Tool orientation and redundancy integrated planning method constrained by stiffness for robotic machining of freeform surfaces

Since industrial robots have redundant degree-of-freedom (DOF), both tool orientation and redundant angle have to be well planned to determine a unique robotic posture. The existing sequential planning method mainly uses the method developed specifically for machine tools to plan tool orientation and then adjusts the redundant angle to improve the robot stiffness, ignoring the differences in stiffness, configuration, etc. between robots and machine tools and the influence of tool orientation on the stiffness. Moreover, due to the kinematics of robot is highly nonlinear, the tool orientation with maximum stiffness cannot guarantee smooth joint motion. To address these problems, this paper proposes an integrated strategy that considers comprehensively robot stiffness and joint motion to plan the tool orientation and redundant angle simultaneously. The stiffness feasible space (SFS) of the robot along the entire tool path is first constructed, which is used as constraint for the subsequent tool orientation and redundant angle planning. Then, a machining error-controllable joint smoothing model is proposed to smooth three joints subjected to the heavy kinematic loads to improve the kinematics performance, and the other three joints are used to maintain the tool at its planned position to control the machining error. To simplify the solving process, an alternate strategy of first generating tool orientation and redundant angle and then checking stiffness constraints is developed, and the iteration solving is repeated until all the generated tool orientations and redundant angles are in their SFSs. Meanwhile, the machining error caused by the smoothing of joint motion is also controlled. Finally, the conducted experiments validate the proposed method.