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.

利用有限傅立叶级数表示连续时间运动，并提出一种调整每个机械手关节运动谐波的新规划方法。通过对动能和潜在能量进行求和计算出机械手运动谐波的哈密顿量。使用支持向量机和高斯核函数学习基于碰撞的哈密顿量，实验证明我们的方法具有高可靠性和效率。