Collision-Free Intersection Crossing of Mobile Robots Using Decentralized Navigation Functions on Predefined Paths Benjamin Fankhauser, Laleh Makarem and Denis Gillet Abstract— This paper deals with the coordination of a group of mobile robots at an intersection. It focusses on decentralized navigation functions (DNFs) to achieve efficient traffic control. The main challenge is to define virtual potentials, which are used by decentralized navigation functions, such that traffic is both fluent and safe, while taking into account real-world limitations like acceleration, braking and speed limits. Our method consists in defining the navigation function with respect to the desired acceleration profile and is accompanied by a set of visibility conditions that increase the capacity of the intersection in terms of vehicle throughput. Priority conditions have been used to both avoid blockades of robots and to save energy by assigning higher priorities to robots with higher inertias. I. I NTRODUCTION Compared with a single robot, multiple mobile robots can introduce additional advantages in terms of flexibility, robustness, efficiency and comfort. Therefore there has been a considerable interest in the field of mobile robot interaction in recent years. Coordination of a group of mobile robots has been mentioned several times in literature due to its increasingly important role in military, commerce and sci- ence. Impressive works in the field of coordination, presented at [1], [2], successfully exploited knowledge from mobile robotics. Accordingly, it could be expected that in the near future autonomous or semi-autonomous driver assistance systems will be available to handle traffic at intersections [3]. This paper addresses the problem of intersection crossing by mobile robots. This problem can be generalized to that of the autonomous crossing of vehicles taking into account complexities of vehicles in dynamics and tasks. Different control approaches for autonomous navigation have been proposed in the literature [4]. One approach is to describe the robots using kinematic models, with the objective of reaching a destination while avoiding collisions with fixed and moving obstacles. In this approach, autonomous navigation is seen as a multi-objective problem for which various solutions have been suggested; such as stochastic optimization [5], cooper- ative methods of control [6], [7], and decentralized control [8]. Among all these methods, decentralized control has so far received more attention as a method that does not need long-range communication and shows more robustness when it comes to various communication failures in the system [9]. The use of navigation functions in the decentralized scheme seems promising, as its implementation is feasible in real- time and as navigation functions also show good flexibility B. Fankhauser, L. Makaraem and D. Gillet are with Real Time Coordination and Distributed Interaction Systems (React) Group, Ecole Polytechnique Federale de Lausanne (EPFL), 1015Lausanne, Switzerland laleh.makarem@epfl.ch, Denis.Gillet@epfl.ch with regard to adding vehicles and a changing environment [10]. In this paper, the focus is on developing a flexible compu- tationally efficient decentralized algorithm for mobile robots at intersections while considering the different inertias of the robots and their priority for passing, as well as their ability to brake and accelerate at the intersections. As such, the robots need the ability to communicate and transfer data about their positions and their inertia. Our proposed navigation function is initially based on the distance of every robot from its goal destination, while the navigation is restricted to a certain path. In a second stage, it is based on the distance between the different robots, their respective speeds and the directions they are heading in. A visibility zone is defined around each vehicle in order to emulate a real detection and communication range. We paid special attention to intersections because they correspond to traffic conditions potentially having a high impact on energy consumption and motion smoothness. In the second section of this paper, a dynamical model of the vehicles is introduced. It is simple enough to enable the handling of complex traffic situations and complex enough to enable energy optimization. In the third section, a decen- tralized navigation function that enables taking dynamical constraints into account is proposed. The evaluation of the proposed approach is presented in section 4. It is compared with a rule-based crossing method and traditional crossing of manned vehicles at an intersection with traffic lights. Finally, concluding remarks and outlook are given in the last section. II. PROBLEM FORMULATION The considered multi-robot system consists of N mobile robots. The goal of each robot is to cross an intersection without having any collision with other robots (Figure 1). The position of robot i is known as q i =(x i ,y i ) in a global frame attached to the intersection. The path of the robot is predefined and could be described by path parameter s i . Hence, the position of a robot in the global frame could be calculated from its location along the path using the parametric function q i = f k (s i ) corresponding to the path k the robot has chosen. The motion of each robot along its path is modeled using second order dynamics: ¨ s i = a i (1) Note that the dynamics proposed for every robot is quite realistic as the assumption of predefined routes is valid. Additionally, we introduce real world limitations like an acceleration limit a max , as well as a braking limit b max .