Discrete-Time Transverse Feedback Linearization⋆

Applications of transverse feedback linearization (TFL) vary from path following mobile robots to vehicle formation control. These applications were restricted to systems adequately modelled in continuous-time. Recent work demonstrated that the established technique fails when applied to a discrete-time system using a zero-order hold. An additional change of coordinates dependent on the sampling period that preserves the required properties was proposed as an alternative. This technique, however, only applies to sampled-data systems. This article instead proposes a direct design approach that starts with a discrete-time system and designs a discrete-time transverse feedback linearizing controller. The discrete-time transverse feedback linearization problem is posed, and resolved for a single-input nonlinear discrete-time system. An example of path following for a forward-Euler discretized, kinematic unicycle model is presented to demonstrate its effectiveness.