
Robot Arm ◽  
Velocity Control ◽  
Redundant Robots ◽  
Operational Space ◽  
Space Projection ◽  
The Stability

SUMMARYThis paper deals with the stability of null-space velocity control algorithms in extended operational space for redundant robots. We compare the performance of the control algorithm based on the minimal null-space projection and generalized-inverse-based projection into the Jacobian null-space. We show how the null-space projection affects the performance of the null-space tracking algorithm. The results are verified with the simulation and real implementation on a redundant mobile robot composed of 3 degrees of freedom (DOFs) mobile platform and 7-DOF robot arm.

Fuzzy weighted subtask controller for redundant manipulator

Robotica ◽  
2014 ◽  
Vol 33 (2) ◽  
pp. 295-313 ◽  
Author(s):  
Young jun Yoo ◽  
Dae sung Jung ◽  
Yu jin Jang ◽  
Sang chul Won
Keyword(s):  
Null Space ◽  
Robot Manipulator ◽  
Tracking Error ◽  
Space Velocity ◽  
Inverse Kinematic ◽  
Control Input ◽  
Task Space ◽  
Simulation And Experiment ◽  
Velocity Tracking ◽  
Pseudo Inverse

SUMMARYWe propose a fuzzy weighted subtask controller for a redundant robot manipulator. To expand the feasibility of the inverse kinematic solution, we introduce a weighted pseudo-inverse that changes the null-space of the Jacobian. The weights of elements in the pseudo-inverse are obtained using fuzzy rules that are related to the null-space velocity tracking error. With the pseudo-inverse, we develop a task space controller to track a desired task space trajectory and subtask control input. We propose a weighted subtask controller for multiple subtasks. The results of a simulation and experiment using a seven-degree-of-freedom whole arm manipulator robot show the effectiveness of the proposed controller with multiple subtasks.

Influence of external forces on the behaviour of redundant manipulators

Robotica ◽  
1999 ◽  
Vol 17 (3) ◽  
pp. 283-292
Author(s):  
Leon Žlajpah
Keyword(s):  
Null Space ◽  
The Body ◽  
Redundant Manipulators ◽  
Redundancy Resolution ◽  
Task Space ◽  
Redundant Manipulator ◽  
Projection Technique ◽  
Position Accuracy ◽  
Two Measures ◽  
External Forces

The paper considers the influence of external forces on the behaviour of a redundant manipulator. It is assumed that the forces can act anywhere on the body of the manipulator. First, the equivalent generalized forces in the task space and the null space are defined and several special manipulator configurations regarding the equivalent forces and torques are identified. Next, two measures for the quantification of the influence of external forces on the task space are proposed. These measures are then used in the control algorithm to minimize the influence of external forces on the task space position accuracy. The control is based on the redundancy resolution at the acceleration level and the gradient projection technique. Improvement of the position accuracy is illustrated using the simulation of a four link planar manipulator.

A Robust Control Strategy of Redundant Manipulator by Workspace Observer

1996 ◽  
Vol 8 (3) ◽  
pp. 235-242 ◽  
Author(s):  
Naoki Oda ◽  
◽  
Toshiyuki Murakami ◽  
Kouhei Ohnishi
Keyword(s):  
Control Strategy ◽  
Force Control ◽  
Inverse Kinematics ◽  
Jacobian Matrix ◽  
Null Space ◽  
Stable Condition ◽  
Redundant Manipulator ◽  
Important Index ◽  
Calculation Process ◽  
Pseudo Inverse

This paper describes a decoupling force control strategy of redundant manipulator by workspace observer. In general, the calculation process of the redundant manipulator becomes complex as the number of degree-offreedom motion increases because the controller includes the pseudo inverse Jacobian matrix. To alleviate this problem, we develop a simplification method of the inverse kinematics solution including null space calculation by using the transposed Jacobian matrix, and the workspace observer. Here the stable condition of the proposed controller is also presented. Its condition is an important index to construct the stable workspace observer.

scholarly journals A singularity handling algorithm based on operational space control for six-degree-of-freedom anthropomorphic manipulators

