Repetitive motion planning (RMP) plays a remarkable role in the operation of robotic manipulators. In this article, the RMP of robotic manipulators wherein the high precision of joint angle repeatability and end-effector motion is guaranteed is investigated. In particular, a novel pseudoinverse-based (P-based) RMP scheme is designed and proposed for robotic manipulators by applying a special difference rule to discretize the existing RMP scheme with P-based formulation. Such scheme is theoretically analyzed and proven to simultaneously guarantee joint angle repetitive precision and end-effector motion precision. Comparative simulation results of a five-link robotic manipulator and a universal robotic manipulator are provided to verify the effective performance of the proposed P-based RMP scheme. The physical realizability of the proposed scheme is further substantiated by implementing the scheme on a practical EPSON robotic manipulator.

In this article, we computationally model the social behavior of beetles and apply it to the tracking control of manipulators. The beetles demonstrate excellent skills to forage food in a previously unknown environment by merely using their olfactory senses. The goal of the beetle is to search the region with the maximum smell. Therefore, the actions of the beetle can be characterized as an optimization algorithm. This article mathematically models this behavior in the form of a recurrent neural network (RNN) with a temporal-feedback connection. We apply the formulated RNN controller for the redundancy resolution and tracking control of the redundant manipulators with an unknown kinematic model. Most of the industrial robots have redundant manipulators, and kinematic trajectory tracking is a fundamental problem for any industrial task. The behavior of the beetle allows us to formulate a position-level controller without relying on the manipulation of the Jacobian matrix. It is in contrast with the conventional velocity-level controllers, which require an accurate kinematic model of the manipulator and calculation of pseudoinverse of Jacobian, a computationally expensive task. The proposed algorithm, called Beetle Antennae Olfactory Recurrent Neural Network (BAORNN) algorithm, is capable of driving the manipulator by only using the feedback from the position and orientation sensors. The stability and convergence of the proposed algorithm are theoretically proved, and the simulations results using a seven-degree-of-freedom (DOF) industrial robotic arm, KUKA LBR IIWA14, are presented to demonstrate the performance of the proposed algorithm.

In this article, we present a metaheuristic-based control framework, called beetle antennae olfactory recurrent neural network, for simultaneous tracking control and obstacle avoidance of a redundant manipulator. The ability to avoid obstacles while tracking a predefined reference path is critical for any industrial manipulator. The formulated control framework unifies the tracking control and obstacle avoidance into a single constrained optimization problem by introducing a penalty term into the objective function, which actively rewards the optimizer for avoiding the obstacles. One of the significant features of the proposed framework is the way that the penalty term is formulated following a straightforward principle: maximize the minimum distance between a manipulator and an obstacle. The distance calculations are based on Gilbert–Johnson–Keerthi algorithm, which calculates the distance between a manipulator and an obstacle by directly using their three-dimensional geometries, which also implies that our algorithm works for a manipulator and an arbitrarily shaped obstacle. Theoretical treatment proves the stability and convergence, and simulations results using an LBR IIWA seven-DOF manipulator are presented to analyze the performance of the proposed framework.

Most traditional methods for solving the kinematic control problem of redundant manipulators are designed from a signal processing perspective. However, such a perspective may make the resultant design difficult for practitioners to understand. If the problem is addressed from an energy perspective, the resultant design may be more comprehensive, because energy is a universal concept and can be used to describe complex large-scale industrial systems. Passivity is a property of engineering systems, which is characterized through energy transformation. In this paper, a passivity-based approach is proposed for the kinematic control of redundant manipulators, where the joint velocity limit of manipulators is also considered. The performance of the approach is theoretically guaranteed. In addition, simulative examples are presented to validate the efficacy of the approach and the theoretical results.

Zeroing neural dynamics (ZND) can be seen as an effective controller to solve various challenging scientific and engineering problems. Computing Lyapunov equation is a kind of important issue in nonlinear systems for stability analysis in control. This paper presents a systematic and constructive procedure on using ZND to design control laws based on the efficient solution of dynamic Lyapunov equation. We particularly address three important aspects in the design: 1) the global stability of ZND, to guarantee the effectiveness of the solution; 2) the robustness against additive noises, to ensure the capability of ZND for using in harsh environments; and 3) the finite-time convergence of ZND, to endow ZND for real-time solution of dynamical problems. To do so, a novel formula is first designed in a unified manner of ZND. Differing from the conventional formula appearing in ZND, the proposed formula simultaneously has finite-time convergence and noise robustness property. According to this novel formula, a novel control law (termed nonlinear neural dynamics, NND) is established to compute dynamic Lyapunov equation in the presence of various additive noises. Both theoretical and simulative results ensure the finite-time convergence and noise robustness property of the NND model for computing dynamic Lyapunov equation in front of various additive noises. As compared to the conventional ZND model for computing dynamic Lyapunov, the superior property of the NND model is further demonstrated.