There are lots of non-equidistant sequences in actual applications due to random sampling, imperfect sensors, event-triggered phenomena, and so on. A new grey prediction method for non-equidistant sequences (r-NGM(1,1)) is proposed based on the basic grey model and the developed fractional-order non-equidistant accumulated generating operation (r-NAGO), and the accumulated order is extended from the positive to the negative. The whole r-NAGO deletes the randomness of original sequences in the form of weighted accumulation and improves the exponential law of accumulated sequences. Furthermore, the Levenberg-Marquardt algorithm is used to optimize the fractional order. The optimal r-NGM(1,1) can enhance the predicting performance of the non-equidistant sequences. Results of three practical cases in engineering applications demonstrate that the proposed r-NGM(1,1) provides the significant predicting performance compared with the traditional grey model.

To enable autonomous vehicles to generate smooth and collision-free trajectories and improve their driving performance on structured roads, this paper proposes a hierarchical trajectory planning algorithm based on an improved artificial potential field method. To improve the applicability of the algorithm to complex scenarios, the Frenet coordinate system was established to address these limitations. First, the safety distance model is applied to the risk assessment of the improved artificial potential field method. Then, the hierarchical solution is carried out, and the road solvable convex space and the rough path solution are solved by combining the artificial potential field method. On this basis, the potential field term and the smoothing term cost function are established, and the sequential quadratic programming (SQP) algorithm is used to solve the exact path that meets the requirements of safety and smoothness. Hierarchical planning shortens the solution time by quickly determining the bounds of the convex space. Finally, in the speed planning, in order to take into account the comfort and safety of the occupants, the speed curve is solved by considering the dynamic constraints of the vehicle. The obstacle avoidance effects of the algorithm on static and dynamic obstacles are tested in different simulation scenarios. The results of the simulation experiment show that the proposed algorithm can successfully achieve obstacle avoidance on complex structured roads.