Sampling-based trajectory imitation in constrained environments using Laplacian-RRT

This paper presents an incremental sampling-based approach for trajectory imitation in cluttered environments using the RRT* algorithm. Inspired by the discrete Laplace-Beltrami operator the underlying distance metric is based upon the difference from a reference trajectory through a quadratic distance term incorporating velocity and acceleration deviations along the trajectory. Mathematically-backed approximations in combination with a task-space bias make it possible to use standard nearest neighbor methods in task space when expanding the RRT*-tree. It is shown that metric-consistent biases considerably increase the convergence speed. The proposed approach is validated in simulations in a 2D environment and in experiments using a HRP-4 humanoid robot.