In this paper, a novel trajectory tracking control method of nonholonomic mobile robots based on the non-negative piecewise predefined-time theorem is proposed. The idea of cascade control is used to divide the posture error system of the mobile robot into two subsystems. Firstly, for the first-order subsystem, an active predefined-time controller is designed to realize that the angle error system converges and stabilizes to zero within a given time, which is preset in advance. Secondly, a novel predefined-time sliding mode controller is designed for the second-order subsystem, which adds a constant to compensate for the influence of singularity. Moreover, compared with the existing fixed-time control algorithm, the control scheme proposed in this paper provides a more accurate upper bound of the settling time estimation. For convenience, the complex expression of the settling time estimation is transformed into an adjustable parameter. Furthermore, the stability of the two developed controllers is analyzed and some conditions for selecting parameters are given. Finally, the simulation results show the feasibility and correctness of the proposed control algorithm. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

This paper concentrates on the global predefined-time synchronization of delayed memristive neural networks with external unknown disturbance via an observer-based active control. First, a global predefined-time stability theorem based on a non-negative piecewise Lyapunov function is proposed, which can obtain more accurate upper bound of the settling time estimation. Subsequently, considering the delayed memristive neural networks with disturbance, a disturbance-observer is designed to approximate the external unknown disturbance in the response system with a Hurwitz theorem and then to eliminate the influence of the unknown disturbance. With the help of global predefined-time stability theorem, the predefined-time synchronization is achieved between two delayed memristive neural networks via an active control Lyapunov function design. Finally, two numerical simulations are performed, and the results are given to show the correctness and feasibility of the predefined-time stability theorem.

A comparative study on the pick-and-place trajectories for high-speed Delta robots is presented in this paper. The Adept Cycle has been widely accepted as a standardized pick-and-place trajectory for industrial robots. The blending curves and optimization methods to smooth this trajectory are briefly surveyed. Three major types of trajectories: Lamé curves, clothoids and piecewise polynomials, are selected as candidates to be compared. The processes to generate these trajectories are briefly reviewed. The trajectories are firstly compared in term of their computation time. Then, based on a dynamic model and an experimental prototype of the Delta robot, different combinations of the geometric paths and motion profiles are compared in terms of power consumption, terminal state accuracy and residual vibration. The effects of trajectory configurations and parameters on the robot’s dynamic performances are investigated. Through a comprehensive analysis on both simulation and experimental results, a near-optimal pick-and-place trajectory for the Delta robot is identified and validated.

This paper deals with the dynamics and vibration analysis of an industrial Delta robot when performing high-speed pick-and-place operations. The transitions between the vertical and the horizontal segments of the pick-and-place trajectories are smoothed using either Lamé or cam curves. Using a simplified dynamics model of Delta robot, energy-based cost functions are defined and utilized to optimize Lamé and CAM curve's geometric parameters. A complete multi-body dynamic model of Delta robot is established with SolidWorks, and then transferred to ADAMS for simulation purpose. These two types of trajectories are compared in terms of residual vibrations and tracking accuracy. The results obtained could lead to practical merits in engineering applications. 1. Introduction Delta parallel robot is a highly-used commercial parallel robot which has 3-DOF translational motion with high-speed capability. It was invented by Clavel early in 1985[1].This parallel robot has many advantages, such as large loading ability, high precision, simple inverse kinematic solutions , minor error, small deadweight load ratio, good dynamic performance, control ease and so on[2][3].There were several ways proposedfor inverse problem solution. The ways of getting direct solution are either Numerical Solution or Analytical Method, which are complex, but using the ADAMS software to get the forward solution is much easier. It will not generate any errors if the model of the robot is correct [4, 5, 6, 7]. This paper aims to build up a Delta parallel Robot by mechanism of constrain Equations. In Sec. A, further introduction and the application of Lamé curves [8] in high speed PPO trajectories are presented. In Sec. B, complete Mechanism of Delta parallel Robot by using SolidWorks and ADAMS software are presented in Sec. C, procedure of get the solution by using ADAMS software and Lamé curve and CAM curve trajectoriesand Direct solutions are followed by Sec. D, the simulation of Lamé and CAM curves related with acceleration and movement of position are discussed in Sec. E, the trajectories generated are tested on a physical prototype of Delta robot and the experiment results verify the effectiveness of the optimized trajectory and vibration analysis are define in Sec. F. Finally, the conclusion and the future research are discussed in Sec. G. 2. Modeling of Delta Parallel Robot 2.1 The Mechanism Constraint Equation. Delta parallel robot is made up of one static platform, one moving platform, three driving rods and three driven mobile parallelograms branch chains (Fig.1 is its structure diagram).The three edges of the static platform have the same kinematic chain join to the moving platform. Each kinematic chain is a closed-loop parallelogram branch chain which is joined with two driven rods by four spherical hinge, this close-loop and one driving rodith rotation joint constitute a series mechanism, the driving rod is fixed to the static platform, the driving rod swing repeat by the drive of determined by these three kinematics chains. The moving p...