In this paper, path construction and path following methods are proposed. The path construction method addresses the problem to generate a path satisfying boundary conditions which are assigned points and tangent directions at the endpoints of the path. This problem is so-called G1 Hermite interpolation, and it has been widely researched, for example, in the area of computer-aided design. The proposed path construction method utilizes one of them, namely the biarc interpolation, as an initial guess for obtaining an optimal path. Trials in some initial conditions show that the proposed method can generate a smooth path with a low computational cost. Meanwhile, the path following method assumes that a linear bicycle model follows a reference path by using the set-point regulator. The proposed method smooths the curvature profile of the reference path to be suited for the path following. Simulation results show that the proposed path construction and following methods achieve smoother tracking than the case without optimal path and smoothing.
This paper presents the optimal motion planning problem for connected and automated vehicles (CAVs) to cross a conflict area at an intersection with state and control constraints. First, we formulate the scheduled merging (or crossing) time for all CAVs as a mixed integer linear programming (MILP) problem where the merging time is solved frequently. Second, we formulate the optimal motion planning problem so that the CAVs can achieve their scheduled merging time as well as minimizing the energy consumption. Since we solve the motion planning problem analytically, not all the solutions are feasible to comply with the frequently updated merging time. To solve this problem, we propose a feasibility enforcement period (FEP). Then, we validate the proposed solution through simulation, and the results show that even the merging time is frequently updated, the CAVs can still achieve the merging time with a minimal deviation. Besides, our proposed framework also shows a significant improvement in terms of travel time as compared to the conventional one.
This paper describes a procedure to design a path following controller of port-Hamiltonian systems based on a training trajectory dataset. The trajectories are generated by human operations, and the training data consist of several trajectories with variations. Hence, we regard the trajectory as a stochastic process model. Then we design a deterministic controller for path following control from the model. In order to obtain reasonable design parameters for a path following controller from the training data, Bayesian inference is adopted in this paper. By using Bayesian inference, we estimate a probability density function of the desired trajectory. Moreover, not only the mean value of the trajectory but also the covariance matrix is acquired. A potential function for path following control is obtained from the probability density function. By incorporating the covariance information into the control system design, it is possible to create a potential function that takes into account uncertainty at each position on the trajectory, and it is expected to construct a control system that generates appropriate assist force for a human operator.