Long Jin

Distributed Task Allocation of Multiple Robots: A Control Perspective

The problem of dynamic task allocation in a distributed network of redundant robot manipulators for path-tracking with limited communications is investigated in this paper, where <inline-formula> <tex-math notation=LaTeX>

G2-Type SRMPC Scheme for Synchronous Manipulation of Two Redundant Robot Arms

{k}

Manipulability Optimization of Redundant Manipulators Using Dynamic Neural Networks

</tex-math></inline-formula> fittest ones in a group of <inline-formula> <tex-math notation=LaTeX>

Discrete-Time Zhang Neural Network for Online Time-Varying Nonlinear Optimization With Application to Manipulator Motion Generation

{n}

Integration-Enhanced Zhang Neural Network for Real-Time-Varying Matrix Inversion in the Presence of Various Kinds of Noises

</tex-math></inline-formula> redundant robot manipulators with <inline-formula> <tex-math notation=LaTeX>

Kinematic Control of Redundant Manipulators Using Neural Networks

{n>k}

Taylor-type 1-step-ahead numerical differentiation rule for first-order derivative approximation and ZNN discretization

</tex-math></inline-formula> are allocated to execute an object tracking task. The problem is essentially challenging in view of the interplay of manipulator kinematics and the dynamic competition for activation among manipulators. To handle such an intricate problem, a distributed coordination control law is developed for the dynamic task allocation among multiple redundant robot manipulators with limited communications and with the aid of a consensus filter. In addition, a theorem and its proof are presented for guaranteeing the convergence and stability of the proposed distributed control law. Finally, an illustrative example is provided and analyzed to substantiate the efficacy of the proposed control law.

Modified ZNN for Time-Varying Quadratic Programming With Inherent Tolerance to Noises and Its Application to Kinematic Redundancy Resolution of Robot Manipulators

In this paper, to remedy the joint-angle drift phenomenon for manipulation of two redundant robot arms, a novel scheme for simultaneous repetitive motion planning and control (SRMPC) at the joint-acceleration level is proposed, which consists of two subschemes. To do so, the performance index of each SRMPC subscheme is derived and designed by employing the gradient dynamics twice, of which a convergence theorem and its proof are presented. In addition, for improving the accuracy of the motion planning and control, position error, and velocity, error feedbacks are incorporated into the forward kinematics equation and analyzed via Zhang neural-dynamics method. Then the two subschemes are simultaneously reformulated as two quadratic programs (QPs), which are finally unified into one QP problem. Furthermore, a piecewise-linear projection equation-based neural network (PLPENN) is used to solve the unified QP problem, which can handle the strictly convex QP problem in an inverse-free manner. More importantly, via such a unified QP formulation and the corresponding PLPENN solver, the synchronism of two redundant robot arms is guaranteed. Finally, two given tasks are fulfilled by 2 three-link and 2 five-link planar robot arms, respectively. Computer-simulation results validate the efficacy and accuracy of the SRMPC scheme and the corresponding PLPENN solver for synchronous manipulation of two redundant robot arms.

Noise-Tolerant ZNN Models for Solving Time-Varying Zero-Finding Problems: A Control-Theoretic Approach

For solving the singularity problem arising in the control of manipulators, an efficient way is to maximize its manipulability. However, it is challenging to optimize manipulability effectively because it is a nonconvex function to the joint angles of a robotic arm. In addition, the involvement of an inversion operation in the expression of manipulability makes it even hard for timely optimization due to the intensively computational burden for matrix inversion. In this paper, we make progress on real-time manipulability optimization by establishing a dynamic neural network for recurrent calculation of manipulability-maximal control actions for redundant manipulators under physical constraints in an inverse-free manner. By expressing position tracking and matrix inversion as equality constraints, physical limits as inequality constraints, and velocity-level manipulability measure, which is affine to the joint velocities, as the objective function, the manipulability optimization scheme is further formulated as a constrained quadratic program. Then, a dynamic neural network with rigorously provable convergence is constructed to solve such a problem online. Computer simulations are conducted and show that, compared to the existing methods, the proposed scheme can raise the manipulability almost 40% on average, which substantiates the efficacy, accuracy, and superiority of the proposed manipulability optimization scheme.

Discrete-time Zhang neural network of O(τ³) pattern for time-varying matrix pseudoinversion with application to manipulator motion generation

In this brief, a discrete-time Zhang neural network (DTZNN) model is first proposed, developed, and investigated for online time-varying nonlinear optimization (OTVNO). Then, Newton iteration is shown to be derived from the proposed DTZNN model. In addition, to eliminate the explicit matrix-inversion operation, the quasi-Newton Broyden-Fletcher-Goldfarb-Shanno (BFGS) method is introduced, which can effectively approximate the inverse of Hessian matrix. A DTZNN-BFGS model is thus proposed and investigated for OTVNO, which is the combination of the DTZNN model and the quasiNewton BFGS method. In addition, theoretical analyses show that, with step-size h = 1 and/or with zero initial error, the maximal residual error of the DTZNN model has an O(τ2) pattern, whereas the maximal residual error of the Newton iteration has an O(τ) pattern, with τ denoting the sampling gap. Besides, when h ≠ 1 and h ∈ (0, 2), the maximal steady-state residual error of the DTZNN model has an O(τ2) pattern. Finally, an illustrative numerical experiment and an application example to manipulator motion generation are provided and analyzed to substantiate the efficacy of the proposed DTZNN and DTZNN-BFGS models for OTVNO.