This paper proposes a spatial-temporal trajectory planning method for multi-robot systems subject to both motion and safety constraints. By decomposing the planning process into three sequential subproblems: path planning, individual time optimisation, and collision coordination, the proposed method not only reduces the complexity of the overall planning task but also facilitates the incorporation of diverse constraints and optimisation objectives. Specifically, the path planning subproblem generates smooth, length-minimised paths while ensuring adherence to static collision avoidance, boundary position and nonholonomic constraints. Building on these optimised paths, the individual time optimisation subproblem aims to minimise trajectory duration while adhering to dynamic constraints. Then, collision coordination subproblem accounts for collision avoidance constraints between moving robots with minimum makespan. The proposed method is applied to warehouse scenarios and the results indicate that it outperforms baseline methods in terms of planning success rate, computational time, as well as overall makespan.