Variable Step-Size Discrete Dynamic Programming for Vehicle Speed Trajectory Optimization

Predictive energy management has become a new focus of the automobile industry for its high potential of further reducing energy consumption. Based on previous works on predictive speed optimization using discrete dynamic programming (DDP), this paper introduces a novel approach of applying DDP with variable step size in stage variable discretization, which can realize a better tradeoff between precision and computational cost. In this approach, a “meshing” algorithm searches the points of interest (POI), such as speed limit change, traffic lights, and road curvatures, where changes in vehicle speed are expected. The algorithm increases the step-size resolution close to these points and reduces the resolutions in positions further away from POI, where the optimized vehicle speed is insensitive to the step size. With this approach, the position of POI can be precisely located to solve the DDP problem. In a test case with a relatively high density of POI, the computational cost is reduced by more than 53% by only sacrificing less than 1% of precision compared to a fixed step-size discretization with high resolutions. It can be expected that, with a lower density of POI, the computational cost will be reduced even further.