This article presents a control strategy to carry out multiobject manipulation on a novel soft robotic table (SoTa), which is a new form of the planar distributed manipulator. Manipulating multiple delicate objects simultaneously is an attractive feature of SoTa. The challenge here is to coordinate multiple objects in a confined planar space while avoiding interference with each other. The SoTa system adopts a manipulation strategy that includes a planning and a tracking stage for the purpose of sorting objects. The planning stage consists of two phases: 1) discrete path planning to find a path for each object on a grid map with respect to time; 2) trajectory generation to optimize and produce workable trajectories for SoTa. In the discrete path planning phase, a hierarchical searching method based on the time-varying potential field is proposed. Constraints of the SoTa system are modeled and incorporated into the path searching process. In the trajectory generation phase, a piecewise B-spline method is adopted to generate trajectories based on previously found discrete paths. Next, in the tracking stage, the objects are led to their goals along the trajectories ensuring safety and SoTa's capability. The performances of the proposed algorithm were simulated, analyzed, and compared with the conflict-based search method, which is optimal for multiagent path finding. A multiobject manipulation experiment of three objects on a $4\times 4$ grid was conducted on the SoTa. The results demonstrated the effectiveness of the proposed control strategy in executing multiobject manipulations for sorting tasks on the SoTa.