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TECHNICAL PAPERS

Autonomous Vehicle-Target Assignment: A Game-Theoretical Formulation

[+] Author and Article Information
Gürdal Arslan

Department of Electrical Engineering, University of Hawaii, Manoa, Honolulu, HI 96822gurdal@hawaii.edu

Jason R. Marden

Department of Mechanical and Aerospace Engineering, University of California, Los Angeles, Los Angeles, CA 90095marden@ucla.edu

Jeff S. Shamma

Department of Mechanical and Aerospace Engineering, University of California, Los Angeles, Los Angeles, CA 90095shamma@ucla.edu

The notion of alignment we adopt here is called factoredness in (10).

This assumption can be relaxed to holding for sufficiently large $k$, as opposed to all $k$.

This theorem also holds in the more general weakly acyclic games, see (33).

We will not deal with the issue of how the autonomous vehicles can randomly choose exactly one vehicle (or multiple vehicles with no common targets) to update its proposal without centralized coordination. In actuality, such asynchronous updating may be easier to implement than implementing the aforementioned negotiation mechanisms that require synchronous updating. One possible implementation of asynchronous updating would be similar to the implementation of well known Aloha protocol in multiaccess communication, where multiple transmitting nodes attempt to access a single communication channel without colliding with each other (34).

If SAP is used as a centralized optimization tool, then the computational burden at each step will be very small because only one entry in $a(k)$ will be updated at each step.

Note that there is no reason to consider a null target $T0$ here.

J. Dyn. Sys., Meas., Control 129(5), 584-596 (Apr 01, 2007) (13 pages) doi:10.1115/1.2766722 History: Received March 31, 2006; Revised April 01, 2007

Abstract

We consider an autonomous vehicle-target assignment problem where a group of vehicles are expected to optimally assign themselves to a set of targets. We introduce a game-theoretical formulation of the problem in which the vehicles are viewed as self-interested decision makers. Thus, we seek the optimization of a global utility function through autonomous vehicles that are capable of making individually rational decisions to optimize their own utility functions. The first important aspect of the problem is to choose the utility functions of the vehicles in such a way that the objectives of the vehicles are localized to each vehicle yet aligned with a global utility function. The second important aspect of the problem is to equip the vehicles with an appropriate negotiation mechanism by which each vehicle pursues the optimization of its own utility function. We present several design procedures and accompanying caveats for vehicle utility design. We present two new negotiation mechanisms, namely, “generalized regret monitoring with fading memory and inertia” and “selective spatial adaptive play,” and provide accompanying proofs of their convergence. Finally, we present simulations that illustrate how vehicle negotiations can consistently lead to near-optimal assignments provided that the utilities of the vehicles are designed appropriately.

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Figures

Figure 1

Illustration of vehicle target assignment

Figure 2

Misaligned vehicle utilities

Figure 3

Misaligned vehicle utilities with no pure Nash equilibrium

Figure 4

Evolution of global utility during typical runs of negotiations

Figure 5

Evolution of global utility during typical runs of negotiations

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