A reactive motion-planning for collaborative robots using the time-layered C-spaces (TLC-spaces) is proposed in this paper. First, the time-augmented C-space (TAC-space) is introduced. TAC-space is an implementation of the configuration-time space with multiple moving obstacles [Latombe JC. Robot motion planning. Kluwer Academic; 1991. p. 22, 23]. The TAC-space is obtained by stacking the current and predicted future C-spaces along the time axis using predicted motions of the obstacles. Then, TLC-spaces is constructed as the collection of only those C-spaces in the TAC-space that are relevant to the motion planning with moving obstacles. The trajectory that reaches the goal configuration at the specified target time is generated under dynamic constraints including robot velocity and acceleration. We focus on a collaborative robot, PaDY, whose task is to deliver tools and parts to the worker in a factory. Similar to an actual assembly process in an automobile production system, six scenarios are selected for the evaluation of the proposed motion planning method. The simulation results using the real-life motion of workers show that the computation time required for the proposed motion planning using TLC-spaces is shorter than that of our previous method using TACspace. The experimental results show that the proposed method is applicable to PaDY in human environments.