This paper presents a contribution to the problem of obtaining an optimal synthesis for shortest paths for a unicycle guided by an on–board limited Field Of–View (FOV) sensor, which must keep a given landmark in sight. Previous works on this subject have provided an optimal synthesis for the case in which the FOV is limited in the horizontal directions (H– FOV, i.e. left and right boundaries). In this paper we study the complementary case in which the FOV is limited only in the vertical direction (V–FOV, i.e. upper and lower boundaries). With respect to the H–FOV case, the vertical limitation is all but a simple extension. Indeed, not only the geometry of extremal arcs is different, but also a more complex structure of the synthesis is revealed by analysis. We will indeed show that there exist initial configurations for which the optimal path does not exist. In such cases, we provide an e–optimal path whose length approximates arbitrarily well any other shorter path. Finally, we provide a partition of the motion plane in regions such that the optimal or e–optimal path from each point in that region is univocally determined.

%B IEEE Transactions on Automatic Control %V 60 %P 1204 - 1218 %G eng %N 5 %M 15059711 %R 10.1109/TAC.2014.2366271 %0 Conference Paper %B IEEE Conference on Decision and Control (CDC2014) %D 2014 %T On Time-Optimal Trajectories for Differential Drive Vehicles with Field-Of-View Constraints %A Cristofaro, A. %A Salaris, P. %A L. Pallottino %A Giannoni, F. %A A. Bicchi %K Embedded Control %K Robotics %XThis paper presents the first step toward the study of minimum time trajectories for a differential drive robot, which is equipped with a fixed and limited Field-Of-View (FOV) camera, towards a desired configuration while keeping a given landmark in sight during maneuvers. While several previous works have provided a complete synthesis of shortest paths in case of both nonholonomic and FOV constraints, to the best of our knowledge, this paper represents the first analysis of minimum time trajectories with the two constraints. After showing the extremals of the problem at hand, i.e. straight lines, rotations on the spot, logarithmic spirals and involute of circles, we provide the optimal control laws that steer the vehicle along the path and the cost in terms of time along each extremal. Moreover, we compare some concatenations of extremals in order to reduce the complexity of the problem toward the definition of a sufficient finite set of optimal maneuvers.

%B IEEE Conference on Decision and Control (CDC2014) %I IEEE %C Los Angeles, USA, December 15-17 %P 2191 - 2197 %@ 978-1-4799-7746-8 %U http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=7039723 %R 10.1109/CDC.2014.7039723