A cooperative conflict resolution technique for traffic intersections Gabriel Rodrigues de Campos, Paolo Falcone and Jonas Sj¨oberg * * Department of Signals and Systems, Chalmers, Sweden. Email: gabriel.campos,paolo.falcone,jonas.sjoberg@chalmers.se Abstract: Conflict resolution at traffic intersections is an important challenge for autonomous driving. In order to reduce reliance on infrastructure, scalable distributed approaches are needed. We propose such a solution based on a pre-defined decision order. Considering this order, vehicles sequentially solve local optimization problems using state constraints to enforce collision avoidance. In this abstract, we present a novel problem formulation and discuss the main related concepts. 1. INTRODUCTION Cooperative driving technology has attracted increasing atten- tion in the last few years in order to address some of the chal- lenges raised by today’s road transportation systems. This arti- cle focus on cooperative behaviors for autonomous cars at road intersections, see Kowshik et al. [2011], Hafner et al. [2013], Kim [2013]. The objective is to provide to each agent/vehicle mechanisms enabling distributed cooperative decision making leading to a solution that is guaranteed to be collision-free. We propose a decentralized solution to the intersection con- flict resolution problem, suitable for fully autonomous vehicles (contrary to Hafner et al. [2013], which focus on intervention). Our solution relies on a pre-determined decision order (enabling sequential decision making) combined with model predictive control for the computation of optimal collision-free trajectories (contrary to Colombo and Del Vecchio [2012], which focuses on feasible crossings sequences and not optimality). 2. PROBLEM STATEMENT We consider N> 1 autonomous vehicles (termed agents in the remainder of the paper) approaching a traffic intersection as shown in Fig. 1. For each agent i, we assume that: • the initial and final destinations of all vehicles are known and the path leading each vehicle to its destination is assigned by its driving task, also known; • the vehicles perfectly follow their paths; • the control variable is the acceleration of each car along the predefined trajectory; • at the initial instant, all agents are before the intersection. Let xi =[pi vi ] T ∈ Xi = Pi × Vi denote the state of each vehicle i ∈N = {1,...,N }, where pi ∈ Pi , vi ∈ Vi in which Pi and Vi represent the sets of all admissible (scalar) longitudinal positions and velocities along the path, respectively. Each agent is modeled as a discrete time double integrator: xi (t + 1) = Axi (t)+ Bui (t), (1) where A =  11 01  , B =  0 1  . L1 H1 L2 H2 H3 L3 p1 p2 p3 Fig. 1. Illustration of the considered traffic intersection scenario. Several autonomous vehicles approach an intersection defined by a range of positions over pre- defined paths. As a part of the assigned driving task, each agent i has a given reference (i.e., desired) velocity denoted by v di ∈ Vi . Moreover, each vehicle is assumed to be subject to: u min i ≤ ui (t) ≤ u max i , ∀t ≥ 0, (2) 0 <v min i ≤ vi (t) ≤ v max i , ∀t ≥ 0, (3) which yields Ui = { ui | ui ∈ [u min i ,u max i ] }. Note that v min i and v max i are constants defining the allowed velocity range (set by the user or constrained by e.g., the traffic rules). We also assume that a full measurement of the state xi (t) is available at each time. Throughout the rest of the article, t is considered to be the current time and (·)(t) the value of (·) at time t. Furthermore, we will also consider for the clearness of the notation that (·)(t + k) denotes the predicted value of variable (·) at time t + k, computed at time t. Let us now introduce two important concepts. For each agent i ∈N , let Cri denote the critical set , i.e., the set of all positions along the path for which a collision is possible and defined as Cri  { xi ∈ Xi | pi ∈ [Li ,Hi ] } , (4) where Li <Hi are bounds on the position along the path of vehicle i defining the intersection. Furthermore, let the occupancy interval of the intersection for a given predicted control sequence can be expressed as: Γi,t (ui (t),ui (t + 1),...)= {k| xi (k) ∈ Cri }, (5)