A novel intelligent reflecting surface (IRS)-aided multi-robot network is proposed, where multiple mobile wheeled robots are served by an access point (AP) through non-orthogonal multiple access (NOMA). The goal is to maximize the sum-rate of all robots by jointly optimizing trajectories and NOMA decoding orders of robots, reflecting coefficients of the IRS, and the power allocation of the AP, subject to the quality of service (QoS) of each robot. To tackle this problem, a dueling double deep Q-network (D^{3}QN) based algorithm is invoked for jointly determining the phase shift matrix and robots' trajectories. Specifically, the trajectories for robots contain a set of local optimal positions, which reveals that robots make the optimal decision at each step. Numerical results demonstrated that the proposed D^{3}QN algorithm outperforms the conventional algorithm, while the performance of IRS-NOMA network is better than the orthogonal multiple access (OMA) network.