Design of electronic cam for lower hook mechanism of fishing net-weaving machine based on polynomial fitting

The working efficiency and stability of the double hook-based fishing net-weaving machine is mainly determined by the lower hook mechanism. In this work, a new kind of lower hook mechanism, which is driven by four servo motors, is presented, and the electronic cam curve of the lower hook mechanism is introduced. First, cubic B-spline interpolation is used to get the basic motion path of the lower hook plate, and then the piecewise quintic polynomial fitting method is used to fit the motion path. Finally, self-adaptive mutation-based particle swarm optimization is put forward and used to obtain the optimal parameters of the quintic polynomial, which performs better compared with the other two particle swarm optimization algorithms in this study. Experiments suggest that the electronic cam curve generated by the piecewise quintic polynomial fitting has got 55.91% (horizontal motors) and 60.96% (vertical motors) optimization in maximum motor torque compared with curves generated by cubic B-spline interpolations. In addition, the new lower hook mechanism and its moving curve described in this paper improved the theoretical weaving speed of the fishing net-weaving machine, providing a basis for digital improvement of the knotted net-weaving industry.

Research on Path Planning and Tracking Control of Automatic Parking System

In this paper, we focus on the parking path planning and path tracking control under parallel parking conditions with automatic parking system as the research object. In order to solve the problem of discontinuity of curvature in the path planning of traditional arc-straight combined curve, a quintic polynomial is used to smooth the path. we design a path tracking controller based on the incremental model predictive control (MPC). The preview control based on pure tracking algorithm is used as the comparison algorithm for path tracking. The feasibility of the controller is verified by building a Simulink/CarSim co-simulation platform. In addition, the practicality of the parking controller is further verified by using the ROS intelligent car in the laboratory environment.

Feasible Trajectories Generation for Autonomous Driving Vehicles

This study presents smooth and fast feasible trajectory generation for autonomous driving vehicles subject to the vehicle physical constraints on the vehicle power, speed, acceleration as well as the hard limitations of the vehicle steering angle and the steering angular speed. This is due to the fact the vehicle speed and the vehicle steering angle are always in a strict relationship for safety purposes, depending on the real vehicle driving constraints, the environmental conditions, and the surrounding obstacles. Three different methods of the position quintic polynomial, speed quartic polynomial, and symmetric polynomial function for generating the vehicle trajectories are presented and illustrated with simulations. The optimal trajectory is selected according to three criteria: Smoother curve, smaller tracking error, and shorter distance. The outcomes of this paper can be used for generating online trajectories for autonomous driving vehicles and auto-parking systems.

Kinematics decoupling analysis of a hyper-redundant manipulator driven by cables

The mapping relationship between the driving space and the workspace is essential for the precise control of a cable-driven hyper-redundant robot. For a hyper-redundant robot driven by cables, the relationships between the driving space and the joint space and between the joint space and the workspace were studied. A joint-decoupling kinematics analysis method was proposed and a kinematic analysis was presented. Based on the analysis of the coupling effect between the cable-driving space and the joint space, a decoupling analysis of the whole cable-driving space and joint space was conducted to eliminate the coupling effect between the joints, and the mapping relationship between the driving cables and the joint angles was obtained. Given the initial and target orientations of the hyper-redundant robot, the variation law for each joint angle was obtained using quintic polynomial trajectory planning and the pseudo-inverse Jacobian matrix, and then the driving cable variation law could be solved. Based on the results, the joint angle changes and the workspace trajectories were solved in turn. By comparing with the initial trajectory, the simulation results verified the appropriateness of the decoupling analysis.

Motion Planning for Vibration Reduction of a Railway Bridge Maintenance Robot with a Redundant Manipulator

Motivated by the potential applications of maintenance and inspection tasks for railway bridges, we have developed a biped climbing robot. The biped climbing robot can climb on the steel guardrail of the railway bridge with two electromagnetic feet and implement the maintenance and inspection tasks by a redundant manipulator with 7 degrees of freedom. To reduce the vibration of the manipulator caused by the low rigidity of the guardrail and the discontinuous trajectories of joints, a motion planning algorithm for vibration reduction is proposed in this paper. A geometric path accounting for obstacle avoidance and the manipulator’s center of gravity is determined by the gradient projection method with a singularity-robust inverse. Then, a piecewise quintic polynomial S shape curve with a smooth jerk (derivative of joint angular acceleration) profile is used to interpolate the sequence of joint angular position knots that are transformed from the via-points in the obstacle-avoidance path. The parameters of the quintic polynomial S-curve are determined by a nonlinear programming problem in which the objective function is to minimize the maximus of the torque exerted by the manipulator on the guardrail throughout the jerk-continuous trajectory. Finally, a series of simulation experiments are conducted to validate the effectiveness of the proposed algorithm. The simulation results show that the tracking errors of the trajectory with the proposed optimization algorithm are significantly smaller than the tracking errors of the trajectory without optimization. The absolute values of mean deviation of the tracking errors of the three coordinate axes decreased by at least 48.3% compared to the trajectory without vibration-reduction in the triangle working path and linear working path trajectory following simulations. The analysis results prove that the proposed algorithm can effectively reduce the vibration of the end effector of the manipulator.

