MPC (Model predictive control)-based motion planning and trajectory generation are essential in applications such as unmanned aerial vehicles, robotic manipulators, and rocket control. However, the real-time implementation of such optimization-based planning faces significant challenges arising from non-convex problem structures and inherent limitations of nonlinear programming -- notably the difficulty in guaranteeing solution quality and the unpredictability of computation time. To improve robustness and computational efficiency, this paper introduces a two-layer motion planning algorithm for intelligent ground vehicles based on convex optimization. The proposed algorithm iteratively constructs discrete optimal control subproblems with small, fixed terminal times, referred to as planning cycles. Each planning cycle is further solved within progressively constructed convex sets generated by utilizing customized search algorithms. The entire solution to the original problem is obtained by incrementally composing the solutions of these subproblems. The proposed algorithm demonstrates enhanced reliability and significantly reduced computation time. We support our approach with theoretical analysis under practical assumptions and numerical experiments. Comparative results with standard sequential convex programming (SCP) methods demonstrate the superiority of our method -- include a significant improved computational speed under dynamic environments while maintain a near optimal final time.

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