The object of the study is a mobile robot KUKA youBot. Because of two pairs of mecanum-wheels its platform has full omnidirectional motion capabilities. We consider ideal contact of the wheel rollers and the floor. Under this assumption a complete (kinematics and dynamics) non-holonomic model of the system is developed. The dynamical model of the mecanum-wheeled robot consider mass eccentricity of its platform and linear viscous friction in platform-and-wheel and wheel-and-roller joints. The motion equations are derived using Appel's equations in terms of longitudinal and transversal velocities of the robot platform center, and rotational velocity of the platform. Values of the robot parameters (coefficients in the equations of motion) are not available and have to be determined. Calibration motions, such that all parameters are observable on them and it is possible to decompose identification problem, are designed. The physical robot inputs and outputs are respectively the motor torques and the wheel rotational velocities (for each wheel). Using measurements of them and kinematics and dynamics relations longitudinal, transversal, and rotational velocities of the platform and generalized control forces in the equations of motion are computed. Because of the presence of the unmesaurable accelerations the equations of the robot motion can not be used directly for parameter estimation as a robot estimation model. To avoid the accelerations in the estimation model a filter technique is used. The "inputs" to the estimation model are the filtered versions of longitudinal, transversal, and rotational velocities of the platform. The estimation model "outputs" are filtered generalized control forces. The estimate of the parameters is generated by continuous-time recurrent least squares algorithm (LSM-estimator). Using experimental data measured on series of calibration motions the robot parameters is estimated.