Planning for a Forward-Only Car-Like Robot
This problem involves differential (nonholonomic) constraints on a
car-like robot. The robot has a limited steering angle, and is
required to roll along the ground (i.e., it cannot move sideways).
The robot moves forward only.
The equations of motion are:
dx = Speed*u*cos(x);
dx = Speed*u*sin(x);
dx = tan(u)/CarLength;
in which dx represents dx/dt, u represents the input vector, and
x represents the state vector.
An RRT that takes into account these differential constraints
is shown below.
An example solution path for a simple problem is shown below. The
RRTs are shown (projected from a 3D configuration space by using only
xy coordinates of the vertices).
An alternative solution, obtained after a second run, is shown below.
An animation of the solution.
A solution for a more challenging problem.
This problem is similar to the previous one, except that the
maximum steering angle is smaller. Note the small curvature
along the path.
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