PhyNRnet: Physics-informed Newton-Raphson Network for Forward Kinematics Solution of Parallel Manipulators

In this paper, approaches for the solution of parallel manipulators forward kinematics have been addressed. Current research on this topic has been analyzed to determine the status and unresolved issues of the research field. Articles on parallel manipulators forward kinematics were reviewed, and numerous approaches for resolving forward kinematics in particular have been identified and published, which may assist researchers in selecting the most appropriate technique for solving the problem in this domain. Researchers have also attempted to apply these methods to a variety of other parallel manipulator-related problems, such as inverse kinematics and dynamics. In robotics, serial manipulators were invented before parallel manipulators. Hence, methodologies for solving forward kinematics were first developed for serial manipulators and many methods are ineffective for parallel manipulators. In this paper, all identified methods can be used for solving forward kinematics of parallel and serial manipulators.

A novel model-based controller for six degree of freedom (dof) parallel manipulator-PID controller with gravity compensation is developed, in order to improve the control precision of six-dof hydraulic driven parallel manipulator with long stroke hydraulic actuator and heavy load. In this paper, six-dof parallel manipulator is described as a thirteen rigid-body systems. The mathematical model of gravity item including upper platform and hydraulic cylinders is built using Kane method in six dimensions generalized coordinates system, based on close-form solutions and Newton-Raphson method, forward kinematics and inverse kinematics of the six-dof parallel manipulator are established. The PID controller with gravity compensation is presented with the feedback of cylinder length of platform, desired trajectories and dynamics gravity as the input. The physical systems of 6dof parallel manipulator are modeled by ADAMS, and the PID controller with gravity compensation is built with Simulink. The whole control system of 6-dof parallel manipulator is obtained by connecting ADAMS plant with PID control system with gravity compensation in Simulink. The simulation of the whole systems is executed in Simulink, the simulation results indicate the PID controller with gravity compensation can eliminate steady state error of 6-dof hydraulic driven parallel manipulator and improve the control precision.

Parallel manipulator kinematics learning using holographic neural network models

Parallel robot inverse kinematics solution is relatively easier to obtain than forward kinematics forward, this paper assumes that the forward kinematics of six-DOF parallel robot is given then using the kinematics inverse solution to approximate the forward solution. To improve efficiency and stability of the approximation, an adaptive parameters differential evolution algorithm is proposed and applied to the forward kinematics problem. The experimental results show that the modified algorithm can gain the forward kinematics of parallel robot efficiently.

In the study of BP neural network for aerodynamic modeling, few studies have considered improving the generalization ability of models. Improving generalization ability is important in the study of neural network models. Two typical methods to improve the generalization ability are tested in this paper, which are based on the LBFGS algorithm rather than the traditional gradient descent method when training BP neural network. Results indicate that when training neural network based on quasi-Newton method for aerodynamic modeling:1, adding the penalty term can improve the generalization ability 2, adding small variance noise will not improve the generalization ability.

Design and testing of a high precision parallel manipulator with hyperbolic–elliptic flexure hinges

The aim of this work is to combine different innovative methods to solve the forward kinematics (FK) problem in a parallel manipulator called Stewart platform. It leads to the solution of a set of simultaneous non-linear equations and results in a series of non-unique multiple sets of solutions. Many efforts have been made to solve this challenging problem and usually results in having to find the solution of a 16/sup th/ order polynomial by means of numerical methods such as Hooks-Jeeves, Steepest descent search and Newton-Raphson method (NR). Accuracy, speed and convergence of these methods are fully dependent to the initial guess vector that is fed to the numerical algorithm. In this paper, a simple feed forward network has been trained to calculate the approximate position of the mobile platform as the initial input vector. This vector is fed to the tuning package to acquire the precise solution of the FK problem. Two methods have been used to optimize the solution and the results have been compared. At the end, the optimized FK solution was applied in a numerical algorithm to calculate payload's velocity and acceleration.

This paper presents the most important steps of the wrist rehabilitation robot design. In this work, kinematic synthesis problem of a 3-RRR spherical parallel manipulator is considered including a solution for forward and inverse kinematic problems. In order to maximize dexterity of the parallel manipulator over its workspace, its design is developed by finding optimal link shape parameters. The CAD design for the prototype is obtained based on this optimization.

This paper presents a unified and efficient method of solving the inverse kinematics for six degree-of-freedom serial connections of two three degree-of-freedom serial and parallel manipulators. Based on the kinematic analysis of three degree-of-freedom serial and parallel manipulators, the forward kinematics are formulated for six degree-of-freedom serial connections, including parallel-parallel, serial-parallel, parallel-serial, and serial-serial types. A unified method of solving the inverse kinematics for the serial connections is established: for a given task velocity, the inverse kinematics of two arms are obtained separately, thereby significantly reducing a computational cost. This is made possible by projecting a given velocity onto the infeasible velocity space of one arm independently. Through computational analysis, the proposed method is shown to be effective for the serial connections having at least one parallel manipulator.

