Abstract—In this work, the design, analysis, and implementation of an algorithm for automatic parallel parking for a nonholonomic mobile robot is presented. The mobile robot is a four-wheeled scaled vehicle and it is assumed that there is space limitation for the parking maneuver. The main objective was to design a parallel parking path trajectory avoiding collisions. We designed a fuzzy PD+I controller for driving the error generated between the real position and the previously generated objective position to the origin. We presented simulations results to validate the analysis and demonstrating how the fuzzy controller solved the tracking problem for the derived path trajectory to follow. Index Terms—Automatic parking, fuzzy-PID control, mobile robots, nonholonomic system I. INTRODUCTION I n recent years, many car manufacturers have implemented an intelligent driver assistance system to its vehicles. These systems consist of an array of sensors to get information of the environment supporting the driver in different tasks. Some of these applications are lane keeping, blind spot detection, proximity indicators, driver drowsiness detectors, and assisted parallel parking systems, among others [1-4]. With the increase of vehicles in big cities and urban development, the availability of parking spaces is becoming a day to day issue, and parallel parking in confined areas can be a difficult task [5]. When trying to perform parking maneuvers, drivers can cause accidental damage to their cars such as scratches or slight dents to the vehicle. In the last decade, much interest has been put by researchers and car companies to develop assisted or automatic parking systems. The system aims to improve the Manuscript received May 6, 2018; revised August 26, 2018. E. Ballinas is with Centro de Investigación y Desarrollo de Tecnología Digital (CITEDI) del Instituto Politécnico Nacional (IPN), Ave. Instituto Politécnico Nacional No. 1310 Colonia Nueva Tijuana, Tijuana Baja California, México (e-mail: lballinas@ citedi.mx). O. Montiel is with Centro de Investigación y Desarrollo de Tecnología Digital (CITEDI) del Instituto Politécnico Nacional (IPN), Ave. Instituto Politécnico Nacional No. 1310 Colonia Nueva Tijuana, Tijuana Baja California, México. Corresponding author phone: +52(664)6231344; fax: +52(664)6231344; (e-mail: oross@ipn.mx). O. Castillo is with Tijuana Institute of Technology, Calzada Tecnológico s/n, Fracc. Tomas Aquino, CP 22379, Tijuana, México (email: ocastillo@tectijuana.mx). Y. Rubio is with Centro de Investigación y Desarrollo de Tecnología Digital (CITEDI) del Instituto Politécnico Nacional (IPN), Ave. Instituto Politécnico Nacional No. 1310 Colonia Nueva Tijuana, Tijuana Baja California, México (e-mail: rrubio@citedi.mx). L. Aguilar is with Centro de Investigación y Desarrollo de Tecnología Digital (CITEDI) del Instituto Politécnico Nacional (IPN), Ave. Instituto Politécnico Nacional No. 1310 Colonia Nueva Tijuana, Tijuana Baja California, México (email: laguilarb@ipn.mx) security and comfort of inexperienced and disable drivers, in this challenging operation [6,7]. Assisted parking systems facilitate the parking operation for the driver, the level of assistance varies, and commonly the driver has some control of the procedure. Some companies have introduced parallel parking assistance in their vehicles. For example, Toyota Motor Company launched the Toyota Prius in the early 2000’s while Lexus, with their model LS, also includes an option of parking assistance, and Renault is researching Autonomous Valet Parking [7,8]. Motivation: The fact is that parallel parking of autonomous cars is a challenging task that has allowed neither the complete welcome nor the confidence of such vehicles in the worldwide market. Most advanced systems are automatic parallel parking systems, where there is no need for driver input. Such algorithm consists in, once a free space is validated, the parking routine is performed by controlling the steering angle of the vehicle and following a collision-free trajectory from the origin point to a desired point in the parking spot. There exist two main approaches reported in the literature for automatic parking. The first one is based on the stabilization of the vehicle to a target point, where the vehicle travels without a planned path and the objective is to reduce the distance between the reference point of the vehicle and the goal. The second approach consists of performing a path planning that takes the vehicle from an initial point to the target point and then follows the path [9]. Existing path planning strategies for automatic parking in vehicles have three main steps. First, the vehicle sensors check for available space for parking. After that, a collision- free path is calculated. In the last step, a control strategy to follow the calculated path and to evade any unexpected obstacle is used. The existence of unexpected obstacles can lead to a path recalculation [1,9,10]. There have been reported different approaches for planning the collision-free path used by the parking maneuver, being the geometric approach the most common one [9-11]. This methodology is based on human driver’s heuristics when parking: first the drivers turn all the steering wheel to maximum angle in the same direction as the parking space; at a middle point, the driver steers the maximum angle in the opposite direction till the vehicle is parallel to the parking spot. Hence, the whole a path consists of two identical curvatures that connect in the middle point. The geometrical approach works when the length of the parking space is big enough. Under constrained parking spaces, modifications to the trajectory is needed. The identical curvatures remain the same, but in a third step, the steering wheel moves slightly to the opposite side and then moves forward until the vehicle is in the middle of the parallel spot or at a safe distance of the car front of us. Automatic Parallel Parking Algorithm for a Car- like Robot using Fuzzy PD+I Control Enrique Ballinas, Oscar Montiel, Oscar Castillo, Yoshio Rubio, Luis T. Aguilar Engineering Letters, 26:4, EL_26_4_07 (Advance online publication: 7 November 2018) ______________________________________________________________________________________