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# to be compu-

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# to be compu-

DOI link for to be compu-

to be compu- book

## ABSTRACT

Point-mass robot For a point-mass robot A moving in a plane, we typically want to control the force applied to A. So, we define A ’s state to be s = (x ,y ,x ,y ) , where (x, y) is A ’s position. The equations of mo tion are:

where m and (ux,uy) denote A ’s mass and the force applied to it. Bounds on the magnitudes of (x, y) and (ux ,uy) define S and Ω as subsets of R4 and R2, re spectively. Planning query Let S T denote the statextime space S x [0, +oo). Obstacles in the robot’s workspace are mapped into this space as forbidden regions. The free space T C S T is the set of all collision-free points (s, t). A trajectory s : [a, 6] -» S is admissible if, for all t G [a, 6], s(t) is an admissible state and (s(t), t) is collisionfree.