This paper presents the design and analysis of a novel five degrees-of- freedom (DOF) parallel kinematic manipulator (PKM) for part-handling, sorting, general positioning, and robotic machining applications. The 2- R(Pa-IQ)RR, R(Pa-IQ)R manipulator has two rotational DOFs, one parasitic rotation, and three translational DOFs. In comparison with other 5- and 6- DOF PKMs, this PKM possesses three pairs of coplanar legs that contain nested kinematic chains, and it makes exclusive use of revolute and prismatic joints. The inverse kinematic analysis is a novel extension of the geometric (vector) method with the analysis of inner and outer kinematic chains. The forward kinematic analysis was solved using the Newton Raphson (NR) method. The results of the forward and inverse kinematic analyses were validated with SolidWorks ® and MATLAB ® simulations.

Continuum robotics has become a popular area of research, with many applications derived. Though some of the designs and relative modeling have been applied in actual occasions, new modeling approaches are still required for some new designs in structure. A parallel continuum robot (PCR) prototype imitating the bionic trunk from FESTO is designed in this paper. Since the structure design of PCR adopts a cone shape to enhance stiffness, the prototype shows stronger nonlinearity than continuum robots which are modeled based on piecewise constant curvature model. Due to the structure of the PCR, this paper analyzes its nonlinearity via Euler-Bernoulli beam formulations. Three kinds of artificial neural networks (ANN) are established to identify the nonlinear parallel rod system, namely, back propagation (BP), racial basis function (RBF) and a hybrid approach using genetic algorithm (GA) to optimize the weights of BP. After training by the datum obtained from the optotrak certus 3020 active tracking system, the result shows that increasing a suitable amount of iterant training data will heighten the generation ability of the network, and the best approach to model the parallel system is the hybrid approach. For forward kinematics, the mean position error of the end-effector is 0.3%, and for inverse kinematics the mean position error is 0.43%, so, such an approach can solve the forward and inverse kinematics problem of the PCR in an acceptable precision.

Quantization-aware training for low precision photonic neural networks

The parallel manipulators with n<6 spherical joint-prismatic joint-spherical joint (SPS) type active legs and one passive constrained leg have attracted more attention and been used in many practical applications. This kind of parallel manipulator has a larger capability of load bearing and a simple structure of active leg. The paper used 4-SPS/PS four degree-of-freedom (DOF) parallel manipulator for the simulation of ship's heave and swing motion. Mobility property of the 4-SPS/PS parallel manipulator is analyzed by screw theory. The inverse position kinematics model is established and the analytical solution is obtained. It uses extra sensor and Sylvester resultant elimination to derive analytical solutions of forward position kinematics including two real solutions and two imaginary solutions, and uses vector cross product to derive the Jacobian matrix of 4-SPS/PS parallel manipulator. Furthermore, it introduces three performance indicators to analyze the singularity. In order to obtain accurate analysis results of singularity, it calculates the minimum singular value, condition number and manipulability degree of Jacobian matrix for different combination of pose, respectively.

In this paper, the mechanism and kinematics of the six degree of freedom joint manipulator PUMA560 where contains the forward kinematics, inverse kinematics and trajectory planning problems of PUMA560 are analyzed by the standard D-H method, and the forward and inverse kinematics transformation formula is derived. The manipulator was modeled with Robotics Toolbox, and the forward kinematics, inverse kinematics solutions and trajectory planning were simulated which can obtain the required data in MATLAB. This paper studies the changes of the main kinematic indexes of the robot in the process of operation, which intuitively reflects the motion state of each rod and end working part of the robot, and provides a theoretical basis for the specific development and control strategy of the manipulator.

This work presents a new systematic solution to identify the vehicle inertia parameters which are essential inputs for vehicle simulation and vehicle safety research. In conceptual design phase of this work, a virtual three Degree-of-Freedom (DoF) test bench/ parallel manipulator (PM) whose moving platform is used to clamp vehicle under test is developed. In order to realize the kinematic characteristics of the proposed PM, the kinematic analysis consists of inverse kinematic and singularity architecture is carried out. Aiming at obtaining all ten vehicle inertia parameters (i.e., mass, center of gravity and inertia tensor), the observation matrix for parameter identification is derived from the dynamic model of PM. To get the dynamic model, the Euler’s equation and Lagrange approach are applied to implement the dynamic analysis for PM’s moving platform and actuators, respectively. It is beneficial to reduce the complexity of dynamic model and load of numerical computation. In the following section, to minimize the sensitivity of parameter identification to measurement noise, an optimization process of searching for the optimal movement trajectory of PM is proposed. For this purpose, the parameterized finite-Fourier-series are used to definite the general movement trajectory of PM firstly. Subsequently, the parameters of general trajectory are optimized by employing a nonlinear iterative algorithm. Objective of this algorithm is to obtain the minimal condition number of observation matrix and meanwhile to ensure the PM still works in the achievable working space during the test. The results show that the vehicle inertial parameters can be effectively identified by executing the single optimal movement trajectory on the PM. It is expected that the proposed systematic solution could be an important approach to improve the identification efficiency and identification accuracy of vehicle inertial parameters.