Planning for a Forward-Only Left-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).
An additional restriction severely limits the motions of the car: it
is constrained to move forward-only and left-only. It can turn left
in varying degrees, but is unable to turn right or go straight!
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).
Another solution is shown, taken from a second run.
A third solution.
An animation of the previous solution.
A more challenging example.
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