A novel adaptive pseudospectral method for the optimal control problem of automatic car parking

Abstract

This paper proposes a novel adaptive pseudospectral (NAP) method for solving the time-energy optimal control model to minimize the parking time and the energy output of the vehicle. The time-energy optimal control model is first discretized into a nonlinear programming problem at Gauss collocations by the NAP method. Subsequently, we prove the equivalence between the nonlinear programming problem derived from the NAP method and the time-energy optimal control model problem. Compared to those of the interior point method and the piecewise gauss pseudospectal method, simulation results show that the NAP method has higher computational efficiency and accuracy in solving the time-energy optimal control model problem.

Boost-Phase Trajectory Planning with the Nonregular Reachable Area Constraints

“…There have been a great number of research achievements on using the hp-adaptive pseudospectral method to solve the trajectory planning problem [30][31][32]. The convergence of the Gaussian pseudospectral method has been studied and described in reference [33].…”

Research on Automatic Parking System Strategy

“…After that, the algorithm is judged according to the characteristics of the queue. The main way to adapt to the automatic parking strategy is based on Formula (10). For this process, the weight path of grid map with Manhattan distance is proposed, and a new dynamic transfer equation is designed to complete the calculation operation of the shortest path.…”

“…The first is the path planning-based method [5][6][7][8][9], which plans the geometric reverse path of the vehicle by referring to the environmental information in the parking space and finally makes the planning and sends control commands to the actuator. The other is the method based on the experience of experts or operators [10][11][12][13]. The automatic parking system collects control information from the body information data and determines the vehicles that achieve automatic parking.…”

Time‐optimal L1/L2 norms optimal control for linear time‐invariant systems

“…The time‐optimal control makes the system transfer from the initial state to the target set in the shortest time. For example, the time‐energy optimal control model to minimize the parking time and the energy output of the vehicle 21 was constructed for improving computational efficiency and accuracy. The time optimality and the $$$ {L}^1 $$$‐norm control were considered as the cost function in Reference 22, that is, the time‐optimal $$$ {L}^1 $$$‐optimal control.…”