Trajectory planning based on time-varying convex liftings of dynamic environments

This paper presents a novel and integrated framework for motion planning and control in time-varying environments. The proposed method combines a time-parameterized convex-lifting-based path planning approach—including state space partitioning, graph generation, pathfinding, and safe corridor generation—with a spatiotemporal formulation to guide motion planning. To ensure dynamic feasibility, the framework is extended with a Model Predictive Control (MPC) scheme that computes safe trajectories within the identified corridors. A replanning strategy is introduced to adapt to the unpredictable behaviors of surrounding vehicles and maintain the feasibility of trajectories. Simulation results in an overtaking scenario demonstrate the effectiveness of the approach, with the ego vehicle successfully performing trajectory tracking and replanning while satisfying dynamic constraints.