2019 ◽  
Vol 16 (3) ◽  
pp. 172988141985891
Author(s):  
Zhi-Hao Kang ◽  
Ching-An Cheng ◽  
Han-Pang Huang
Keyword(s):  
Null Space ◽  
Singularity Analysis ◽  
Degree Of Freedom ◽  
Control Input ◽  
Real Time Control ◽  
Time Control ◽  
Operational Space ◽  
Industrial Manipulators ◽  
Space Motion ◽  
Six Degree Of Freedom

In this article, we analyze the singularities of six-degree-of-freedom anthropomorphic manipulators and design a singularity handling algorithm that can smoothly go through singular regions. We show that the boundary singularity and the internal singularity points of six-degree-of-freedom anthropomorphic manipulators can be identified through a singularity analysis, although they do not possess the nice kinematic decoupling property as six-degree-of-freedom industrial manipulators. Based on this discovery, our algorithm adopts a switching strategy to handle these two cases. For boundary singularities, the algorithm modifies the control input to fold the manipulator back from the singular straight posture. For internal singularities, the algorithm controls the manipulator with null space motion. We show that this strategy allows a manipulator to move within singular regions and back to non-singular regions, so the usable workspace is increased compared with conventional approaches. The proposed algorithm is validated in simulations and real-time control experiments.

Velocity workspace analysis for multiple arm robot systems

Robotica ◽  
2001 ◽  
Vol 19 (5) ◽  
pp. 581-591 ◽  
Author(s):  
Jihong Lee
Keyword(s):  
Null Space ◽  
Inequality Constraint ◽  
Space Velocity ◽  
Velocity Space ◽  
Robot System ◽  
Slack Variables ◽  
Workspace Analysis ◽  
Robot Systems ◽  
Articulated Robot ◽  
Joint Velocity

In this paper, the analysis of manipulability of robotic systems comprised of multiple cooperating arms is considered. Given bounds on the capabilities of joint actuators for each robot, the purpose of this study is to derive the bounds for task velocity achievable by the system. Since bounds on each joint velocity form a polytope in joint-velocity space and the task space velocity is connected with joint velocity through Jacobian matrices of each robot, the allowable task velocity space, i.e. velocity workspace, for multiple cooperating robot system is also represented as a polytope which is called manipulability polytope throughout this paper. Based on the fact that the boundaries of the manipulability polytope are mapped from the boundaries of allowable joint-velocity space, slack variables are introduced in order to transform given inequality constraint given on joint velocities into a set of normal linear equalities in which the unknowns of the equation are composed of the vertices of manipulability polytope, vectors spanning the null space of the Jacobian matrix, and the slack variables. Either redundant or nonredundant cooperating robot systems can be handled with the proposed technique. Several different application examples including simple SCARA-type robots as well as complex articulated robot manipulators are included, and, under the assumption of firm grip, it will be shown that the calculated manipulability polytope for cooperating robot system is actually the intersection of all the manipulability polytopes of every single robot which is hard to be derived through geometrical manipulation.

Comparison of Damped Velocity and Acceleration Control for Non-Redundant Manipulators

2000 ◽  
Author(s):  
Yu-Che Chen ◽  
Kevin A. O’Neil
Keyword(s):  
Path Tracking ◽  
Least Square ◽  
Dynamics Simulation ◽  
Control Algorithms ◽  
Redundant Manipulators ◽  
Velocity Control ◽  
Redundant Manipulator ◽  
Singular Configurations ◽  
On Line ◽  
Simulation Results

Abstract Damped Least Square (DLS) method has been widely used as an on-line algorithm for manipulator path tracking near and at singular configurations. Wampler (1986) formulated the framework of DLS method applied to velocity control and addressed the applicability of DLS method to acceleration control. The purpose of this paper is to demonstrate the differences in the joint paths generated by damped velocity and damped acceleration control algorithms in non-redundant manipulators. We examine these joint paths, find the cause of the differences, and demonstrate the features of damped acceleration control in non-redundant manipulator dynamics. Simulation results on a planar 2R and a spatial 6R manipulator moving through and near singular configurations verify the phenomena analyzed.

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