Analytical Inverse Kinematic Computation for a special Class of 7-DOF Redundant Manipulators

Abstract

Inverse kinematic solutions of redundant manipulators can be developed using numerical, optimization or analytical methods. Numerical and optimization methods usually involve complicated constraint equations or penalty functions, so the solutions might be difficult to obtain, generate larger errors or violate some kinematic constraints. This work presents an analytical method for the inverse kinematic solutions of 7-DOF redundant manipulators. The conditions that a 7-DOF manipulator can be transform into a 6-DOF industrial manipulator with simple inverse kinematics are proposed. After solving quadratic equations for the solutions of the 6-DOF manipulator, the solutions of the redundant manipulator can be easily obtained using some simple geometric calculations. The method can also efficiently detect the closeness to singular configurations. Since there are eight branches of solutions to choose from, it can choose the branch of solutions that is away from singularity, obstacles or joint limits for trajectory planning.