Nonlinear MPC on Parallel Parking for Autonomous Vehicles Under State-Dependent Switching

In this paper, a framework integrating planning and control is designed to deal with the parallel parking problem of autonomous vehicle. In the planning section, efficient planning is achieved by directly setting target points. In the control part, it is mainly based on nonlinear model predictive control (NMPC) scheme for implementation. Firstly, the parking task is divided into four stages by setting different target points to solve the non-convex state constraint problem in parallel parking. Then, a state-dependent switching law is designed to describe the switching process in different stages based on the different constraints present. In addition, the terminal constraints and terminal cost functions of NMPC scheme are removed to increase the solvability of optimization problems and improve the smoothness of parallel parking for autonomous vehicle. Asymptotic stability and recursive feasibility of autonomous vehicle are ensured. The experimental results show that the NMPC scheme is effective in parallel parking of autonomous vehicle. Note to Practitioners—The motivation of this paper is to solve the problem of parallel parking for autonomous vehicles, with a focus on the design of planning and control framework. In recent years, automatic parallel parking technology has received widespread attention. However, there are still two issues that need further consideration: 1. Most existing planning and control schemes rely on nonlinear optimization processes, but multi-layer nonlinear optimization processes inevitably affect the efficiency and real-time performance of automatic parallel parking schemes. 2. The special construction of parallel parking lots makes it difficult to solve nonlinear optimization problems because the constraint domain is non-convex. To overcome these issues, we first divide the parallel parking process into several stages and directly plan the target points for each stage based on the characteristics of the parallel parking lots, rather than planning the complete parallel parking path. Then, with the help of the prediction and rolling optimization characteristics of the NMPC scheme, the optimal approach to each target point is achieved. In addition, the classic NMPC scheme has been improved (by removing terminal constraints and terminal cost functions) to further enhance its solvability and real-time performance. It is worth noting that the framework of this paper is applicable to most automatic parallel parking needs, as the characteristics of standard parallel parking slots (including size, exit and entrance requirements, safety distance requirements, etc.) are consistent with the planning requirements of the target points in this paper. Moreover, most vehicle models are known, which enables the NMPC scheme in this paper to adapt to different types of autonomous vehicles. In future work, we will further explore the possibility of extending our algorithm to more complex and chaotic environments (including but not limited to the presence of obstacles and external interference) for automatic parking systems.