  Humans often learn new skills by imitating the experts and gradually
developing their proficiency. In this work, we introduce Stochastic Trajectory
Optimization for Demonstration Imitation (STODI), a trajectory optimization
framework for robots to imitate the shape of demonstration trajectories with
improved dynamic performance. Consistent with the human learning process,
demonstration imitation serves as an initial step, while trajectory
optimization aims to enhance robot motion performance. By generating random
noise and constructing proper cost functions, the STODI effectively explores
and exploits generated noisy trajectories while preserving the demonstration
shape characteristics. We employ three metrics to measure the similarity of
trajectories in both the time and frequency domains to help with demonstration
imitation. Theoretical analysis reveals relationships among these metrics,
emphasizing the benefits of frequency-domain analysis for specific tasks.
Experiments on a 7-DOF robotic arm in the PyBullet simulator validate the
efficacy of the STODI framework, showcasing the improved optimization
performance and stability compared to previous methods.
