Constrained directions as a path planning algorithm for mobile robots under slip and actuator limitations

In this paper a dynamic model is proposed for a wheeled mobile robot (WMR) that incorporates a novel slip characterization and is used to study navigation under hard control constraints. Many available dynamic models of WMR assume that either the wheels roll without slipping or has longitudinal slip only. As a result they do not necessarily capture the true dynamics of WMRs. The model proposed in this paper considers a two wheeled differential drive mobile robot moving on a flat surface with possibly non-zero lateral and longitudinal slipping. A novel slip characterizing model is introduced and defining parameters are estimated via a set of experiments. Compared with several existing models in the literature simulation results show that trajectories predicted by the proposed model agree better with experimental data. The introduced dynamics and the corresponding slip model coupled with a novel direction search scheme were then used to ascertain the reachable states under constrained control. The scheme involves a finite dimensional search procedure which eliminates having to deal with two point boundary value problems resulting from classic optimal control formulations. The results of the paper can be easily applied to the design of control schemes for WMRs under realistic surface topography and control input constraints.