Modeling and Path-Following Control for Dubins Dynamics in Complex State Space

A path-following control design in the complex state space for the Dubins vehicle is proposed. The vehicle dynamics are modeled as a bilinear system of two complex ordinary differential equations with a scalar complex control input. The developed control solution represents a feedback linearizing proportional–integral–derivative servomechanism, with real valued control gains applied to complex valued tracking error components. The design is performed within the model reference control framework. It is applied to solving path-following and waypoint routing problems for curves with bounded curvature and vehicles with bounded speeds. The path-following controller regulates the system turn rate and the reference model speed. The vehicle speed dynamics are independently maintained as desired. In that regard, the developed control policy forces the system position to track a virtual target point defined by the reference model. Verifiable sufficient conditions are formulated to enable steering the Dubins vehicle along the designated routes in the presence of unknown bounded environmental disturbances, such as wind and gust. Application examples of the developed path-following control solution to waypoint routing guidance for unmanned aerial platforms are discussed.