Continued great efforts have been dedicated toward high-quality trajectory generation based on optimization methods; however, most of them do not suitably and effectively consider the situation with moving obstacles; and more particularly, the future position of these moving obstacles in the presence of uncertainty within some possible prescribed prediction horizon. To cater to this rather major shortcoming, this work shows how a variational Bayesian Gaussian mixture model (vBGMM) framework can be employed to predict the future trajectory of moving obstacles; and then with this methodology, a trajectory generation framework is proposed which will efficiently and effectively address trajectory generation in the presence of moving obstacles, and incorporate the presence of uncertainty within a prediction horizon. In this work, the full predictive conditional probability density function (PDF) with mean and covariance is obtained and, thus, a future trajectory with uncertainty is formulated as a collision region represented by a confidence ellipsoid. To avoid the collision region, chance constraints are imposed to restrict the collision probability, and subsequently, a nonlinear model predictive control problem is constructed with these chance constraints. It is shown that the proposed approach is able to predict the future position of the moving obstacles effectively; and, thus, based on the environmental information of the probabilistic prediction, it is also shown that the timing of collision avoidance can be earlier than the method without prediction. The tracking error and distance to obstacles of the trajectory with prediction are smaller compared with the method without prediction.

This paper investigates the cooperative planning and control problem for multiple connected autonomous vehicles (CAVs) in different scenarios. In the existing literature, most of the methods suffer from significant problems in computational efficiency. Furthermore, as the optimization problem is nonlinear and nonconvex, it typically poses great difficulty in determining the optimal solution. To address this issue, this work proposes a novel and completely parallel computation framework by leveraging the alternating direction method of multipliers (ADMM). The nonlinear and nonconvex optimization problem in the autonomous driving problem can be divided into two manageable sub-problems; and the resulting sub-problems can be solved by using effective optimization methods in a parallel framework. Here, the differential dynamic programming (DDP) algorithm is capable of addressing the nonlinearity of the system dynamics rather effectively; and the nonconvex coupling constraints with small dimensions can be resolved by invoking the notion of semi-definite relaxation (SDR), which can also be solved in a very short time. Due to the parallel computation and efficient relaxation of nonconvex constraints, our proposed approach effectively realizes real-time implementation; and thus extra assurance of driving safety is provided. In addition, two transportation scenarios for multiple CAVs are used to illustrate the effectiveness and efficiency of the proposed method.