In this paper, an adaptive control for non-holonomic mobile robots is investigated, in which Legendre polynomials are used to estimate model uncertainties and disturbances. A dynamic model of mobile robots with permanent magnet DC motors as actuators is presented. The controller generates a voltage signal to be applied to the DC motors. The proposed controller using Legendre polynomials introduces a model-free technique. Legendre polynomials maintain tracking accuracy and result in fewer tuning parameters in comparison with neural networks to estimate disturbances. Moreover, the controller gains and the learning rate of the adaptation rules of Legendre coefficients have been defined using exponential functions that considerably reduce the initial value of motor voltages as control signals. Also, the stability analysis of the proposed controller is presented in the presence of time-varying gains. Simulation results confirm the superiority of the proposed controller compared to the radial basis function neural networks.
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