Summary: The trajectory planning problem (TPP) has become increasingly crucial in the research of next-generation transportation systems, but it presents challenges due to the non-linearity of its constraints. One specific case within TPP, namely the Eco-trajectory Planning Problem (EPP), poses even greater computational difficulties due to its nonlinear, high-order, and non-convex objective function. This paper proposes a translatable explicit predictive model control (teMPC) framework to address the eco-trajectory planning problem in scenarios without lane-changing behavior. The teMPC framework consists of an offline module and an online module. In the offline module, an optimal eco-trajectory batch is constructed by solving a sequence of simplified optimization problems to minimize fuel consumption, considering various initial and terminal system states. Each candidate trajectory in the batch yields the lowest fuel consumption subject to a specific travel time from the vehicle entry to the departure from the intersection. In the online module, two dynamic trajectory planning algorithms are provided. Both algorithms greatly improve the computational efficiency of planning and only suffer from a limited extent of optimality losses through a batch-based selection process because optimization and calculation are pre-computed in the offline module. The latter algorithm can also handle possible emergencies and prediction errors. Theoretical analysis and numerical tests are presented and discussed to evaluate the computational quality and efficiency of the teMPC framework under a mixed-traffic flow environment that incorporates human-driving vehicles (HDV) and connected and automated vehicles (CAV) with different market penetration rates (MPR)