Dynamical Resolution of Redundancy for Robot Manipulators

1993 ◽  
Vol 115 (3) ◽  
pp. 592-598 ◽  
Author(s):  
A. Ghosal ◽  
S. Desa
Keyword(s):  
Large Class ◽  
Robot Manipulator ◽  
Robot Manipulators ◽  
Dynamic State ◽  
Redundancy Resolution ◽  
End Effector ◽  
Dynamical Approach ◽  
Pseudo Inverse

A large class of work in the robot manipulator literature deals with the kinematical resolution of redundancy based on the pseudo-inverse of the manipulator Jacobian. In this paper an alternative dynamical approach to redundancy resolution is developed which utilizes the mapping between the actuator torques and the acceleration of the end-effector, at a given dynamic state of the manipulator. The potential advantages of the approach are discussed and an example of a planar 3R manipulator following a circular end-effector trajectory is used to illustrate the proposed approach as well as to compare it with the more well-known approach based on the pseudo-inverse.

Pseudoinverse-type bi-criteria minimization scheme for redundancy resolution of robot manipulators

Robotica ◽  
2014 ◽  
Vol 33 (10) ◽  
pp. 2100-2113 ◽  
Author(s):  
Bolin Liao ◽  
Weijun Liu
Keyword(s):  
Robot Manipulator ◽  
Robot Manipulators ◽  
Weighting Factor ◽  
Redundancy Resolution ◽  
Type Solution ◽  
Revolute Joints ◽  
Joint Velocity ◽  
Joint Acceleration ◽  
Minimum Velocity ◽  
Minimization Scheme

SUMMARYIn this paper, a pseudoinverse-type bi-criteria minimization scheme is proposed and investigated for the redundancy resolution of robot manipulators at the joint-acceleration level. Such a bi-criteria minimization scheme combines the weighted minimum acceleration norm solution and the minimum velocity norm solution via a weighting factor. The resultant bi-criteria minimization scheme, formulated as the pseudoinverse-type solution, not only avoids the high joint-velocity and joint-acceleration phenomena but also causes the joint velocity to be near zero at the end of motion. Computer simulation results based on a 4-Degree-of-Freedom planar robot manipulator comprising revolute joints further verify the efficacy and flexibility of the proposed bi-criteria minimization scheme on robotic redundancy resolution.

Trajectory Synthesis and Redundancy Resolution for High Speed Point to Point Motions of Redundant Robot Manipulators

1997 ◽  
Author(s):  
W. Kim ◽  
J. Rastegar
Keyword(s):  
High Speed ◽  
Degrees Of Freedom ◽  
Robot Manipulator ◽  
Robot Manipulators ◽  
Dynamic Performance ◽  
High Harmonic ◽  
Harmonic Excitation ◽  
Redundancy Resolution ◽  
Tracking Accuracy ◽  
Point To Point

Abstract Trajectory synthesis for robot manipulators with redundant kinematic degrees-of-freedom has been studied by numerous investigators. Redundant manipulators are of interest since the redundant degrees-of-freedom can be used to improve the local and global kinematic and dynamic performance of a system. As a robot manipulator is forced to track a given trajectory, the required actuating torques (forces) may excite the natural modes of vibration of the system. Noting that manipulators with revolute joints have nonlinear dynamics, high harmonic excitation torques are generally generated even though such harmonics have been eliminated from the synthesized trajectories and filtered from the drive inputs. In this paper, a redundancy resolution method is developed based on the Trajectory Pattern Method (TPM) to synthesize trajectories such that the actuating torques required to realize them do not contain higher harmonic components with significant amplitudes. With such trajectories, a robot manipulator can operate at higher speeds and achieve higher tracking accuracy with suppressed residual vibration. As an example, optimal trajectories are synthesized for point to point motions of a plane 3R manipulator.

