Generation of Range-based Trajectories Using a Unicycle

The paper focuses on the generation of planar trajectories using an autonomous agent modelled as a unicycle. The agent can be controlled using its linear and angular speeds. It is assumed that only range information is available to the agent with respect to a stationary point, known as the target. The latter could be representative of any beacon, a building of interest or a landmark in real world scenarios. Both of the speeds are designed as continuous functions of range with the linear speed constrained to be positive. We present a complete characterisation of agent trajectories in the given framework which shows that the trajectories can remain bounded or become unbounded depending on both the control inputs and the initial conditions. We also present the conditions necessary to generate each kind of the above mentioned trajectories. Finally, numerical simulation have been presented to elucidate the results.