Planning for a Smooth 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 can move in both forward or reverse. The steering angle
appears as a fourth state variable, and it required to be continuous
The equations of motion are:
dx = Speed*u*cos(x);
dx = Speed*u*sin(x);
dx = Speed*u*tan(x)/CarLength;
dx = u;
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 4D state space by using only
xy coordinates of the vertices).
An alternative solution, obtained from a second run.
An animation of the previous solution.
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