Micro/Macro or Link-Integrated Micro-actuator Manipulation—A Kinematics and Dynamics Perspective

2006 ◽  
Vol 129 (10) ◽  
pp. 1086-1093 ◽  
Author(s):  
J. Zhang ◽  
J. Rastegar
Keyword(s):  
Dynamic Response ◽  
Closed Loop ◽  
Robot Manipulator ◽  
Robot Manipulators ◽  
High Harmonic ◽  
Kinematics And Dynamics ◽  
Control Problems ◽  
End Effector ◽  
Micro Actuators ◽  
And Control

Smart (active) materials based actuators, hereinafter called micro-actuators, have been shown to be well suited for the elimination of high harmonics in joint and/or end-effector motions of robot manipulators and in the reduction of actuator dynamic response requirements. Low harmonic joint and end-effector motions, as well as low actuator dynamic response requirements, are essential for a robot manipulator to achieve high operating speed and precision with minimal vibration and control problems. Micro-actuators may be positioned at the end-effector to obtain a micro- and macro-robot manipulation configuration. Alternatively, micro-actuators may be integrated into the structure of the links to vary their kinematics parameters, such as their lengths during the motion. In this paper, the kinematics and dynamics consequences of each of the aforementioned alternative are studied for manipulators with serial and closed-loop chains. It is shown that for robot manipulators constructed with closed-loop chains, the high harmonic components of all joint motions can be eliminated only when micro-actuators are integrated into the structure of the closed-loop chain links. The latter configuration is also shown to have dynamics advantage over micro- and macro-manipulator configuration by reducing the potential vibration and control problems at high operating speeds. The conclusions reached in this study also apply to closed-loop chains of parallel and cooperating robot manipulators.

Smart Actuator Positioning and Displacement Transmissibility in Serial and Parallel Robot Manipulators for Performance Enhancement

2004 ◽  
Vol 127 (4) ◽  
pp. 589-595 ◽  
Author(s):  
J. Rastegar ◽  
L. Yuan ◽  
J. Zhang
Keyword(s):  
Smart Materials ◽  
Performance Enhancement ◽  
Robot Manipulator ◽  
Robot Manipulators ◽  
High Harmonic ◽  
Harmonic Component ◽  
Operating Speed ◽  
End Effector ◽  
High Harmonics ◽  
Joint Motions

A method is presented for the evaluation of the transmissibility of displacement from smart (active) actuators integrated in the structure of robot manipulators to the manipulator joint and end-effector displacements. The method is based on studying the characteristics of the Jacobian of the mapping function between the two displacements for a given position of the robot manipulator. The developed method provides a tool for the determination of the positioning of smart actuators to provide maximum effectiveness in eliminating high harmonics of the joint or the end-effector motion. In robots with serial and parallel kinematics chains containing nonprismatic joints, due to the associated kinematics nonlinearity, if the joint motions were synthesized with low harmonic trajectories, the end-effector trajectory would still contain high harmonics of the joint motions. Alternatively, if the end-effector motion were synthesized with low harmonic components, due to the inverse kinematics nonlinearity, the actuated joint trajectories would contain a significant high harmonic component. As a result, the operating speed and tracking precision are degraded. By integrating smart materials based actuators in the structure of robot manipulators to provide small amplitude and high frequency motions, the high harmonic component of the actuated joint and/or the end-effector motions can be significantly reduced, thereby making it possible to achieve higher operating speed and tracking precision.

Optimal Integration of Smart Actuators in the Structure of Serial and Parallel Robot Manipulators to Enhance Speed and Tracking Precision

2003 ◽  
Author(s):  
J. Rastegar ◽  
L. Yuan ◽  
J. Zhang
Keyword(s):  
Robot Manipulator ◽  
Robot Manipulators ◽  
High Harmonic ◽  
Harmonic Component ◽  
Optimal Placement ◽  
Operating Speed ◽  
End Effector ◽  
High Harmonics ◽  
Smart Actuators ◽  
Joint Motions

A method to determine optimal placement of smart (active) materials based actuators in the structure of robot manipulators for the purpose of achieving higher operating speed and tracking precision is developed. The method is based on the evaluation of the transmissibility of the displacement from the integrated smart actuators to the robot manipulator joint and end-effector displacements. By studying the characteristics of the Jacobian of the mapping function between the two displacements for a given position of the robot manipulator, the optimal positioning of the smart actuators that provides maximum effectiveness in eliminating high harmonics of the joint motion or the end-effector motion is determined. In robots with serial and parallel kinematics chains containing non-prismatic joints, due to their associated kinematics nonlinearity, if the joint motions were synthesized with low harmonic trajectories, the end-effector trajectory would contain high harmonics of the joint motions. Alternatively, if the end-effector motion were synthesized with low harmonic motions, due to the inverse kinematics nonlinearity, the actuated joint trajectories would contain a significant high harmonic component. As the result, the operating speed and tracking precision are degraded. By integrating smart materials based actuators in the structure of robot manipulators to provide small amplitude and higher frequency motions, the high harmonic component of the actuated joint and/or the end-effector motions are eliminated. As the result, higher operating speed and tracking precision can be achieved.

