Trajectory Optimization for Distributed Manipulation by Shaping a Physical Field

Trajectory optimization is used to solve various planning tasks. In this paper we present a optimization-based method that solves a planning problem for multiple independent objects manipulated by a spatially continuous physical field. The field is generated and controlled (shaped) in real time by an array of actuators. In the paper we first formulate a trajectory optimization problem and a related initialization scheme, and then we demonstrate the proposed method using an experimental platform for distributed magnetic manipulation. The demonstrated task is that of planar reconfiguration of an ensemble of multiple objects, which significantly benefits from the inherent parallelism of the manipulation enabled by the array of actuators shaping the physical field. We show that the system can rearrange up to eight objects simultaneously while avoiding collisions.