Considered is the problem of the attraction domain estimation in the space “distance to the trajectory – orientation” for the problem of the planar motion control of a wheeled robot. This problem has received much attention in connection with precision farming applications [11]. The mathematical model of the robot takes into account kinematic relationships between velocity of a given target point, orientation of the platform, and control. It is supposed that the four wheels platform moves without slipping. The rear wheels are assumed to be driving while the front wheels are responsible for the rotation of the platform. The control goal is to drive the target point to the desired trajectory and to stabilize its motion. The case of the straight line trajectory is considered in the paper. The control was obtained using the feedback linearization approach [5] and is subject to the two-sided constraints. The system is then rewritten in the so called Lurie form [1,12] and embedded in the class of systems with nonlinearities constrained by the sector condition. Based on this, the method of attraction domain estimation in the state space of the system is proposed. The negativity condition for the derivative of the Lyapunov function with respect to the system’s dynamics under sector conditions is formulated in terms of solvability of the linear matrix inequality (LMI) [2]. To take into account quadratic constraints the S-procedure [12] is applied. The Lyapunov function is supposed to be a quadratic form with addition of an integral over nonlinearity (so called Lurie-Postnikov function). Earlier, other classes of Lyapunov functions were used for this problem, see for example [8]. The optimization problem was formulated as a semidefinite programming (SDP) problem with LMI constraints. Numerical results are presented. The estimates achieved show less conservativeness in comparison with ellipsoidal ones.