# Time-optimal paths for a Dubins airplane

@article{Chitsaz2007TimeoptimalPF, title={Time-optimal paths for a Dubins airplane}, author={Hamidreza Chitsaz and Steven M. LaValle}, journal={2007 46th IEEE Conference on Decision and Control}, year={2007}, pages={2379-2384} }

We consider finding a time-optimal trajectory for an airplane from some starting point and orientation to some final point and orientation. Our model extends the Dubins car by L.E. Dubins (1957) to have altitude, which leads to Dubins airplane. We assume that the system has independent bounded control over the altitude velocity as well as the turning rate in the plane. Through the use of the Pontryagin Maximum Principle, we characterize the time-optimal trajectories for the system. They are…

## 231 Citations

Geometric Modeling of Dubins Airplane Movement and its Metric

- Mathematics
- 2010

The time-optimal trajectory for an airplane from some starting point to some final point is studied by many authors. Here, we consider the extension of robot planer motion of Dubins model in three…

Time optimal control in presence of moving obstacles for a Dubins airplane

- Mathematics
- 2019

It is shown that for a Dubins airplane with an initial position, the control variable can be obtained using the exact penalty function method so that the airplane reaches the end position in the shortest time in the presence of obstacles.

Parametrization of nonlinear trajectory for time optimal 2D path planning for Unmanned Aerial Vehicles

- Mathematics2016 2nd International Conference on Control, Automation and Robotics (ICCAR)
- 2016

This paper presents an effective path decision method to find a two-dimension path that is time optimal and obstacle free using parametrization in Complex domain. Such a path is used only for moving…

Cooperative Aerial Tracking and Rendezvous Along Time-Optimal 3-Dimensional Curves

- Computer Science
- 2011

A low computation cost, unconstrained optimization routine is presented that can be used to determine a time-optimal path that will result in the interception of another aircraft.

Rectilinear Path Following in 3D Space

- MathematicsFIRA
- 2010

The numerical method used here for simulation is based on multiple shooting and is found to be comparatively more efficient than other methods for solving such two point boundary value problem.

Time-Optimal Motion of Spatial Dubins Systems

- MathematicsWAFR
- 2018

This paper presents a generic numerical approach to find the kinematic time-optimal trajectories for 3D rigid bodies with a finite set of translation, rotation, and screw controls, in an…

DUBINS VEHICLE TRACKING OF A TARGET WITH UNPREDICTABLE TRAJECTORY

- Mathematics
- 2011

Motivated by a fixed-speed, fixed-altitude Unmanned Aerial Vehicle (UAV), we seek to control the turning rate of a planar Dubins vehicle that tracks an unpredictable target at a nominal standoff…

Optimal path planning for an aerial vehicle in 3D space

- Mathematics49th IEEE Conference on Decision and Control (CDC)
- 2010

This work addresses optimal path planning in three-dimensional space for an aerial vehicle with bounded turn radius by generating an optimal path of minimum length when the initial and final positions and orientations of the vehicle are given.

Optimal Trajectory Planning for Unmanned Aerial Vehicles in Three-Dimensional Space

- Mathematics
- 2014

T HIS paper generates an optimal path from an initial configuration (position, heading, and flight-path angle) to a final configuration in three-dimensional (3-D) space for a turn-rateconstrained…

An exact penalty function method for optimal control of a dubins airplane in the presence of moving obstacles

- MathematicsOptim. Lett.
- 2022

Using an exact penalty function method, the existence of the control variable for a Dubins airplane with given initial and final positions is shown so that the airplane could reach its destination in the shortest time while avoiding fixed and moving obstacles.

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