An Efficient and Accurate Inverse Kinematics for 7-DOF Redundant Manipulators Based on a Hybrid of Analytical and Numerical Method

Abstract

This paper proposes an efficient and accuracy inverse kinematic algorithm for 7-DOF redundant manipulators with obstacles avoidance and singularities avoidance based on the hybrid of analytical and numerical method (IK-HAN). Specially, the paper focuses on how to solve the inverse kinematics problem accurately and efficiently for a novel configuration, i.e. SSRMS-type manipulator. First, the elbow orientation is introduced and the algebraic relationship between the elbow orientation and joint angles is derived. Second, the optimization algorithm is designed to find the optimal elbow orientation based on Particle Swarm Optimization. To improve the efficiency, the equivalent optimization model based on the azimuth angle is investigated. Third, optimal models are developed to avoid obstacles and singularities and improve manipulability in the constraint domain. Moreover, how to employ optimization resolution to solve the inverse kinematics problem is discussed. Finally, the validity of the algorithm is verified via kinematics simulations and the result illustrates that the algorithm performs well in accuracy, stability and efficiency. INDEX TERMS Elbow orientation, obstacles avoidance, redundant manipulators, real-time inverse kinematics, singularities avoidance.

Precise semi-analytical inverse kinematic solution for 7-DOF offset manipulator with arm angle optimization

“…This method was verified through a simulation in which the end-effector tracked a circle with a constant orientation and arm angle. Jin et al [43] proposed an optimization algorithm for determining the optimal elbow orientation on the basis of particle swarm optimization and solved the inverse kinematics by using the relationship between elbow orientation and joint angles. Xu et al [44] solved the inverse kinematic solution of the SRS manipulator through arm angle parameterization and generalized the results to the EMM (referred to as the SSRMS manipulator in their paper) in accordance with the relationship of joint angles between the EMM and the SRS manipulator.…”

Inverse kinematics of redundant manipulators with guaranteed performance

“…A general IK description is that the joint trajectory of a redundant manipulator needs to be determined for a given end-effector desired path. Many studies have been conducted and reported on IK because it is related to the path planning and/or kinematic control of redundant manipulators [1,2,3,4,5,6,7,8,13,10,11,12]. Hassan et al [7] presented the IK of redundant manipulators via the formulation of quadratic programming.…”

“…Hassan et al [7] presented the IK of redundant manipulators via the formulation of quadratic programming. Jin et al [10] developed an IK algorithm for redundant manipulators with avoidance of obstacles and singularities. Chen et al [11] investigated an IK scheme with multilevel simultaneous minimization for jerk-bounded redundant manipulators.…”

Intelligent Trajectory Tracking Behavior of a Multi-Joint Robotic Arm via Genetic–Swarm Optimization for the Inverse Kinematic Solution

“…However, the traditional IK methods cannot consider the continuity of configurations, collision avoidance and kinematic singularities that arises when attempting to follow the end-effector path [ 14 ]. In addition, solving IK problems is a difficult challenge because manipulators with more than 5DoF result in an infinite number of possible solutions for joint trajectories that determine the same position in the Cartesian space [ 15 ]. Traditional analytical solutions cannot directly calculate the one-to-many possible relationships in the Cartesian space.…”