Minimum Velocity Norm Research Articles

Inverse kinematics solution and motion simulation of seven-degree-of-freedom ascending platform based on neural network

A pseudoinverse-based inverse kinetic solving scheme for 7-degree-of-freedom redundant aerial platform robotic arm, the scheme combines Minimum Velocity Norm scheme and damped least-square method, a close-loop damped minimum velocity norm scheme is set up which allows to avoid the joints’ limitation and to ensure the solution’s stability near the singularity position. Further, a genetic algorithm optimized BP neural network is built. Genetic algorithm can improve the training efficiency and avoid trapping in local optimal solution. The application of neural network can ensure the real-time of solution.

Velocity-Level Tri-Criteria Optimization Scheme for Different Complex Path Tracking of Redundant Manipulators

In order to remedy the position deviation of the joint angles and ensure the smooth motion trajectory of the end-effector at velocity level, a velocity-level tri-criteria optimization (VLTCO) scheme of redundant manipulator’s is proposed. The proposed VLTCO scheme combines the minimum velocity norm (MVN), the repetitive motion planning (RMP), and the infinity-norm velocity minimization (INVM) through the weighting factors, which guarantees the joint velocity to be near zero after finishing the redundant manipulators task. At the same time, the scheme considers the joint-angle and joint-velocity physical limits, which can keep the joint angle and joint velocity within their given range and prevent the occurrence of high joint velocity during the task duration. Finally, the VLTCO scheme is reformulated as one general quadratic program (QP) problem. The QP problem is then solved by a linear-variational-inequality-based primal–dual neural network solver (LVI-PDNN). The validity and advantages of the VLTCO scheme are substantiated by the simulation results and the physical experiment based on the JACO2 redundant manipulator.

Feedback-Added Pseudoinverse-Type Balanced Minimization Scheme for Kinematic Control of Redundant Robot Manipulators

In this paper, a new feedback-added pseudoinverse-type balanced minimization (FPBM) scheme is proposed and studied for the kinematic control of redundant robot manipulators. Such a scheme is designed by combining the minimum acceleration norm (MAN) solution and the weighted minimum velocity norm (WMVN) solution and by introducing the feedback. With the MAN and WMVN combination, the proposed FPBM scheme can not only remedy the phenomena of high velocity and acceleration but also generate a near-zero velocity after task execution. With the feedback introduction, the proposed FPBM scheme can guarantee a nondivergent end-effector tracking error. Based on a four-link robot manipulator, the simulation results are presented to show the effectiveness of the proposed FPBM scheme.

Tricriteria Optimization-Coordination Motion of Dual-Redundant-Robot Manipulators for Complex Path Planning

To remedy the discontinuity phenomenon existing in the infinity-norm velocity minimization (INVM) scheme, prevent the occurrence of high joint velocity, and decrease the joint-angle drift of redundant robot manipulators, a new type of tricriteria optimization-coordination-motion (TCOCM) scheme is proposed and investigated for dual-redundant-robot manipulators to track complex end-effector paths. Besides, the proposed scheme considers joint physical constraints (i.e., joint-angle limits and joint-velocity limits) and guarantees the joint velocity to approach zero at the end of tasks. Such a new-type TCOCM scheme combines the minimum velocity norm (MVN), repetitive motion planning (RMP), and INVM solutions via two weighting factor, and thus is termed MVN-RMP-INVM-TCOCM scheme. The proposed scheme consists of two subschemes, i.e., subscheme for the left robot manipulator and subscheme for the right robot manipulator. To control the dual arms simultaneously and collaboratively, two subschemes are reformulated as two general quadratic programming (QP) problems and further unified into one QP formulation. The unified QP problem is then solved by a simplified linear-variational-inequalities-based primal–dual neural network solver. Computer simulation results based on dual PUMA560 robot manipulators are illustrated to substantiate the advantage, efficacy, and applicability of the proposed MVN-RMP-INVM-TCOCM scheme to resolve the redundancy of dual-robot manipulators.

A Velocity-Level Bi-Criteria Optimization Scheme for Coordinated Path Tracking of Dual Robot Manipulators Using Recurrent Neural Network.

A dual-robot system is a robotic device composed of two robot arms. To eliminate the joint-angle drift and prevent the occurrence of high joint velocity, a velocity-level bi-criteria optimization scheme, which includes two criteria (i.e., the minimum velocity norm and the repetitive motion), is proposed and investigated for coordinated path tracking of dual robot manipulators. Specifically, to realize the coordinated path tracking of dual robot manipulators, two subschemes are first presented for the left and right robot manipulators. After that, such two subschemes are reformulated as two general quadratic programs (QPs), which can be formulated as one unified QP. A recurrent neural network (RNN) is thus presented to solve effectively the unified QP problem. At last, computer simulation results based on a dual three-link planar manipulator further validate the feasibility and the efficacy of the velocity-level optimization scheme for coordinated path tracking using the recurrent neural network.

