Spatial adaption of robot trajectories based on laplacian trajectory editing

Abstract

Assuming that a robot trajectory is given from a high-level planning or learning mechanism, it needs to be adapted to react to dynamic environment changes. In this article we propose a novel approach to deform trajectories while keeping their local shape similar, which is based on the discrete Laplace---Beltrami operator. The approach can be readily extended and covers multiple deformation techniques including fixed waypoints that must be passed, positional constraints for collision avoidance or a cooperative manipulation scheme for the coordination of multiple robots. Due to its low computational complexity it allows for real-time trajectory deformation both on local and global scale and online adaptation to changed environmental constraints. Simulations illustrate the straightforward combination of the proposed approach with other established trajectory-related methods like artificial potential fields or prioritized inverse kinematics. Experiments with the HRP-4 humanoid successfully demonstrate the applicability in complex daily-life tasks.