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.
Note to Practitioners
—This work was motivated by how to automatically and effectively acquire the energy-saving trajectory of a robotic system, executing sculptured surface machining. This article suggests a new approach that transforms the original trajectory optimization into a minimal modification of the initial energy-optimal BFC, obtained under velocity constraints. This approach calculates the complex energy formula only once. A CBM, for constraint-based BFC modification, is proposed, to revise the redundant reduction of the feedrate. The proposed modification algorithm significantly decreases the detrimental effect of two coupling problems, on the adjustment of the BFC. Results show that the computational efficiency of the proposed method is significantly superior to the one of the direct optimization method. The performance of the proposed modification algorithm is obviously advanced compared to the existing B-spline evolution algorithm. In blade machining, after optimizing the trajectory using the proposed method and algorithm, both energy and time decrease by more than 45% compared to the conservative feed. The proposed algorithm improves significantly the trajectory compared to the prior art algorithm. Technologists benefit from reduced planning time and improved machining performance. However, incorporation into a CAM or manufacturing system has not yet been realized and remains a significant work to be done in the future.