Journal ArticleDOI
Time optimal Zermelo's navigation problem with moving and fixed obstacles
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This paper considers a time optimal Zermelo's navigation problem (ZNP) with moving and fixed obstacles that can be formulated as an optimal control problem with continuous inequality constraints and terminal state constraints using the control parametrization technique together with the time scaling transform.Citations
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Visual MISER: An efficient user-friendly visual program for solving optimal control problems
TL;DR: The basic concepts underlying the MISER software, which include the control parameterization technique, a time scaling transform, a constraint transcription technique, and the co-state approach for gradient calculation, are described in this paper.
Journal ArticleDOI
On the Suicidal Pedestrian Differential Game
TL;DR: It is shown that the case of point-capture reduces to a special version of Zermelo’s Navigation Problem (ZNP) for the pursuer, which can be used to validate the results obtained through the differential game framework, as well as to characterize the time-optimal trajectories.
Journal ArticleDOI
3D Trajectory Optimization for Energy-Efficient UAV Communication: A Control Design Perspective
TL;DR: In this paper , a control-based UAV trajectory optimization problem for UAV aided wireless communication is studied, which takes into account both of the UAV's kinematic equations and the dynamic equations.
Journal ArticleDOI
Numerical solution of a pursuit-evasion differential game involving two spacecraft in low earth orbit
TL;DR: In this paper, the authors considered a zero-sum differential game in which there were two players, a pursuing spacecraft that tried to minimize a payoff and an evading spacecraft that attempted to maximize the same payoff.
Proceedings ArticleDOI
An asymmetric version of the two car pursuit-evasion game
TL;DR: It is shown that the problem reduces to a special version of Zermelo's Navigation Problem (ZNP) for the pursuer, and the well-known ZNP solution can be used to validate the results obtained through the differential game framework as well as to characterize the time-optimal trajectories.
References
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Journal ArticleDOI
A nonsmooth Newton's method for discretized optimal control problems with state and control constraints
Matthias Gerdts,Martin Kunkel +1 more
TL;DR: In this paper, a nonsmooth Newton's method was used for the numerical solution of discretized optimal control problems subject to pure state constraints and mixed control-state constraints.
Proceedings ArticleDOI
Time-optimal synthesis for the Zermelo-Markov-Dubins problem: The constant wind case
TL;DR: In this article, a combination of the Markov-Dubins problem and Zermelo's navigation problem is considered, and the problem of characterizing minimum-time paths with prescribed positions and tangents for a vehicle with Dubins-type kinematics in the presence of uniform winds/currents is considered.
Journal ArticleDOI
Inequality path constraints in optimal control: a finite iteration ε-convergent scheme based on pointwise discretization
TL;DR: In this article, the authors present a new approach to the analysis and implementation of path constraints in optimal control problems (OCPs) by discretizing path constraints on a finite number of points, yielding a set of interior-time point constraints replacing the original path constraints.
Journal ArticleDOI
A class of optimal state-delay control problems
TL;DR: It is shown that this optimal state-delay control problem can be formulated as a nonlinear programming problem in which the cost function is an implicit function of the decision variables and an efficient numerical method for determining thecost function’s gradient is developed.
Journal ArticleDOI
Optimal Path Finding in Direction, Location and Time Dependent Environments.
TL;DR: A dynamic programming model is presented which integrates earlier results for direction‐dependent, time and space homogeneous environment, and consequently, improves its accuracy, efficiency, and run‐time.
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