A hierarchical approach for splitting truck platoons near network discontinuities

Highlights

• A hierarchical decision and control framework for cooperative platoons interacting with merging traffic efficiently.

• A supervisory tactical strategy generates optimal vehicle order after the merge, new equilibrium gaps of cooperative vehicles at the merging point, and anticipation horizon that the platoon starts to act to track the new equilibrium gaps.

• The lower-level operational layer gives the optimal vehicle accelerations so that new equilibrium gaps have been created when merging vehicles start to change lane and the transient maneuvers are efficient, safe and comfortable.

• Robust framework against model parameter uncertainties and system delay.

Abstract

Truck platooning has attracted substantial attention due to its pronounced benefits in saving energy and promising business model in freight transportation. However, one prominent challenge for the successful implementation of truck platooning is the safe and efficient interaction with surrounding traffic, especially at network discontinuities where mandatory lane changes may lead to the decoupling of truck platoons. This contribution puts forward an efficient method for splitting a platoon of vehicles near network merges. A model-based bi-level control strategy is proposed. A supervisory tactical strategy based on a first-order car-following model with bounded acceleration is designed to maximize the flow at merge discontinuities. The decisions taken at this level include optimal vehicle order after the merge, new equilibrium gaps of automated trucks at the merging point, and anticipation horizon that the platoon members start to track the new equilibrium gaps. The lower-level operational layer uses a third-order longitudinal dynamics model to compute the optimal truck accelerations so that new equilibrium gaps are created when merging vehicles start to change lane and the transient maneuvers are efficient, safe and comfortable. The tactical decisions are derived from an analytic car-following model and the operational accelerations are controlled via model predictive control with guaranteed stability. Simulation experiments are provided in order to test the feasibility and demonstrate the performance and robustness of the proposed strategy.

Introduction

Automated driving have attracted considerable attention in the recent years, because of the fundamental changes they bring to transportation systems and new services enabled by them. The literature has shown that individual automation can hardly enhance traffic operations while it is commonly agreed that connected/cooperative automated vehicles (CAVs) possess great potential in increasing roadway capacity and traffic flow stability  (Shladover, 2005, Shladover, Nowakowski, Lu, Ferlis, 2015, Mahmassani, 2016, Roncoli, Papamichail, Papageorgiou, 2016, Wang, 2018). Vehicle platooning is one of multiple applications that stands out in the domain, characterized by a string of CAVs respecting a specified equilibrium spacing policy   (Shladover, Nowakowski, Lu, Ferlis, 2015, Bang, Ahn, 2017, Milanes, Shladover, Spring, Nowakowski, Kawazoe, Nakamura, 2014, Saeednia, Menendez, 2016). The reduction of the equilibrium spacing breaks the capacity limits of today’s network and enhances fuel economy.

Truck platooning is expected to be deployed earlier than passenger cars due to the pronounced benefits in terms of fuel saving (Alam et al., 2010) and promising business models  (Bhoopalam, Agatz, Zuidwijk, 2018, Nowakowski, Thompson, Shladover, Kailas, Lu, 2016). Several on-road pilots have identified problems that truck platooning brings to traffic at freeway entrances and exits  (Nowakowski, Thompson, Shladover, Kailas, Lu, 2016, Tsugawa, Jeschke, Shladover, 2016, Bhoopalam, Agatz, Zuidwijk, 2018), which is of paramount importance to traffic safety and throughput of the road network. Therefore, coordination and control at network discontinuities are important challenges for vehicle platooning in the real world. This was well recognized early in Automated Highway Systems studies in the 1990s (Varaiya, Shladover, 1991, Varaiya, 1993). Often, a hierarchical framework where a platoon coordination layer is placed between the link traffic control layer and the vehicle control layer is adopted. The platoon coordination layer is primarily concerned with platoon-level maneuvers such as platoon formation, split, merge, and exit, which is the focus of this paper.

A few active platooning strategies have been proposed in the literature under within a full CAV environment. A set of protocols for platoon maneuvers on highways was proposed in Hsu et al. (1993), including merge, split, and lane change. The design of the protocol is based on a finite state description of platoon maneuvers under the command of an upper-level traffic control layer. Despite the pioneering role of this work, the design of the split protocol did not address important decisions regarding where/when to split the platoon at highway entrance and optimal trajectories for vehicles. In Godbole et al. (1995), entry and exit platoon maneuvers on highway were discussed. The proposed strategies were applicable in cases where dedicated automated vehicle lanes and transitional lanes are disposed near highway entries and exits. The design was based on the assumption that the merging vehicle is a CAV and it required infrastructure changes, e.g. a parallel transition lane or dedicated ramps, raising concerns over the applicability in reality. In Halle et al. (2004), two basic platoon maneuver strategies, merge and split, were proposed to facilitate a CAV merge into an existing platoon and a platoon member leaving the formation respectively. The split strategy was further elaborated by sub-tasks of initiating split request, creating safe gap and changing lane. A similar design using finite state machine approach was also reported in Amoozadeh et al. (2015) for platoon maneuver protocols. The protocols were combined with cooperative adaptive cruise control (CACC) logic used to represent longitudinal behavior. However, the optimal moment to start the gap creation process and how the transient maneuver looks like were not formulated, leaving the operational strategies and corresponding algorithms for platoon maneuvers unanswered.

