Trajectory planning of a closed five-bow-shaped bar linkage based on finite Fourier series

Abstract

With aim to reduce the energy consumption, a trajectory planning method is presented for a closed five-bow-shaped bar linkage, which can be propelled itself by morphing configuration. The objective herein is to optimize the driving joints trajectories within the global feasible region when the linkage rolls along the ground with a desired acceleration. The driving joint trajectories were represented by finite Fourier series, whose coefficients were solved by genetic algorithm to ensure a minimal energy consumption of the linkage. The impact of the number of terms of finite Fourier series on the energy consumption was also discussed through numerical examples. As a result, the energy consumption based on this strategy had been reduced by 19%, comparing with the constant potential energy strategy. A number of terms between six and eight using to denote the joint trajectories are appropriate, because that a small number of terms is incapable of expressing the joint trajectories accurately, whereas, a large number makes the joints to be subjected to vibration shock. At last, simulation on a virtual model and experiments on a prototype were carried out to verify the effectiveness of the proposed method.