Optimal Motion Planning using Finite Fourier Series in a Learning-based
  Collision Field
Feng Yichang Wang Jin Lu Guodong
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.