Cooperative automated maneuvering protocols were designed for a highway lane drop scenario and an unsignalized T-intersection in (Ploeg et al., 2017). Field tests by 9 teams with CAVs under a real network but restricting normal traffic show the performance of the maneuver protocols. These protocols determine largely the efficiency of the resulting traffic operations. However, this relation is not taken into account explicitly in the design and it does not handle mixed traffic conditions. In Milanes et al. (2011), a decision algorithm that computes a target reference path for each vehicle and a fuzzy longitudinal controller that guarantees the merge for a vehicle approaching from the minor road tracks were proposed, but the design was restricted to autonomous vehicle systems rather than CAVs. In a more recent work (Ntousakis et al., 2016) proposed an optimal vehicle trajectory design for cooperative merging, where gap policies are imposed at the initial and final time of the maneuver according to a specified merging sequence. In this approach, trajectories are first designed via an optimal control problem and then applied to the vehicles, before applying the decision the controller selects the most restrictive acceleration. A different vehicle string modeling approach was presented in Bang and Ahn (2017), where a spring-mass-damper analogy was adopted to describe platooning dynamics. This modeling approach allows one to model platoon dynamics near highway entry and exit by controlling the spring constant and damping coefficient, where a CAV joins or leaves a platoon, but does not generate optimal merging decisions and trajectories. More recently, the cooperative merging problem was treated in   Rios-Torres and Malikopoulos (2017b), in this case the optimal control problem aims to optimize the fuel efficiency of the system as CAVs approach the merging zone. Finally, Jin et al. (2018) formulates a stochastic switched system model in which is analyzed how platoon-induced congestion varies with the fraction of platooned vehicles at merge, yet the decisions on when and where to split the platoon is not addressed.

Notice that another body of literature focused on platoon formation strategies (Halle, Laumonier, Chaib-Draa, 2004, Saeednia, Menendez, 2016, Tuchner, Haddad, 2017), for a more general review on coordinated control on vehicles at intersections we invite the reader to explore (Rios-Torres and Malikopoulos, 2017a). We restrict the discussion on platoon formation since this paper concentrates on how to split a platoon rather than forming a platoon. Literature shows that quite some effort in defining platoon maneuver protocols at highway entry and exit. These studies focus on dynamics and interactions between platoons or between a platoon and an individual CAV, which implies communication between interacting platoons/vehicles. Some even require additional changes in the infrastructure, which may impede the near-term application of the strategies. In addition, there is a gap between finite state description of the platoon maneuvers and the detailed operational truck platooning strategies for the transition between states. In case of truck platooning, it is likely that the platoon has to be detached to facilitate merging vehicles from on-ramp sections. A decision-making strategy to support when and where to split the truck platoon before the merge section and the corresponding operational algorithm to execute the longitudinal motion of trucks remains as a scientific challenge. Although an attempt was made in Duret et al. (2018), it assumes a single merging vehicle and the question of how to control the continuous trajectories of interacting vehicles remains unanswered.

This contribution proposes a hierarchical decision and control framework for automated truck platoons to facilitate lane-changing maneuvers of surrounding vehicles near on-ramps and off-ramps. The tactical layer uses a first-order traffic flow model to generate decisions about when and where to yield a safe and comfortable gap that maximizes throughput. The operational layer uses a third-order longitudinal dynamics model to control truck accelerations such the gap has been created when the merging vehicle starts the lane change and the transient maneuvers are efficient, safe and comfortable. The tactical layer considers limited acceleration and deceleration capabilities and the operational layer takes into account safety constraints in addition to admissible acceleration and speed with guaranteed stability under receding horizon optimal control approach. We remark that although the contribution is motivated by truck platooning, the proposed design is generic and is applicable in all CAV platoons.

The remainder of the paper is organized as follows. Section 2 presents the general hierarchical decision and control framework. Sections 3 and 4 present the mathematical formulations of tactical and operational levels, respectively. Section 5 illustrates the performance of the proposed control framework under various connectivity assumptions and network configurations. Finally, Section 6 concludes the paper.