Manipulator trajectory planning based on work subspace division

Abstract The manipulator workspace is an essential element in the field of manipulator research and is of great significance for manipulator motion planning. However, little research has been conducted on dividing the manipulator workspace into working subspaces. No precise division method has been proposed; the inverse kinematics of multiple solutions in manipulator trajectory planning may also cause abrupt joint changes, thus affecting the planned trajectory. The article proposes a working subspace division method for all ball‐wrist 6DOF(degree‐of‐freedom) manipulators that satisfy the Piper criterion to address the above problems. The kinematic model of the manipulator is established, and the Jacobi matrix of the manipulator is obtained. The space of joints of the manipulator is divided into unique domains containing only single inverse kinematic solutions by means of singular trajectory lines when the determinant of the Jacobi matrix is zero; The solution from the joint space to the workspace is achieved by a nonlinear mapping, which completes the partitioning of the work subspace, and each work subspace contains only unique inverse kinematic solutions. When trajectory planning is carried out from the independent area of a single workspace to the overlapping area of multiple workspaces, selecting the inverse kinematic solution in a single working subspace can effectively avoid abrupt changes in the joints of the manipulator and trajectory misalignment caused by numerous inverse solution selection problems and make the planned trajectory smooth and consistent with the operational requirements of each scene.