This paper utilizes finite Fourier series to represent a time-continuous motion and proposes a novel planning method that adjusts the motion harmonics of each manipulator joint. Primarily, we sum the potential energy for collision detection and the kinetic energy up to calculate the Hamiltonian of the manipulator motion harmonics. Though the adaptive interior-point method is designed to modify the harmonics in its finite frequency domain, we still encounter the local minima due to the non-convexity of the collision field. In this way, we learn the collision field through a support vector machine with a Gaussian kernel, which is highly convex. The learning-based collision field is applied for Hamiltonian, and the experiment results show our method's high reliability and efficiency.

翻译：本文利用有限傅里叶级数表示时间连续运动，并提出一种通过调整机械臂各关节运动谐波分量的新型规划方法。首先，我们汇总碰撞检测的势能与动能，计算机械臂运动谐波分量的哈密顿量。尽管设计了自适应内点法来修正有限频率域内的谐波分量，但由于碰撞场的非凸性，局部极小值问题仍然存在。为此，我们通过带有高斯核的支持向量机学习碰撞场，使其高度凸化。将基于学习的碰撞场应用于哈密顿量计算，实验结果表明该方法具有高可靠性和高效性。