The lecture is devoted to the problem of optimal control of mobile wheel robot on a plane surface. The design, the functional and the algorithms for controlling mobile robots are often determined by conditions of applied problems. However, despite different modifications of mobile wheeled robots, each of which has its own advantages, disadvantages and limitations, one can carry out research for generalized models and specify the control algorithms later to the specific model. In view of the restrictions on possible trajectories which are imposed by the design of mobile wheeled robots, one of the most important problems is to form some control ensuring their motion from one point to another taking into account the orientation of the robot on the plane. One of the control methods suitable for solving such a problem is motion along optimal trajectories in the form of Euler elasticae. The control of the mobile robot that implements its motion along Euler elasticae is optimal in sense of minimization of maneuvers or control action. Several practical issues of implementation of the control algorithm for motion along Euler elasticae will be discussed during the lecture. Such a control algorithm can be used as basis for developing algorithms for motion along other different classes of optimal curves, e.g. sub-Riemannian and sub-Finsler geodesics which appear in time-minimization problems for a mobile wheel robot which might tow passive trailers.