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.

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.

Local torque minimization for redundant manipulators: a correct formulation

Robotica ◽  
1996 ◽  
Vol 14 (2) ◽  
pp. 235-239 ◽  
Author(s):  
Shugen Ma ◽  
Dragomir N. Nenchev
Keyword(s):  
Redundant Manipulators ◽  
Redundancy Resolution ◽  
Instability Problem ◽  
Correct Formulation ◽  
Joint Velocity ◽  
Recent Formulation ◽  
Joint Acceleration ◽  
Stable Scheme

SUMMARYLocal torque minimization for redundant manipulators has been considered by using a redundancy resolution approach. Since its initial formulation, however, proposed solutions have been plagued by performance instabilities. Till now, the reason was not clear. In this paper it is shown that the instability problem occurred because of incorrect formulation. A correct formulation is proposed, which is used to analyze the reason for instability. Special attention is paid to joint acceleration terms at the selfmotion manifold. This helps explaining the recent formulation of a stable scheme based on local joint velocity minimization in terms of torque. The results obtained. are related to dynamic redundancy resolution in general.

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.

scholarly journals Embedded Optimal Control of Robot Manipulators with Passive Joints

2015 ◽  
Vol 2015 ◽  
pp. 1-21 ◽  
Author(s):  
Alberto Olivares ◽  
Ernesto Staffetti
Keyword(s):  
Optimal Control ◽  
Dynamical Systems ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Robot Manipulator ◽  
Robot Manipulators ◽  
Operating Modes ◽  
Change Dynamics ◽  
Revolute Joints ◽  
Underactuated Robot

This paper studies the optimal control problem for planar underactuated robot manipulators with two revolute joints and brakes at the unactuated joints in the presence of gravity. The presence of a brake at an unactuated joint gives rise to two operating modes for that joint: free and braked. As a consequence, there exist two operating modes for a robot manipulator with one unactuated joint and four operating modes for a manipulator with two unactuated joints. Since these systems can change dynamics, they can be regarded as switched dynamical systems. The optimal control problem for these systems is solved using the so-called embedding approach. The main advantages of this technique are that assumptions about the number of switches are not necessary, integer or binary variables do not have to be introduced to model switching decisions between modes, and the optimal switching times between modes are not unknowns of the optimal control problem. As a consequence, the resulting problem is a classical continuous optimal control problem. In this way, a general method for the solution of optimal control problems for switched dynamical systems is obtained. It is shown in this paper that it can deal with nonintegrable differential constraints.

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.

Tri-Criteria Optimization Motion Planning at Acceleration-Level of Dual Redundant Manipulators

Robotica ◽  
2019 ◽  
Vol 38 (6) ◽  
pp. 983-999
Author(s):  
Zhaoli Jia ◽  
Siyuan Chen ◽  
Zhijun Zhang ◽  
Nan Zhong ◽  
Pengchao Zhang ◽  
...  
Keyword(s):  
Motion Planning ◽  
Joint Angle ◽  
Weighting Factor ◽  
Quadratic Program ◽  
Redundant Manipulators ◽  
Repetitive Motion ◽  
Acceleration Level ◽  
Primal Dual ◽  
Joint Velocity ◽  
Joint Acceleration

SUMMARYIn order to solve joint-angle drift problem of dual redundant manipulators at acceleration-level, an acceleration-level tri-criteria optimization motion planning (ALTC-OMP) scheme is proposed, which combines the minimum acceleration norm, repetitive motion planning, and infinity-norm acceleration minimization solutions via weighting factor. This scheme can resolve the joint-angle drift problem of dual redundant manipulators which will arise in single criteria or bi-criteria scheme. In addition, the proposed scheme considers joint-velocity joint-acceleration physical limits. The proposed scheme can not only guarantee joint-velocity and joint-acceleration within their physical limits, but also ensure that final joint-velocity and joint-acceleration are near to zero. This scheme is realized by dual redundant manipulators which consist of left and right manipulators. In order to ensure the coordinated operation of manipulators, two motion planning problems are reformulated as two general quadratic program (QP) problems and further unified into one standard QP problem, which is solved by a simplified linear-variational-inequalities-based primal-dual neural network at the acceleration-level. Computer-simulation results based on dual PUMA560 redundant manipulators further demonstrate the effectiveness and feasibility of the proposed ALTC-OMP scheme to resolve joint-angle drift problem arising in the dual redundant manipulators.

