# In path planning, what kind of path is feasible for a nonholonomic robot?

For a car-like nonholonomic robot, What kind of path is feasible?

Is it right that a path is feasible for a car-like robot if it's curvature continuous, and the curvature on any point doesn't exceed the turning limit of the robot?

I'm not quite sure about this because I noticed some paper said their path planning algorithms deal with the differential constraint of the vehicle. I don't understand what this means. I think if a path is smooth enough, the vehicle should be able to track this path exactly (ignoring the dynamic model).

So what kind of path satisfies the differential constraints of vehicles? Or what kind of path doesn't satisfy the differential constraints of vehicles? I really need some help here. Thanks!

When a paper says deal with the differential constraint of the vehicle they mean that the robot cannot, for example, rotate on the spot (skid steer) or actuate in the y or z direction. This is important in path planning because there is no point in considering paths the robot cannot achieve.