Efficient hybrid method for forward kinematics analysis of parallel robots based on signal decomposition and reconstruction

Abstract

This article combines a new method based on signal decomposition and reconstruction with a fifth-order numerical algorithm and proposes an efficient hybrid method for solving forward kinematics problem of parallel manipulators. In this hybrid method, new method can first generate an approximate solution of the forward kinematics problem, which will be taken as initial guess for the fifth-order numerical technique. The answer with desired level of accuracy is then obtained. The superposition principle is proposed stating that each rod's displacement required to drive the mobile platform with 6-degree-of-freedom coupled motion is approximately a sum of the rod's displacement required to drive it with each of six single basic motions including roll q 1 , pitch q 2 , yaw q 3 , surge q 4 , sway q 5 , and heave q 6 . By solving the equations established in accordance with the superposition principle, the approximate solution is also gained. Superposition principle is more applicable to the robots with small rotational workspace. The solution is directly solved under superposition principle. Even though the rotational workspace is expanded, the solution still meets the required accuracy of initial value of high-order iterative technique for obtaining its exact solution. The proposed method is then applied to a test bench for bogie parameters and a Stewart platform. Simulation results demonstrate that maximum absolute error of displacement along X-, Y-, and Z-axis is 0.174 mm and its relative error is about 3.4&. Using this method will reduce about 34.1% of the required number of iterations to solve the forward kinematics problem compared with improved hybrid method and up to 49.8% compared with the Newton-Raphson method.

Dynamic analysis and decoupled control of a heavy-duty walking robot with flexible feet based on super twisting algorithm

“…where L = TÀU, Q is dissipative energy, C is the constraint equation, l is the Lagrange generator corresponding to the constraint, F is the generalized external force. By substituting equations (12), (13), and (14) into equation (15), the dynamic differential equation of flexible body follows:…”

“…9 However, this kind of leg mechanism has complex dynamics and control algorithm problems 10,11 as well as difficult forward kinematics. 12 The kinematic model can reflect the mapping relationship between joint motion and spatial motion of the mechanism without considering the effect of force, while the dynamic model is to study the relationship between mechanical motion and force. 13,14 In the dynamic model, using CTC as dynamic compensation can make the robot become a more easily controlled system.…”

“…9 However, this kind of leg mechanism has complex dynamics and control algorithm problems 10,11 as well as difficult forward kinematics. 12…”

An Efficient Numerical Method for Forward Kinematics of Parallel Robots

“…The inverse kinematics problem (IKP) can be easily solved geometrically. Compared with the IKP, the forward kinematics problem (FKP) is more difficult due to the high nonlinearity and the various structures of parallel robots [6] and the efficiency for solving the FKP is important for real-time applications.…”

Workspace analysis of the bogie 6-degree-of-freedom dynamic simulation test bench

“…The test bench can simulate the motion pose of the bogie and complete the test of its performance parameters under various dynamic conditions. 21 For convenience, some mating devices were installed on the test bench, like the beginning and the intermediate transition platforms and the braced frames. Thus, the workspace of the 6-DOF motion platform is bound by many factors, such as telescopic stroke, spherical hinge angle, and the surrounding obstacles.…”