Discrete-time dynamic modeling and calibration of differential-drive mobile robots with friction

Abstract

Fast and high-fidelity dynamic model is very useful for planning, control, and estimation. Here, we present a fixed-time-step, discrete-time dynamic model of differential-drive vehicle with friction for reliable velocity prediction, which is fast, stable, and easy to calibrate. Unlike existing methods which are predominantly formulated in the continuous-time domain (very often ignoring dry friction) that require numerical solver for digital implementation, our model is formulated directly in a fixed-time-step discrete-time setting, which greatly simplifies the implementation and minimizes computational cost. We also explicitly take into account friction, using the stable formulation developed by Kikuuwe [1]. Friction model, while non-trivial to implement, is necessary for predicting wheel locks and velocity steady-states which occur in real physical systems. In this paper, we present our dynamic model and evaluate it on a physical platform, a commercially-available electric powered wheelchair. We show that our model, which can run over 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">5</sup> times faster than real-time on a typical laptop, can accurately predict linear and angular velocities without drift. The calibration of our model requires only a time-series of wheel speed measurements (via encoders) and command inputs, making it readily deployable to physical mobile robots.