Revisit and compare Ma equivalence and Zhang equivalence of minimum velocity norm (MVN) type

In this paper, by revisiting Ma et al.’s inspiring work (specifically, Ma equivalence, ME) and Zhang et al.’s inspiring work (specifically, Zhang equivalence, ZE), which both investigate the equivalence relationships of redundancy-resolution schemes at two different levels, but with different formulations, the general scheme formulations and equivalence analyses of ME and ZE are presented. Besides, being a case study, the ME and ZE of minimum velocity norm (MVN) type are investigated for the inverse-kinematics (IK) problem solving. Moreover, the link and difference between the MVN-type ME and ZE are analyzed, summarized and presented methodologically, systematically, and computationally in this paper. In order to numerically compare the ME and ZE of MVN type, a Rhodonea-path tracking task based on PUMA560 robot manipulator is tested and fulfilled by employing the original velocity-level MVN schemes and its equivalent acceleration-level MVN schemes of ME and ZE. The simulative and numerical results not only verify the effectiveness of the velocity-level and acceleration-level schemes of MVN-type ME and ZE, but also validate the reasonableness of such two proved equivalence relationships. More importantly, these results show quantitatively and comparatively the respective advantages and future applications of MVN-type ME and ZE for the IK problem solving.

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

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.

Physical-limits-constrained minimum velocity norm coordinating scheme for wheeled mobile redundant manipulators

SUMMARYIn order to resolve the redundancy of a wheeled mobile redundant manipulator comprising a two-wheel-drive mobile platform and a 6-degree-of-freedom manipulator, a physical-limits-constrained (PLC) minimum velocity norm (MVN) coordinating scheme (termed as PLC-MVN-C scheme) is proposed and investigated. Such a scheme can not only coordinate the mobile platform and the manipulator to fulfill the end-effector task and to achieve the desired optimal index (i.e., minimizing the norm of the rotational velocities of the wheels and the joint velocities of the manipulator) but also consider the physical limits of the robot (i.e., the joint-angle limits and joint-velocity limits of the manipulator as well as the rotational velocity limits of the wheels). The scheme is then reformulated as a quadratic program (QP) subject to equality and bound constraints, and is solved by a discrete QP solver, i.e., a numerical algorithm based on piecewise-linear projection equations (PLPE). Simulation results substantiate the efficacy and accuracy of such a PLC-MVN-C scheme and the corresponding discrete PLPE-based QP solver.

Variable Joint-Velocity Limits of Redundant Robot Manipulators Handled by Quadratic Programming

In this paper, a variable joint-velocity limits (VJVL)-constrained minimum-velocity-norm (MVN) scheme (termed VJVL-constrained MVN scheme) is proposed and investigated for redundant manipulators, i.e., the JVL change with the end-effector and joints movement. The scheme is then formulated as a quadratic program (QP), which is subject to an equality constraint and a bound constraint, and such a QP problem is solved by a discrete QP solver, i.e., a numerical algorithm. In addition, experimental results performed on a planar six degrees-of-freedom (6-DOF) push-rod (PR) redundant robot manipulator substantiate the physical realizability and efficacy of such a VJVL-constrained MVN scheme and the corresponding discrete QP solver. Furthermore, the position-error analyses verify the accuracy of the proposed scheme on redundant manipulators.

A New Inequality-Based Obstacle-Avoidance MVN Scheme and Its Application to Redundant Robot Manipulators

This paper proposes a new inequality-based criterion/constraint with its algorithmic and computational details for obstacle avoidance of redundant robot manipulators. By incorporating such a dynamically updated inequality constraint and the joint physical constraints (such as joint-angle limits and joint-velocity limits), a novel minimum-velocity-norm (MVN) scheme is presented and investigated for robotic redundancy resolution. The resultant obstacle-avoidance MVN scheme resolved at the joint-velocity level is further reformulated as a general quadratic program (QP). Two QP solvers, i.e., a simplified primal-dual neural network based on linear variational inequalities (LVI) and an LVI-based numerical algorithm, are developed and applied for online solution of the QP problem as well as the inequality-based obstacle-avoidance MVN scheme. Simulative results that are based on PA10 robot manipulator and a six-link planar robot manipulator in the presence of window-shaped and point obstacles demonstrate the efficacy and superiority of the proposed obstacle-avoidance MVN scheme. Moreover, experimental results of the proposed MVN scheme implemented on the practical six-link planar robot manipulator substantiate the physical realizability and effectiveness of such a scheme for obstacle avoidance of redundant robot manipulator.

Torque optimization schemes for kinematically redundant manipulators

AbstractOne of the important applications for the resolution of redundant manipulators is torque optimization, due to the fact that the actuators used for driving a manipulator have finite power ratings. Nevertheless, not many algorithms have been proposed to accomplish this objective. A survey of the existing local torque optimization control schemes is given in this article. It will be shown that all of them either encounter instability problems for long trajectories or fail in certain cases. For remedying these problems, the authors present the Minimum Velocity Norm (MVN) method, which is the most common approach for kinematic redundancy resolution and has never been adopted for torque optimization by other researchers. Simulation results show that the simple MVN method is moderate for short movements and is stable for long movements. Also, the MVN method can be applied to cases that may not be accomplished by some other approaches. Therefore, the MVN method is better than the other existing approaches for torque optimization. © 1994 John Wiley & Sons, Inc.