Research on Kinematics Analysis and Trajectory Planning of Novel EOD Manipulator

To address the problems of mismatch, poor flexibility and low accuracy of ordinary manipulators in the complex special deflagration work process, this paper proposes a new five-degree-of-freedom (5-DOF) folding deflagration manipulator. Firstly, the overall structure of the explosion-expulsion manipulator is introduced. The redundant degrees of freedom are formed by the parallel joint axes of the shoulder joint, elbow joint and wrist pitching joint, which increase the flexibility of the mechanism. Aiming at a complex system with multiple degrees of freedom and strong coupling of the manipulator, the virtual joint is introduced, the corresponding forward kinematics model is established by D–H method, and the inverse kinematics solution of the manipulator is derived by analytical method. In the MATLAB platform, the workspace of the manipulator is analyzed by Monte Carlo pseudo-random number method. The quintic polynomial interpolation method is used to simulate the deflagration task in joint space. Finally, the actual prototype experiment is carried out using the data obtained by simulation. The trajectory planning using the quintic polynomial interpolation method can ensure the smooth movement of the manipulator and high accuracy of operation. Furthermore, the trajectory is basically consistent with the simulation trajectory, which can realize the work requirements of putting the object into the explosion-proof tank. The new 5-DOF folding deflagration manipulator designed in this paper has stable motion and strong robustness, which can be used for deflagration during the COVID-19 epidemic.

Joint Motion Planning of Industrial Robot Based on Modified Cubic Hermite Interpolation with Velocity Constraint

As for industrial robots’ point-to-point joint motion planning with constrained velocity, cubic polynomial planning has the problem of discontinuous acceleration; quintic polynomial planning requires acceleration to be specified in advance, which will likely cause velocity to fluctuate largely because appropriate acceleration assigned in advance is hardly acquired. Aiming at these problems, a modified cubic Hermite interpolation for joint motion planning was proposed. In the proposed methodology, knots of cubic Hermite interpolation need to be reconfigured according to the initial knots. The formulas for how to build new knots were put forward after derivation. Using the newly-built knots instead of initial knots for cubic Hermite interpolation, joint motion planning was carried out. The purpose was that the joint planning not only satisfied the displacement and velocity constraints at the initial knots but also guaranteed C2 continuity and less velocity fluctuation. A study case was given to verify the rationality and effectiveness of the methodology. Compared with the other two planning methods, it proved that the raised problems can be solved effectively via the proposed methodology, which is beneficial to the working performance and service life of industrial robots.

Trajectory Planning of Robot Manipulator Based on RBF Neural Network

Robot manipulator trajectory planning is one of the core robot technologies, and the design of controllers can improve the trajectory accuracy of manipulators. However, most of the controllers designed at this stage have not been able to effectively solve the nonlinearity and uncertainty problems of the high degree of freedom manipulators. In order to overcome these problems and improve the trajectory performance of the high degree of freedom manipulators, a manipulator trajectory planning method based on a radial basis function (RBF) neural network is proposed in this work. Firstly, a 6-DOF robot experimental platform was designed and built. Secondly, the overall manipulator trajectory planning framework was designed, which included manipulator kinematics and dynamics and a quintic polynomial interpolation algorithm. Then, an adaptive robust controller based on an RBF neural network was designed to deal with the nonlinearity and uncertainty problems, and Lyapunov theory was used to ensure the stability of the manipulator control system and the convergence of the tracking error. Finally, to test the method, a simulation and experiment were carried out. The simulation results showed that the proposed method improved the response and tracking performance to a certain extent, reduced the adjustment time and chattering, and ensured the smooth operation of the manipulator in the course of trajectory planning. The experimental results verified the effectiveness and feasibility of the method proposed in this paper.

Analytical Solutions of Some Strong Nonlinear Oscillators

Oscillators are omnipresent; most of them are inherently nonlinear. Though a nonlinear equation mostly does not yield an exact analytic solution for itself, plethora of elementary yet practical techniques exist for extracting important information about the solution of equation. The purpose of this chapter is to introduce some new techniques for the readers which are carefully illustrated using mainly the examples of Duffing’s oscillator. Using the exact analytical solution to cubic Duffing and cubic-quinbic Duffing oscillators, we describe the way other conservative and some non conservative damped nonlinear oscillators may be studied using analytical techniques described here. We do not make use of perturbation techniques. However, some comparison with such methods are performed. We consider oscillators having the form x¨+fx=0 as well as x¨+2εẋ+fx=Ft, where x=xt and f=fx and Ft are continuous functions. In the present chapter, sometimes we will use f−x=−fx and take the approximation fx≈∑j=1Npjxj, where j=1,3,5,⋯N only odd integer values and x∈−AA. Moreover, we will take the approximation fx≈∑j=0Npjxj, where j=1,2,3,⋯N, and x∈−AA. Arbitrary initial conditions are considered. The main idea is to approximate the function f=fx by means of some suitable cubic or quintic polynomial. The analytical solutions are expressed in terms of the Jacobian and Weierstrass elliptic functions. Applications to plasma physics, electronic circuits, soliton theory, and engineering are provided.

Torque Curve Optimization of Ankle Push-Off in Walking Bipedal Robots Using Genetic Algorithm

Ankle push-off occurs when muscle–tendon units about the ankle joint generate a burst of positive power at the end of stance phase in human walking. Ankle push-off mainly contributes to both leg swing and center of mass (CoM) acceleration. Humans use the amount of ankle push-off to induce speed changes. Thus, this study focuses on determining the faster walking speed and the lowest energy efficiency of biped robots by using ankle push-off. The real-time-space trajectory method is used to provide reference positions for the hip and knee joints. The torque curve during ankle push-off, composed of three quintic polynomial curves, is applied to the ankle joint. With the walking distance and the mechanical cost of transport (MCOT) as the optimization goals, the genetic algorithm (GA) is used to obtain the optimal torque curve during ankle push-off. The results show that the biped robot achieved a maximum speed of 1.3 m/s, and the ankle push-off occurs at 41.27−48.34% of the gait cycle. The MCOT of the bipedal robot corresponding to the high economy gait is 0.70, and the walking speed is 0.54 m/s. This study may further prompt the design of the ankle joint and identify the important implications of ankle push-off for biped robots.