41,804 research outputs found
Automatic differentiation of non-holonomic fast marching for computing most threatening trajectories under sensors surveillance
We consider a two player game, where a first player has to install a
surveillance system within an admissible region. The second player needs to
enter the the monitored area, visit a target region, and then leave the area,
while minimizing his overall probability of detection. Both players know the
target region, and the second player knows the surveillance installation
details.Optimal trajectories for the second player are computed using a
recently developed variant of the fast marching algorithm, which takes into
account curvature constraints modeling the second player vehicle
maneuverability. The surveillance system optimization leverages a reverse-mode
semi-automatic differentiation procedure, estimating the gradient of the value
function related to the sensor location in time N log N
An Analytic Study of Pursuit Strategies
The Two-on-One pursuit-evasion differential game is revisited where the holonomic players have equal speed, and the two pursuers are endowed with a circular capture range ℓ \u3e 0. Then, the case where the pursuers\u27 capture ranges are unequal, ℓ1 \u3e ℓ2 ≥ 0, is analyzed. In both cases, the state space region where capture is guaranteed is delineated and the optimal feedback strategies are synthesized. Next, pure pursuit is considered whereupon the terminal separation between a pursuer and an equal-speed evader less than the pursuer\u27s capture range ℓ \u3e 0. The case with two pursuers employing pure pursuit is considered, and the conditions for capturability are presented. The pure pursuit strategy is applied to a target-defense scenario and conditions are given that determine if capture of the attacker before he reaches the target is possible. Lastly, three-on-one pursuit-evasion is considered where the three pursuers are initially positioned in a fully symmetric configuration. The evader, situated at the circumcenter of the three pursuers, is slower than the pursuers. We analyze collision course and pure pursuit guidance and provide evidence that conventional strategy for “optimal” evasive maneuver is incorrect
Vehicle Motion Planning Using Stream Functions
Borrowing a concept from hydrodynamic analysis, this paper presents stream functions which satisfy Laplace's equation as a local-minima free method for producing potential-field based navigation functions in two dimensions. These functions generate smoother paths (i.e. more suited to aircraft-like vehicles) than previous methods. A method is developed for constructing analytic stream functions to produce arbitrary vehicle behaviors while avoiding obstacles, and an exact solution for the case of a single uniformly moving obstacle is presented. The effects of introducing multiple obstacles are discussed and current work in this direction is detailed. Experimental results generated on the Cornell RoboFlag testbed are presented and discussed, as well as related work applying these methods to path planning for unmanned air vehicles
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