A virtual repulsive potential field algorithm of posture trajectory planning for precision improvement in robotic multi-axis milling

Abstract

Industrial robot's advantages in flexibility and workspace make them used increasingly in multi-axis milling process. However, because of their posture-dependent mechanical and kinematic performance, the quality of the trajectory affects the milling precision directly. Therefore, a virtual repulsive potential field (VRPF) algorithm of posture trajectory planning considering mechanical and kinematic constraints is proposed. In this algorithm, the mechanical and kinematic constraints are transformed into a VRPF, which generates virtual repulsive moment to drive the robot end effector (EE) away from the constraints boundaries. And as the tool center point (TCP) moves along a given tool path, the posture trajectory is planned under the effect of the virtual repulsive moment. Considering the constraints of the joint range, the configuration singularity, the tool orientation, the force-induced error, and the C3 continuity of joint movement, a posture trajectory planning model for general robotic multi-axis milling is established. And a VRPF function that transforms all the constraints into virtual repulsive potential energy is proposed to construct the VRPF. To describe the rotation of robot EE posture in the VRPF, a virtual dynamics model is built. And by solving the model with a proposed numerical algorithm, the robot EE posture trajectory is planned in continuous domain. To improve the quality of the planning posture trajectory, a preliminary setting method of the parameters in the VRPF algorithm is proposed. Compared with the planning algorithms in discrete space, the proposed VRPF algorithm in continuous domain shows advantages in milling quality and computing cost.