Optimal Partitioning for Task Assignment of Spatially Distributed Autonomous Vehicles and Feedback Steering Laws in the Presence of an Uncertain Drift Field
Thursday, November 1, 3:30PM – 5PM
The interest in applications of autonomous vehicles is expected to grow significantly in the near future as new paradigms for their use are constantly being proposed for a diverse spectrum of real world applications. One of the fundamental problems related to the planning of missions for autonomous vehicles is 1) to find ways to efficiently assign tasks among the vehicles, when they operate as members of a team of spatially distributed vehicles, and 2) to provide them with decision making mechanisms that will allow them to cope with unpredictable and/or uncertain environmental factors, which might affect, for example, their motion and their ability to carry out their assigned tasks. In the first part of this talk, I will present a computationally tractable framework for characterizing the baseline solution of a class of target assignment problems involving groups of spatially distributed autonomous vehicles. In particular, I will introduce a generalized Voronoi partition of the operating space of the vehicles, such that every set of this partition constitutes the “area of influence” of a particular vehicle from the team. In this way, a unique correspondence between the group of vehicles and the different non-overlapping subsets of the partition is established. The key feature of the proposed partitioning scheme is that the proximity relations between the vehicles and a target located at an arbitrary point in the operating space are induced by a state-dependent (pseudo-) metric (proximity metric), such as the minimum time and control effort associated with the transition of each vehicle to the target, rather than the more “conventional” distance functions as, for example, the Euclidean distance, which are typically used in the literature. The advantage of using state-dependent proximity metrics has to do with their ability to succinctly capture the essential features of each vehicle’s kinematics and control authority as well as the effects of several environmental factors on the vehicle’s motion (for example, effects of local winds/currents). In the second part of the talk, I will discuss about the problem of steering a single vehicle to its assigned target. It is assumed that the motion of the vehicle, whose kinematics are described by the so-called Dubins vehicle, is affected by the presence of either a deterministic or a stochastic drift field. This steering problem is subsequently formulated as either a deterministic or a stochastic optimal control problem, which deal, in turn, with the minimization of, respectively, the time of arrival and the expected time of arrival of the vehicle to the target. The feedback law that solves the deterministic optimal control problem is derived under the assumption that the prevailing drift field is equal to its mean value, and consequently, the control law does not take into account any information about the statistics of the drift field. On the contrary, the feedback control law that solves the stochastic optimal control problem accounts appropriately for the statistics of the drift field, which are assumed to be known a priori. The analysis and numerical simulations show that, on the one hand, the feedback law that solves the deterministic optimal control problem captures, in many cases, the salient features of the feedback law that solves the stochastic optimal control problem, and thus, providing support for the use of the former in the presence of relatively weak drift fields. On the other hand, the feedback law that anticipates the stochastic variation of the drift field is, in general, more robust and leads to smaller miss target distance.
Biosketch: Dr. Bakolas joined the Department of Aerospace Engineering and Engineering Mechanics at The University of Texas at Austin as an Assistant Professor in fall 2012. Dr. Bakolas received his Ph.D. in Aerospace Engineering from the Georgia Institute of Technology in 2011, where he was a post-doctoral fellow during the spring of 2012. His research interests are in the area of systems and control theory with a particular emphasis on optimal control, differential game theory, and autonomous vehicles.
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