Combination of different trajectory description approaches improves the trajectory synthesis performance: Validation by a coarse-to-fine method

Abstract

In the past decade, trajectory synthesis methods seem to reach a bottleneck. These methods occasionally fail when some complex trajectories and linkage configurations are encountered. One important reason is that each trajectory description approach has its limitations. Is it possible to combine these description approaches to obtain better synthesis precision and versatility of different configurations? In this study, a coarse-to-fine optimal method for trajectory synthesis is proposed to verify the above conjecture. This method incorporates a well-designed multi-objective optimization model based on Fourier series (FS) and a single-objective optimization model based on discrete points (DP). FS and DP are selected because they are able to describe the overall shape and local details of the trajectory well, respectibely. In a synthesis problem of a leg mechanism, the method achieves better synthesis accuracy than others and demonstrates the applicability to both complex trajectories and multiple configurations. This work proves that the combination of different trajectory description methods leads to a better synthesis performance, which we believe provides new ideas for developing more efficient trajectory synthesis methods.