The current research of the global chassis control problem for the full drive-by-wire vehicle focuses on the control allocation(CA) of the four-wheel-distributed traction/braking/steering systems. However, the path following performance and the handling stability of the vehicle can be enhanced a step further by automatically adjusting the vehicle speed to the optimal value. The optimal solution for the combined longitudinal and lateral motion control(MC)problem is given. First, a new variable step-size spatial transformation method is proposed and utilized in the prediction model to derive the dynamics of the vehicle with respect to the road, such that the tracking errors can be explicitly obtained over the prediction horizon at varying speeds. Second, a nonlinear model predictive control(NMPC) algorithm is introduced to handle the nonlinear coupling between any two directions of the vehicular planar motion and computes the sequence of the optimal motion states for following the desired path. Third, a hierarchical control structure is proposed to separate the motion controller into a NMPC based path planner and a terminal sliding mode control(TSMC) based path follower. As revealed through off-line simulations, the hierarchical methodology brings nearly 1700% improvement in computational efficiency without loss of control performance. Finally, the control algorithm is verified through a hardware in-the-loop simulation system. Double-lanechange(DLC) test results show that by using the optimal predictive controller, the root-mean-square(RMS) values of the lateral deviations and the orientation errors can be reduced by 41% and 30%, respectively, comparing to those by the optimal preview acceleration(OPA) driver model with the non-preview speed-tracking method. Additionally,the average vehicle speed is increased by 0.26 km/h with the peak sideslip angle suppressed to 1.9°. This research proposes a novel motion controller, which provides the full drive-by-wire vehicle with better lane-keeping and collision-avoidance capabilities during autonomous driving. The current research of the global chassis control problem for the full drive-by-wire vehicle focusing on the control allocation (CA) of the four-wheel-distributed traction / braking / steering systems. However, the path following performance and the handling stability the optimal solution for the combined longitudinal and lateral motion control (MC) problem is given. First, a new variable step-size spatial transformation method is proposed and utilized in the prediction model to derive the dynamics of the vehicle with respect to the road, such that the tracking errors can be explicitly obtained over the prediction horizon at varying speeds. Second, a nonlinear model predictive control (NMPC) algorithm is introduced to handle the nonlinear coupling between any two directions of the vehicular planar motion and computes the sequence of the optimal motion states for following the desire d path. Third, a hierarchical control structure is proposed to separate the motion controller into a NMPC based path planner and a terminal sliding mode control (TSMC) based path follower. As revealed through off-line simulations, the hierarchical methodology provides nearly 1700% improvement in computational efficiency without loss of control performance. Finally, the control algorithm is verified through a hardware in-the-loop simulation system. Double-lane change (DLC) test results show that by using the optimal predictive controller, the root-mean- square (RMS) values ​​of the lateral deviations and the orientation errors can be reduced by 41% and 30%, respectively, comparing to those by the optimal preview acceleration (OPA) driver model with the non-preview speed-tracking method. Additionally, the average vehicle speed is increased by 0.26 km / h with the peak sideslip angle suppressed to 1.9 °. This research proposes a novel motion controller, which provides a full drive-by-wire vehicle wi th better lane-keeping and collision-avoidance capabilities during autonomous driving.