Path planning has always been a hot research topic in various sensor applications of car-like mobile robots (CLMRs). In a known or unknown map information environment, a safe collision-free path of a CLMR from the starting point to the endpoint is planned according to strict indexes such as the shortest time and distance and the lowest energy consumption. To minimize the additional delay caused by the time-delay system in a remote sensing CLMR, a new predictive control algorithm is proposed for use in nonvisual environments. On the basis of the dynamic analysis and remote sensing model of the CLMR, the Smith predictor is used to compensate for the signal delay between the PHANTOM Omni controller and the CLMR, and reduce the positioning error caused by the delay. The grey prediction (GP) model is used to predict the values of the sensors on the CLMR and reduce the remote-control disoperation due to the delay. The feasibility of the GP algorithm is demonstrated by simulation, and a control experiment of force feedback between the PHANTOM Omni controller and a CLMR in a nonvisual environment demonstrated the feasibility of the system. The compensation effect was clearly shown, despite the experiments being performed by remote control with manipulators.