Spatiotemporal Optimal Trajectory Planning for Safe Planar Manipulation of a Moving Object

This article explores a specialized problem of safely manipulating a moving object on a surface concerning moving obstacles with an industrial manipulator. To address this challenge, we formulate it as an optimal trajectory optimization problem to yield a safe, smooth, and locally time-optimal trajectory. Specifically, we propose a task-oriented trajectory planning algorithm that enables reaching and controlling a moving target on the surface as quickly as possible without specifying the reaching moment. Then we formally construct a spatiotemporal safe manifold to handle time-varying obstacles on the surface. The initially planned trajectory is projected onto this manifold, generating a safe but nonsmooth and time-consuming result. Finally, we leverage this result as an initial estimate for the optimization problem to efficiently generate a preferable trajectory while keeping the constraints not violated. Simulations and practical experiments in a production environment demonstrate the approaches presented. The results confirm the effectiveness of our algorithms, which offers an efficient solution to the challenge of manipulating a moving object on a surface.