Trajectory planning for a tractor-trailer vehicle is challenging because the vehicle kinematics consists of underactuated and nonholonomic constraints that are highly coupled. Prevalent sampling-based or search-based planners suitable for rigid-body vehicles are not capable of handling the tractor-trailer vehicle cases. This work aims to deal with generic n-trailer cases in the tiny environments. To this end, an optimal control problem is formulated, which is beneficial in being accurate, straightforward, and unified. An adaptively homotopic warm-starting approach is proposed to facilitate the numerical solution process of the formulated optimal control problem. Compared with the existing sequential warm starting strategies, our proposal can adaptively define the subproblems with the purpose of making the gaps between adjacent subproblems “pleasant” for the solver. Unification and efficiency of the proposed adaptively homotopic warm-starting approach have been investigated in several extremely tiny scenarios. Our planner finds solutions that other existing planners cannot. Online planning opportunities are briefly discussed as well.

In this paper, we propose a cooperative motion planning method for a group of connected and automated vehicles (CAVs) crossing a lane-free intersection without using explicit traffic signaling. This multi-vehicle motion planning task is formulated as a centralized optimal control problem. However, the solution to this optimal control problem is numerically intractable due to the high dimensionality of the collision-avoidance constraints and the nonlinearity of the vehicle kinematics. A two-stage strategy is proposed for generating online solutions: at Stage 1, the CAVs are requested to reach a standard formation before entering the intersection; at Stage 2, the vehicles cross the intersection. As the motion planning sub-problem at Stage 2 begins with a standard configuration, the optimal solution to this standard sub-problem can be computed offline in advance and applied online directly. On the other hand, the formation reconfiguration sub-problem at Stage 1 is easy to solve online. Through dividing the entire dynamic process into two periods, the difficulties in the original optimal control problem are significantly reduced so that the real-time performance is achieved.

This paper focuses on the scheme of cooperative lane change motion planning of multiple connected and automated vehicles, so as to minimize the time for lane change while penalizing large steering angles subject to hard collision avoidance constraints. Nominally this scheme should be formulated in a centralized way with the constraints of all the vehicles considered simultaneously. In order to facilitate the numerical solving process of this centralized optimization problem, we propose a stepwise computation framework. Starting with a sub-problem with all of the collision avoidance constraints removed, a sequence of sub-problems are defined by adding back the removed collision avoidance constraints gradually until the original problem takes shape in the end. The optimum of one sub-problem is always used as the initial guess when solving the next sub-problem. This iterative process continues until the optimum of the original problem is obtained. In this way, the difficulties in the original centralized problem are divided into multiple parts, and every progress made to address the partial difficulties is “solidified” by the initial guess.