RRT and the piano mover’s problem
Fig.5: RRT algorithm in a convex shape of map
2.
Approach to the problem
2.1 Differences between the RRT algorithm and the piano mover’s problem
There are two main differences between the RRT algorithm and the piano mover’s problem. First, the properties of the object to be moved are different: the RRT algorithm considers the object to be an infinitely small point, while in PMP the object has its size (length, width or even height). Second, the information needed to uniquely identify the state of an object in the space: in a 2-dimensional RRT algorithm the x and y coordinates will be enough to uniquely represent an object, but since we can rotate the object in a PMP, an additional rotation angle around its centre θ is introduced.
Fig.6: representation of object in PMP 7
7 See https://www.coursera.org/learn/robotics-motion-planning/lecture/Yh5fc/2-3-piano-movers-problem.
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