The Trajectory Parameter Space (TP-Space): A New Space Representation for Non-Holonomic Mobile Robot Reactive Navigation

The reactive navigation of a non-holonomic mobile robot implies selecting at each instant of time a motion command satisfying two conditions: to avoid collisions and to comply with the robot non-holonomic constraints. Most proposed reactive navigation approaches deal with these requirements simultaneously in an indivisible way. This paper proposes a clear separation of these problems by introducing a representation space where a robot losses its kinematics restrictions and can be dealt as a "free-flying-point." The collision avoidance can therefore be solved by existing holonomic methods, which are able to steer non-holonomic, any-shaped robots when applied in this space, named the trajectory parameter space (TP-space). We also formalize the transformation between this space and the robot physical space introducing the parameterized trajectory generator (PTG), a translation between both spaces by means of a family of parameterized trajectories. This formalization is addressed in a generalized form to allow us deriving any number of different transformations. Unlike previous non-holonomic approaches that use just one single transformation, the proposed method considers a variety of them simultaneously which becomes an obvious improvement to reactive approaches: each one can detect a collision-free path that the others can not. We present some experimental results to show the suitability of our method and its advantages compared with traditional approaches