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I have seen that it is possible to use MoveIt! for path planning and obstacle avoidance for quadcopters/quadrotors.

For example:

Is MoveIt! as suitable for path planning and obstacle avoidance for fixed-wings aircraft as it is for quadrotors?

The main difference I can think of is that quadrotors can stop at will, while fixed-wing aircraft have to continue moving to stay in the air. Will this be a problem for path-planning and obstacle avoidance in MoveIt?

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Not really MoveIt! is designed for robotic arms, and is being heavily adapted for the applications you see here, fixed wing aircraft typically use very diffrent types of motion planning becouse of the fact that they must maintain some forward velocity that is related to its bank angle. Aircraft motion planning typically also contains maxium g force constraints as well.

When picking a motion planning algorithm you need to pick what you want to optimize, typically Speed or Energy. Depending on your environment you might find the excellent thesis Path Planning for Fixed-Wing Unmanned Aerial Vehicles to be helpful, using a sampling based path planning from OMPL.

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