Minimum-time-trajectory planning in cluttered environment via highly accurate discrete-time modeling for wheeled mobile systems

Motion planning for wheeled systems is crucial for enabling efficient automation in applications such as automobiles, wheeled construction machinery, and forklifts. In particular, when operating in cluttered environments, there has been growing interest in methods that utilize sampling-based techniques for coarse path planning, followed by subsequent optimization. However, many such frameworks still violate several constraints under certain conditions or produce low-quality trajectories from the perspective of the total duration or other criteria. Thus, in this study, we propose a novel trajectory-planning algorithm that ensures that the produced trajectories satisfy all constraints, including the vehicle-kinematic and collision avoidance. The proposed algorithm is structured hierarchically: first, it employs the Hybrid A* algorithm to plan a coarse path, and this is subsequently optimized within an optimal control framework. A key aspect of this approach is the use of barrier function-based optimization to ensure constraint satisfaction. To utilize the barrier function, a feasible initial trajectory is essential. To generate a strictly feasible initial trajectory that adheres to the Hybrid A* path, we introduce a new discrete-time model for the general bicycle model. This model aligns with the analytical solutions of continuous-time differential equations when the steering angle is constant and maintains high accuracy even with varying steering angles. We evaluate the effectiveness of our method through a comparison with existing methods, finding that our approach successfully generates trajectories that satisfy all constraints in scenarios where others fail. Additionally, our method achieves a significantly lower jerk cost or reduced total duration compared to existing methods.