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The tractor–trailer wheeled robot (TTWR) is a typical modular mobile robot system. It is widely used in industry and agriculture transportation because of its simple structure, heavy load, high efficiency, strong adaptability, and flexibility. Because it is a nonlinear and underactuated system subjected to nonholonomic constraints, the complexity of the system and influence of the inner wheel difference pose great challenges to its trajectory prediction and path planning. To solve this problem, this paper proposes a trajectory prediction algorithm for an unpowered trailer for the TTWR system. In contrast to traditional single-path planning, the algorithm combines the motion characteristics of the Ackermann chassis tractor, analyzes the trailer motion law, and fully considers the lateral deviation of the trailer during the turning process. The algorithm can plan a reasonable cooperative path for the TTWR system. To verify the feasibility and effectiveness of the algorithm, the algorithm is transplanted to the TTWR intelligent experimental platform. A comparison of the simulation and experimental results shows that under the control of the preview tracking algorithm, the maximum error between the actual trajectory of the trailer and the trajectory predicted by the algorithm is generally no more than 9 cm, and the average error is 3.7 cm. This algorithm can provide an effective basis for TTWR system trajectory planning and path tracking. This algorithm is of great significance to TTWRs in warehousing logistics, freight forwarding, and skidding transportation.

According to the existing multi-antenna relay forwarding protocol, the relay matrix can be split into two parts-relay nodes forward and backward filters direct concatenation, then in actual channel matrix design, relay's forward and backward channel conditions are not ideal, which make system bit error rate (BER) performance is poor. Based on this problem, this paper proposes a modular algebraic precoding relay system model based on lattice reduction. At first, this method re-builds the relay's forward and backward channel matrices, which can make the channel satisfy the orthogonality characteristics. Then, a modified equivalent relay channel matrix is precoding, which solves tradition algorithms' poor performance problem when channel orthogonality is not good, and based on this idea, two improved algorithms are proposed. These two new algorithms can achieve better BER performance under poor relay channel conditions, make each user's performance average, and satisfy system fairness requirements. Simulation results show that comparing with tradition algorithms, this paper proposes a relay channel model which is based on the lattice reduction precoding method, it gains a certain bit error performance. Finally, the improved algorithms are compared and analyzed with the sorting-based algorithm. The results show that the proposed algorithms have better performance. Therefore, in order to ensure users fairness, the optimization algorithm can be used instead of the high complexity sorting-based algorithm in the actual system.