1. Feasible Trajectories for Mobile Robots with Kinematic and Environment Constraints Jean-Paul Laumond

2. Car-Like Robot y x    dx/dt = v cos  dy/dt = v sin  d  dt = (v/L) tan    | <  dy/dx = tan  L Configuration (x,y,  )

3. Reachable Configurations (x,y)   CYL(x,y,  /2,  ) x y

4. Type 1 Maneuver  sidewise motion CYL(x,y, ,  )  = 2  /cos   = 2  (1/ cos  - 1) 

5. Type 2 Maneuver  rotation around a point

6. Coverage of a Path by Cylinders x y  +

7. Path Transform

8. Example

9. Other Example

10. “Good” Set of Maneuvers Reeds and Shepp Curves J.A. Reeds and L.A. Shepp. Optimal Paths for a Car That Goes Both Forwards and Backwards. Pacific Journal of Mathematics, 145(2):367-393, 1990.