An Optimization-Based Method for the Inverse Kinematics of Seven Degree-of-Freedom Manipulator

The method of decoupling joint space to Cartesian space using virtual arm angle constraints is an effective approach for solving the inverse kinematics of a seven-degree-of-freedom redundant manipulator. However, there is insufficient analysis regarding to optimization under constraints. This paper proposes an arm angle optimization method based on optimization process: first, the effective motion range of the seven joint axes is used as constraints to obtain the effective arm angle interval; then, by integrating the target pose with the desired pose of the manipulator, the arm angle that maintains optimal manipulability is calculated; finally, the joint inverse solution corresponding to the target pose is obtained based on the optimal arm angle. The proposed method can meet the requirement of the motion range constraints of each joint in an analytical manner, effectively improving the stability of the solution and the operability of the manipulator in Cartesian space. This paper firstly introduces the concept of arm angle constraints, then presents an optimal arm angle solving strategy based on optimization, and finally verifies the correctness of the solution using MATLAB. The continuous motion simulation based on the ROS platform further validate the stability and effectiveness of the algorithm in consecutive execution.