  A novel reconfigurable intelligent surface-aided multi-robot network is
proposed, where multiple mobile robots are served by an access point (AP)
through non-orthogonal multiple access (NOMA). The goal is to maximize the
sum-rate of whole trajectories for the multi-robot system by jointly optimizing
trajectories and NOMA decoding orders of robots, phase-shift coefficients of
the RIS, and the power allocation of the AP, subject to predicted initial and
final positions of robots and the quality of service (QoS) of each robot. To
tackle this problem, an integrated machine learning (ML) scheme is proposed,
which combines long short-term memory (LSTM)-autoregressive integrated moving
average (ARIMA) model and dueling double deep Q-network (D$^{3}$QN) algorithm.
For initial and final position prediction for robots, the LSTM-ARIMA is able to
overcome the problem of gradient vanishment of non-stationary and non-linear
sequences of data. For jointly determining the phase shift matrix and robots'
trajectories, D$^{3}$QN is invoked for solving the problem of action value
overestimation. Based on the proposed scheme, each robot holds an optimal
trajectory based on the maximum sum-rate of a whole trajectory, which reveals
that robots pursue long-term benefits for whole trajectory design. Numerical
results demonstrated that: 1) LSTM-ARIMA model provides high accuracy
predicting model; 2) The proposed D$^{3}$QN algorithm can achieve fast average
convergence; and 3) RIS-NOMA networks have superior network performance
compared to RIS-aided orthogonal counterparts.
