This paper describes the design and implementation of a fuzzy control system for a car-like autonomous vehicle. The problem addressed is the diagonal parking in a constrained space, a typical problem in motion control of nonholonomic robots. The architecture proposed for the fuzzy controller is a hierarchical scheme which combines seven modules working in series and in parallel. The rules of each module employ the adequate fuzzy operators for its task (making a decision or generating a smoothly varying control output), and they have been obtained from heuristic knowledge and numerical data (with geometric information) depending on the module requirements (some of them are constrained to provide paths of near-minimal lengths). The computer-aided design tools of the environment Xfuzzy 3.0 (developed by some of the authors) have been employed to automate the different design stages: 1) translation of heuristic knowledge into fuzzy rules; 2) extraction of fuzzy rules from numerical data and their tuning to give paths of near-minimal lengths; 3) offline verification of the control system behavior; and 4) its synthesis to be implemented in a true robot and be verified on line. Real experiments with the autonomous vehicle ROMEO 4R (designed and built at the Escuela Superior de Ingenieros, University of Seville, Seville, Spain) demonstrate the efficiency of the described controller and of the methodology followed in its design.