Harnessing steering singularities in passive path following for robotic walkers

Assistive passive robotic walkers are naturally modelled as rear-driven bicycle with control on the front steering wheels. Standard path following algorithms used for unicycle-like robots can then be readily available, e.g. using backstepping techniques, to control the walker on desired paths. However, such an approach is usually singular in the very common situation of zero velocity, e.g. whenever the vehicle starts its motion or the user stops for any reason. The paper proposes a non-singular passive path following algorithm for an assistive robotic walker equipped with front steering wheels. The control law avoids the singularities, since it is velocity-independent, and allows the designer to specify saturation limits on the steering angles. The converging properties of the non-singular velocity-independent controller in the presence of saturation constraints are firstly formally proved and tested in simulations. Then extensive experiments performed on 14 testers are presented. These tests underline the promising performance of the proposed controller and the importance of singularities-avoidance in real-world scenarios to increase human comfort along the planned trajectory.