scholarly journals A Fuzzy Backstepping Control of a Mobile Manipulator with Torque Limits Avoidance

1970 ◽  
Vol 5 (2) ◽  
pp. 127-133
Author(s):  
Mohamed Boukattaya ◽  
Tarak Damak ◽  
Mohamed Jallouli
Keyword(s):  
Control Algorithm ◽  
Null Space ◽  
Joint Torque ◽  
Mobile Manipulator ◽  
Redundancy Resolution ◽  
Task Space ◽  
End Effector ◽  
Simulation Results ◽  
Pseudo Inverse ◽  
Selection Of

In this paper, we present a dynamic redundancy resolution technique for mobile manipulator subject to joint torque limits. First, the dynamic model of the mobile manipulator in feasible motion space is given. Next, a control algorithm is proposed which completely decouples the motion of the system into the end-effector motion in the task space and an internal motion in the null space and controls them in prioritized basis with priority given to the primary task space and enables the selection of characteristics in both subspaces separately. A special attention is given to the joints torque limits avoidance where a new weighted pseudo-inverse of the Jacobian that accounts for both inertia and torque limits is proposed to solve problems inherent to torque limits of the system. Simulation results are given to illustrate the coordination of two subsystems in executing the desired trajectory without violating the joint torque limits.

Uncertainty and Compliance of Robot Manipulators with Applications to Task Feasibility

1991 ◽  
Vol 10 (3) ◽  
pp. 200-213 ◽  
Author(s):  
Dinesh K. Pai ◽  
M.C. Leu
Keyword(s):  
Robot Manipulator ◽  
Robot Manipulators ◽  
Point Contact ◽  
Positive Semidefinite ◽  
Efficient Computation ◽  
Position Uncertainty ◽  
Total Uncertainty ◽  
End Effector ◽  
Work Space ◽  
Compliant Joints

The uncertainty and compliance of a robot manipulator used to perform a task are considered. A formula is derived for the efficient computation of a tight bound on the uncertainty of the end effector, given the uncertainty in the kinematic pa rameters of the robot. It is shown that the total uncertainty is the Minkowski difference of the manipulator uncertainty and the task position uncertainty. Simulations are performed in which the results are used to determine configurations of a robot for which the total uncertainty is within a specified tolerance. The suitability of the compliance of a manipulator for performing a planar peg-in-hole type assembly task is also studied. Manipulators are modeled as having rigid links and compliant joints, following experimental results. It is shown that given any symmetric positive semidefinite compliance, a robot manipulator of the above type can be constructed that will realize this compliance at some point in its work space. A new condition on the stiffness is proposed for preventing jamming. If the peg is supported by the end effector of a robot, we can determine configurations of the robot at which jam ming can be avoided. Simulations are performed to compute the no-jam configurations of a manipulator. The results developed here have direct application to sev eral areas of robotics: determining whether a robotic task is feasible in the presence of uncertainty and joint compliance, choosing work space locations for a robotic task, and the design and selection of robot manipulators. 1. This is called two- point contact in Whitney (1982). 2. That is, errors resulting from both the end-effector and task position uncertainties. 3. The symbol ( ) T denotes the transpose. 4. The half-size of a box is half the length of the box in a specified coordinate direction. 5. Also called the set-sum. 6. The effective compliance refers to the compliance at the peg tip resulting from the compliance of the robot or some other support.

