Energy-Saving Trajectory Planning for Robotic High-Speed Milling of Sculptured Surfaces

In the field of sculptured surfaces machining, the robot trajectory planning, under high-order complex constraints, aiming at minimizing energy or time, is always a challenge. The complexity of curvature characteristics of sculptured surfaces and the nonlinearity of relevant constraints are the main reasons. This article proposes an efficient planning method of minimum-energy robot trajectory, for high-speed machining of sculptured surfaces. First, the energy characteristic model of the robot machining system (RMS) is established, to acquire the energy-optimal feedrate, under velocity constraints, to use in the subsequent trajectory planning. Next, a trajectory planning model, with complex constraints, is developed. The proposed method transforms the original trajectory planning into a minimal modification of the initial objective-optimal B-spline feedrate curve (BFC). Furthermore, two main coupling problems, which influence the minimal change of curves, in the direct evolution-based BFC modification, are addressed. Based on the derived solutions, a novel modification algorithm of BFC, with a callback mechanism (CBM), is proposed. Finally, the performance of the proposed method and the specific algorithm is validated by two case studies. Results show that the proposed method can significantly improve the efficiency of robot trajectory planning, aiming at minimum energy, while exhibiting excellent performance.