Abstract
The problem of intercepting a target moving along a prescribed trajectory by a Dubins caris stated and formalized as a time-optimal control problem with an arbitrary car velocity directionat the interception. The conditions available in the literature under which the optimal trajectoryis a geodesic line drawn from the initial position of the car to the interception point are refined.Algebraic equations for calculating the optimal interception time are obtained. The optimalcontrol is synthesized based on these equations. A software module is developed for constructingthe optimal car trajectories for various target trajectories.
Highlights
The first papers on finding a line of bounded curvature and minimum length joining two given points are due to A.A
The first problem was stated as the search for a line connecting two points on the plane and having the minimum length and bounded curvature, with the direction of exit of this line fixed at the first point
Let us show that the optimal point of interception of the moving target lies on the boundary B(t) of the reachability set R(t) except for one case
Summary
The first papers on finding a line of bounded curvature and minimum length joining two given points are due to A.A. In contrast to [18], the present paper considers the nongame problem of the time-optimal interception of a moving target by a Dubins car. Sufficient conditions for an arc–straight-line trajectory to be an optimal path were established in [22] These conditions impose constraints on the ratio of the minimum vehicle trajectory curvature radius to the distance between the target and the vehicle at the initial time. Meyer et al [25, 26] identified several assertions related to the problem considered in the present paper They established that if the target trajectory avoids unit disks tangent to the initial velocity vector of the Dubins car, the time-optimal interception occurs along a geodesic line. It was assumed in both papers that the target is sufficiently far from the vehicle at the initial time
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