Clothoid-based Lane Change Trajectory Computation for Self-Driving Vehicles

Çankaya University Journal of Science and Engineering Volume 14, No. 2 (2017) 152–179 Clothoid-based Lane Change Trajectory Computation for Self-Driving Vehicles 1 Ardam Haseeb Mohammed Ali Kahya and 2 Klaus Werner Schmidt 1 Department of Electronic and Communication Engineering, Çankaya University, Ankara, Turkey 2 Department of Mechatronics Engineering, Çankaya University, Ankara, Turkey e-mail: , Abstract: The subject of this paper is the efficient computation of lane change trajectories for self-driving vehicles. The paper first identifies that a certain type of clothoid-based bi-elementary paths can be used to represent lane change trajectories for vehicles. It is further highlighted that the curvature of such trajectories must be adjusted to the driving situation in order to obtain feasible lane change trajectories. Accordingly, the paper establishes an analytical relation between the maximum admissible curvature of the lane change trajectory and the velocity profile during a lane change. Using this relation, the paper proposes an efficient Newton iteration for computing the parameters of bi-elementary paths for lane changes. The resulting lane change trajectories are as short as possible, while meeting the constraint on the maximum curvature. Simulation experiments for various driving situations show that the computed bi-elementary paths can be computed efficiently and constitute suitable lane change trajectories. Keywords: Autonomous vehicles, lane changes, clothoid trajectories. 1. Introduction Today, the need for a more efficient and smarter usage of the available transportation infrastructure leads to the emergence of Intelligent Transportation Systems (ITS). ITS deployments aim at increasing the traffic throughput and safety, reducing the total travel time and traffic congestion using novel achievements of communication and control technologies [30, 29, 28, 24]. As an important application of ITS, the development of self-driving vehicles (SDVs) gains increasing interest in the recent years. It is expected that SDVs will be available in the near future [2] and it is predicted by IEEE that SDVs will constitute 75 % of cars by 2040 [1]. The usage of SDVs requires the development of advanced methods for controlling the longitudinal and lateral vehicle behavior. In particular, it is required to design vehicle trajectories for different vehicle maneuvers. Hereby, trajectories are considered suitable if they can be easily computed and applied in real-time vehicle applications, while ensuring driving comfort and safety. The main subject of this paper is the fast computation of trajectories for lane changes of SDVs. To this end, this paper suggests utilizing a certain type of bi-elementary paths for representing ISSN 2564–7954 c 2017 Çankaya University CUJSE 14, No. 2 (2017) 153 lane change trajectories. Bi-elementary paths are based on clothoid curves and are found suitable for lane change computations in the recent literature [11]. As the first contribution, this paper develops an efficient method for computing the parameters of such bi-elementary path based on a Newton iteration. It is proved that the proposed Newton iteration always converges to a unique solution, whereby fast convergence is observed from computational experiments. As the second contribution of this paper, it is argued that the parameters of bi-elementary paths for lane changes have to be chosen carefully depending on the driving situation. To this end, this paper determines an analytical bound on the admissible path curvature depending on the maximum velocity profile of a vehicle during a lane change. Using this bound, this paper proposes a computational procedure for selecting the parameters of bi-elementary paths that are suitable for lane change trajectories. This parameter selection can be efficiently carried out in real-time based on the current vehicle velocity and a bound on the admissible acceleration. Using the proposed procedure, it is possible to uniquely determine the shortest bi-elementary path that fulfills the imposed curvature constraint depending on the driving situation. Simulation experiments with a nonlinear vehicle model show that the proposed method determines suitable lane change trajectories. In the existing literature, the generation of lane change trajectories is mostly studied in the context of model predictive control (MPC) or optimal control. [33] used MPC to formulate constraints for finding a lane change trajectory and suitable input signals while avoiding collisions. A disadvantage of MPC is that trajectories are not known in advance but evolves based on the computed lane change steering maneuver. Optimal control is used in [8, 25, 16, 31]. [8] presents an optimal-control based method for quantifying the maneuverability of actively controlled passenger vehicles during emergency highway-speed situations. Necessary conditions for optimality and optimal control laws are found for different cases including rear steering. [25] provide optimal control-based strategies to explore the dynamic capabilities of a single-track car model with tire models and longitudinal load transfer. That paper explores the system dynamics by using nonlinear optimal control techniques to compute aggressive car trajectories. An optimal path-planning method is proposed for self-driving ground vehicles in case of overtaking a moving obstacle in [16]. The trajectory generation problem faced by a self-driving vehicle in moving traffic is investigated in [31]. A semi-reactive planning strategy that realizes long-term maneuvers and ensures short-term collision avoidance is proposed. Although the cited methods determine feasible Lane change trajectories, their main disadvantage is that the trajectories are computed offline when using optimal control. In particular, the required computation times are not suitable for an evaluation in real-time. The research on the computation of lane change trajectories without using optimization methods is limited. An incremental trajectory planner based on rapidly-exploring random trees and a dynamic vehicle model is proposed in [23]. A lane change model for self-driving vehicles was presented in [6]. In this study the emphasis was made on generating a safe path based 154 A. Haseeb et. al on a piecewise Bezier curve. Moreover, the work in [11] analyzes the suitability lane change trajectories based on bi-elementary paths. Different from the existing work, this paper develops a computational procedure for determining suitable parameters for short lane change trajectories depending on the driving situation in real-time. The remainder of this paper is organized as follows. Section 2 motivates the lane change trajectory computation for self-driving vehicles and formulates the problem studied in this paper. The usage of bi-elementary paths for lane changes and the proposed parameter computation method are discussed in Section 3. In Section 4, the pr (...truncated)