Multi-maneuver Vertical Parking Trajectory Planning and Tracking Control in Narrow Environments

Abstract

As parking scenarios become narrower, vehicles often cannot enter the parking lot in one step. This paper presents a multi-maneuver vertical parking trajectory planning and tracking control strategy based on a predefined geometric set method. Firstly, to minimize the space required for parking, a multi-constraint nonlinear programming path function model based on arc-line-arc is established to find the key points of the path for vehicles to enter the parking space while considering the vehicle structure and road boundary constraints comprehensively. Secondly, the double-S speed planner carries out the speed planning. Finally, based on the vehicle–road deviation prediction model, an MPC lateral motion controller with the steering system delay compensation is established. A vehicle speed-tracking controller is designed on the basis of PID control. The proposed parking planning and control strategy is then tested on the autonomous vehicle platform to verify its feasibility and effectiveness. The results demonstrate that the proposed method can solve the problem of multi-maneuver vertical parking trajectory planning and tracking control in narrow environments. Under the action of the lateral and longitudinal controller, the vehicle can be safely and accurately guided to track the parking trajectory into the parking space. The lateral error is controlled within 0.054 m, and the heading deviation is controlled within 0.02 rad.

Appendix: List of symbols

$L_{{\text{w}}}$:

Width ab of the parking space

$L_{{\text{l}}}$:

Length $ad$ of the parking space

$L$:

Length of wheelbase

$L_{{\text{k}}}$:

Width of the vehicle

$L_{{\text{f}}} ,L_{{\text{r}}}$:

Front/Rear overhang

$l_{{\text{f}}} ,l_{{\text{r}}}$:

Distance from the center of gravity (C.G.) to the front/rear axle

$R0$:

Minimum turning radius

$L_{{\text{s}}}$:

Safe distance

$D_{{{\text{road}}}}$:

Road width of the parking space

$D_{{{\text{single}}}} ,D_{{{\text{multi}}}}$:

Road width for single/multi-maneuver parking

$\delta_{{\text{f}}}$:

Front-wheel steering angle

$\delta_{{\text{f ref}}}$:

Reference front-wheel steering angle

$\delta_{\max }$:

Maximum of front-wheel steering angle

$\Delta \delta_{\max }$:

Maximum of front-wheel steering angle increment

$\phi_{\max }$:

Maximum of front-wheel steering angle speed

$\tau$:

Steering system delay time

$v$:

Vehicle velocity at the rear axle

$v_{{\text{d}}} ,v_{{\text{p}}}$:

Target vehicle velocity for travel/parking tracking

$e_{{\text{d}}} ,e_{\psi }$:

Lateral/Heading deviation at the current point

$a_{\max }$:

Maximum of vehicle acceleration

$T_{{\text{s}}}$:

Sample time of lateral motion controller

$N_{{\text{p}}}$:

Prediction horizon of MPC lateral motion controller

$N_{{\text{c}}}$:

Control horizon of MPC lateral motion controller