Analytic Formulation of Reciprocal Screws and Its Application to Nonredundant Robot Manipulators

2003 ◽  
Vol 125 (1) ◽  
pp. 158-164 ◽  
Author(s):  
Doik Kim ◽  
Wan Kyun Chung
Keyword(s):  
Algebraic Equation ◽  
Kinematic Analysis ◽  
Parallel Manipulator ◽  
Jacobian Matrix ◽  
Robot Manipulator ◽  
Robot Manipulators ◽  
The Given ◽  
Pseudo Inverse

One of the most important and widely used concepts in the kinematic analysis of robot manipulators is the reciprocal screw. However, there are no general expressions and easy methods to obtain the reciprocal screw in an analytic manner. This paper suggests an analytic formulation of the reciprocal screws of arbitrarily aligned screw systems. Since the reciprocal screws obtained in this paper are represented by the direction vectors and the position vectors of the given screws, we can analyze the relation between the reciprocal screw system and the given screw system easily. With the results, to find a reciprocal screw is to solve an algebraic equation of the corresponding system of screws. In order to show the usefulness of the result, several examples related to the robot manipulator are provided. For a nonredundant serial manipulator, the pseudo inverse of the Jacobian matrix is shown to be equivalent to the wrench matrix obtained by the reciprocity. For a parallel manipulator, a leg is isolated to obtain an independent part from the manipulator and is analyzed analytically. The proposed method can be applied to any arbitrarily aligned screw system.

Micro-Macro or Link-Integrated Micro-Actuator Manipulation: A Kinematics and Dynamics Perspective

2005 ◽  
Author(s):  
J. Zhang ◽  
J. Rastegar
Keyword(s):  
Dynamic Response ◽  
Closed Loop ◽  
Robot Manipulator ◽  
Robot Manipulators ◽  
Active Material ◽  
Kinematics And Dynamics ◽  
Control Problems ◽  
End Effector ◽  
Micro Actuators ◽  
And Control

Smart (active) material based actuators, hereinafter called micro-actuators, have been shown to be well suited for the elimination of high harmonics in joint and/or end-effector motions of the robot manipulators and reduce actuator dynamic response requirements. Low harmonic joint and end-effector motions as well as low actuator dynamic response requirements are essential for a robot manipulator to be capable of operating at high speeds with greater precision and with less vibration and control problems. Micro-actuators may be positioned at the end-effector to obtain a micro and macro robot manipulation. Alternatively, micro-actuators may be integrated into the links to vary a link parameter such as the link length. In this paper, the kinematics and dynamics consequences of each alternative are studies for manipulators with serial and closed-loop chains. It is shown that for the robot manipulator constructed with closed-loop chains, the high harmonic components of all joint motions can be eliminated only when micro-actuators are integrated into the structure of the closed-loop chain links. The latter configuration is also shown to have dynamics advantage over micro and macro configuration. thereby reducing the potential vibration and control problems at higher operating speeds. The conclusions also apply to closed-loop chains of parallel and cooperating robot manipulators.

Bi-criteria minimization with MWVN–INAM type for motion planning and control of redundant robot manipulators

Robotica ◽  
2018 ◽  
Vol 36 (5) ◽  
pp. 655-675 ◽  
Author(s):  
Dongsheng Guo ◽  
Kene Li ◽  
Bolin Liao
Keyword(s):  
Motion Planning ◽  
Robot Manipulator ◽  
Robot Manipulators ◽  
Redundancy Resolution ◽  
Redundant Robot ◽  
Planning And Control ◽  
New Type ◽  
Joint Velocity ◽  
And Control ◽  
Joint Acceleration

SUMMARYThis study proposes and investigates a new type of bi-criteria minimization (BCM) for the motion planning and control of redundant robot manipulators to address the discontinuity problem in the infinity-norm acceleration minimization (INAM) scheme and to guarantee the final joint velocity of motion to be approximate to zero. This new type is based on the combination of minimum weighted velocity norm (MWVN) and INAM criteria, and thus is called the MWVN–INAM–BCM scheme. In formulating such a scheme, joint-angle, joint-velocity, and joint-acceleration limits are incorporated. The proposed MWVN–INAM–BCM scheme is reformulated as a quadratic programming problem solved at the joint-acceleration level. Simulation results based on the PUMA560 robot manipulator validate the efficacy and applicability of the proposed MWVN–INAM–BCM scheme in robotic redundancy resolution. In addition, the physical realizability of the proposed scheme is verified in practical application based on a six-link planar robot manipulator.

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