8095 Copyright © 1996 IFAC 13th Triennial World Congress, San Francisco, USA 8f-Ol 3 SHORTEST TRAJECTORY CONTROL OF AUTONOMOUS MOBILE ROBOTS USING NONLINEAR OBSERVERS Antonio Moran and Minoru Hayase Tokyo Uni'ueTsity of Ag'f'ic'Ult'u'f'e and Technology Koganei-shi 2-24-16, Tokyo 184, JAPAN Abstract: This paper deals with two problems related to autonomous mobile robots. The first problem is to determine the control strategy so that the robot describes the shortest trajectory linking an arbitrary position inside a working area and a path to be followed. This problem is solved by considering an equivalent minimum- time control problem and the control switching functions for obtaining the shortest trajectory has been determined in a general form. The second problem is the navigation problem and consists in designing a nonlinear observer for' the dynamic estimation of the variables required to implement the shortest-trajectory control. A Luenberger-like observer for MIMO nonlinear systems is proposed and analyzed. Theoretical and experimental analyses show that the observer converges fastly enough so that path tracking be efficiently implemented. Keywords: Autonomous Mobile Robots, Observability, Nonlinear Observers, Nonlinear Control, Optimal Control 1. INTRODUCTION There is a significant interest in autonomous mobile robots which can be defined as vehicles that are capable of intel- ligent motion without requiring neither a guide to follow nor teleoperator control but autonomously plan and con- trol their own motion. All autonomous vehicles must nav- igate within an environrnent and in order to achieve this, autonomous vehicles must be capable of (1) sensing its envi- ronment, (2) interpreting this sensor information to refine the knowledge of its position and the environment struc- ture, and (3) planning a route frolll an initial position to a goal position in the presence of k1l0Wll or perhaps unknown obstacles. This paper analyzes the kinel1latical lllodeling of car-like mobile robots and the design of optimal control strategies to obtain the shortest trajectories for path tracking. Given a path to follow, the shortest trajectories linking the path and arbitrary positions inside the working area are deter- mined considering the present inclination and position of the robot. The problem is solved by formulating an equiva- lent minimum-time nonlinear control problem and the con- trol switching functions which minimize the Hall1iltonia.n function of the minimurn-time problem are determined in it general form. To implement this control strategy (and in general any other control strategy), the present position and inclination of the robot are required to be known (navigation prob- lem). Given the large size of the robot working areas it is not always possible to directly measure the robot coor- dinates and inclination. This paper proposes a dynamica.l navigation method which integrates the robot kinematical Inodel with the signal coming from two optical (or ultra- sonic) sensors placed in two fixed points of the working area. A Luenberger-like MIMO lIonlinear observer is pro- posed to estimate the robot position and inclination using the signals from the optical sensors. An experimental mobile robot was constructed to analyze the feasibility and practical implementation of the proposed minimum-trajectory control strategy as well as the perfor- mance of the non linear observer. It was found that the ob-