Joint velocity uniformity in redundant robot manipulators

Robotica ◽  
1990 ◽  
Vol 8 (1) ◽  
pp. 69-72 ◽  
Author(s):  
A. Hemami
Keyword(s):  
Robot Manipulator ◽  
Robot Manipulators ◽  
Velocity Change ◽  
Redundant Robot ◽  
Joint Velocity

SUMMARYA redundant robot manipulator has several certain or expected advantages over a nonredundant one. It is expected, among other capabilities, that the joints vary with constant velocities during the execution of those tasks which in a nonredundant manipulator require variable joint velocities. In this way, motion becomes more precise because of the elimination of errors associated with velocity change in joints. In this paper, it is shown that this expected advantage is not possible for all the joints, and that only as many joints as the degree of redundancy can have constant velocities.

On-line multi-criteria based collision-free posture generation of redundant manipulator in constrained workspace

Robotica ◽  
2002 ◽  
Vol 20 (6) ◽  
pp. 625-636 ◽  
Author(s):  
Jin-Liang Chen ◽  
Jing-Sin Liu ◽  
Wan-Chi Lee ◽  
Tzu-Chen Liang
Keyword(s):  
Null Space ◽  
Large Degree ◽  
Redundancy Resolution ◽  
Secondary Tasks ◽  
End Effector ◽  
Robotic Arms ◽  
Tracking Motion ◽  
On Line ◽  
Joint Limits ◽  
Joint Velocity

The manipulator with a large degree of redundancy is useful for realizing multiple tasks such as maneuvering the robotic arms in the constrained workspace, e.g. the task of maneuvering the end-effector of the manipulator along a pre-specified path into a window. This paper presents an on-line technique based on a posture generation rule to compute a null-space joint velocity vector in a singularity-robust redundancy resolution method. This rule suggests that the end of each link has to track an implicit trajectory that is indirectly resulted from the constraint imposed on tracking motion of the end-effector. A proper posture can be determined by sequentially optimizing an objective function integrating multiple criteria of the orientation of each link from the end-effector toward the base link as the secondary task for redundancy resolution, by assuming one end of the link is clamped. The criteria flexibly incorporate obstacle avoidance, joint limits, preference of posture in tracking, and connection of posture to realize a compromise between the primary and secondary tasks. Furthermore, computational demanding of the posture is reduced due to the sequential link-by-link computation feature. Simulations show the effectiveness and flexibility of the proposed method in generating proper postures for the collision avoidance and the joint limits as a singularity-robust null-space projection vector in maneuvering redundant robots within constrained workspaces.

Bi-criteria velocity minimization of robot manipulators using LVI-based primal-dual neural network and illustrated via PUMA560 robot arm

Robotica ◽  
2009 ◽  
Vol 28 (4) ◽  
pp. 525-537 ◽  
Author(s):  
Yunong Zhang ◽  
Kene Li
Keyword(s):  
Neural Network ◽  
Piecewise Linear ◽  
Linear Structure ◽  
Robot Arm ◽  
Planning Scheme ◽  
Primal Dual ◽  
Joint Limits ◽  
Joint Velocity ◽  
High Computational Efficiency ◽  
Minimization Scheme

SUMMARYIn this paper, to diminish discontinuity points arising in the infinity-norm velocity minimization scheme, a bi-criteria velocity minimization scheme is presented based on a new neural network solver, i.e., an LVI-based primal-dual neural network. Such a kinematic planning scheme of redundant manipulators can incorporate joint physical limits, such as, joint limits and joint velocity limits simultaneously. Moreover, the presented kinematic planning scheme can be reformulated as a quadratic programming (QP) problem. As a real-time QP solver, the LVI-based primal-dual neural network is developed with a simple piecewise linear structure and high computational efficiency. Computer simulations performed based on a PUMA560 manipulator model are presented to illustrate the validity and advantages of such a bi-criteria velocity minimization neural planning scheme for redundant robot arms.

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