This paper presents a study of analysis of minimum-time trajectories for a differential drive robot equipped with a fixed and limited field-of-view camera, which must keep a given landmark in view during maneuvers. Previous works have considered the same physical problem and provided a complete analysis/synthesis for the problem of determining the shortest paths. The main difference in the two cost functions (length vs. time) lays on the rotation on the spot. Indeed, this maneuver has zero cost in terms of length and hence leads to a 2D shortest path synthesis. On the other hand, in case of minimum time, the synthesis depends also on the orientations of the vehicle. In other words, the not zero cost of the rotation on the spot maneuvers leads to a 3D minimum-time synthesis. Moreover, the shortest paths have been obtained by exploiting the geometric properties of the extremal arcs, i.e., straight lines, rotations on the spot, logarithmic spirals and involute of circles. Conversely, in terms of time, even if the extremal arcs of the minimum-time control problem are exactly the same, the geometric properties of these arcs change, leading to a completely different analysis and characterization of optimal paths. In this paper, after proving the existence of optimal trajectories and showing the extremal arcs of the problem at hand, we provide the control laws that steer the vehicle along these arcs and the time-cost along each of them. Moreover, this being a crucial step toward numerical implementation, optimal trajectories are proved to be characterized by a finite number of switching points between different extremal arcs, i.e., the concatenations of extremal arcs with infinitely many junction times are shown to violate the optimality conditions.

10aRobotics1 aCristofaro, A1 aSalaris, P.1 aPallottino, L.1 aGiannoni, F.1 aBicchi, A. uhttp://download.springer.com/static/pdf/641/art%253A10.1007%252Fs10957-017-1110-7.pdf?originUrl=http%3A%2F%2Flink.springer.com%2Farticle%2F10.1007%2Fs10957-017-1110-7&token2=exp=1492507070~acl=%2Fstatic%2Fpdf%2F641%2Fart%25253A10.1007%25252Fs10957-017-11101487nas a2200181 4500008004100000245007400041210006900115260001200184300001400196490000700210520093400217653002101151653001301172100001401185700001601199700001901215856007101234 2016 eng d00aControllability analysis of a pair of 3D Dubins vehicles in formation0 aControllability analysis of a pair of 3D Dubins vehicles in form c09/2016 a94 - 1050 v833 aIn this paper we consider the controllability problem for a system consisting of a pair of Dubins vehicles moving in a 3D space (i.e. pair of *3D–Dubins* vehicles) while maintaining constant distance. Necessary and sufficient conditions for the existence of a limited control effort to steer the system between any two configurations are provided. The proposed controllability analysis and the developed motion planning algorithm are a step toward the solution of planning problems for example in case the robots are physically constrained to a payload to be deployed. Moreover, results obtained in this paper are relevant in order to solve formation control problems for multiple robots as aerial or underwater vehicles, which move in 3D spaces. Simulation results highlight the sufficiency of the obtained conditions showing that even from critical configurations an admissible control can be determined.

Most of the neuroscientific results on synergies and their technical implementations in robotic systems, which are widely discussed throughout this book (see e.g. Chaps. 2, 3, 4, 8, 10, 12 and 13), moved from the analysis of hand kinematics in free motion or during the interaction with the external environment. This observation motivates both the need for the development of suitable and manageable models for kinematic recordings, as described in Chap. 14, and the calling for accurate and economic systems or “gloves” able to provide reliable hand pose reconstructions. However, this latter aspect, which represents a challenging point also for many human-machine applications, is hardly achievable in economically and ergonomically viable sensing gloves, which are often imprecise and limited. To overcome these limitations, in this chapter we propose to exploit the bi-directional relationship between neuroscience and robotic/artificial systems, showing how the findings achieved in one field can inspire and be used to advance the state of art in the other one, and vice versa. More specifically, our leading approach is to use the concept of kinematic synergies to optimally estimate the posture of a human hand using non-ideal sensing gloves. Our strategy is to collect and organize synergistic information and to fuse it with insufficient and inaccurate glove measurements in a consistent manner and with no extra costs. Furthermore, we will push forward such an analysis to the dual problem of how to design pose sensing devices, i.e. how and where to place sensors on a glove, to get maximum information about the actual hand posture, especially with a limited number of sensors. We will study the optimal design of gloves of different nature. Conclusions that can be drawn take inspiration from and might inspire further investigations on the biology of human hand receptors. Experimental evaluations of these techniques are reported and discussed.

1 aBianchi, M.1 aSalaris, P.1 aBicchi, A. uhttp://www.centropiaggio.unipi.it/publications/synergy-based-optimal-sensing-techniques-hand-pose-reconstruction.html01827nas a2200193 4500008004100000022001400041245008300055210007100138300001600209490000700225520116900232653002101401653001301422100001601435700001901451700001901470700001501489856012901504 2015 eng d a0018-928600aEpsilon–optimal synthesis for vehicles with vertically bounded Field-Of-View0 aEpsilon–optimal synthesis for vehicles with vertically bounded F a1204 - 12180 v603 aThis 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.

10aEmbedded Control10aRobotics1 aSalaris, P.1 aCristofaro, A.1 aPallottino, L.1 aBicchi, A. uhttp://www.centropiaggio.unipi.it/publications/epsilon%E2%80%93optimal-synthesis-vehicles-vertically-bounded-field-view.html02070nas a2200205 4500008003900000020002200039245009600061210006900157260004300226300001600269520139100285653002101676653001301697100001901710700001601729700001901745700001701764700001501781856006801796 2014 d a978-1-4799-7746-800aOn Time-Optimal Trajectories for Differential Drive Vehicles with Field-Of-View Constraints0 aTimeOptimal Trajectories for Differential Drive Vehicles with Fi aLos Angeles, USA, December 15-17bIEEE a2191 - 21973 aThis 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.

10aEmbedded Control10aRobotics1 aCristofaro, A.1 aSalaris, P.1 aPallottino, L.1 aGiannoni, F.1 aBicchi, A. uhttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=7039723