We study a new type of motion planning problem in dimension 2 and 3 via linear and quadratic quantifier elimination. The object to be moved and the free space are both semilinear sets with no convexity assumptions. The admissible motions are finite continuous sequences of translations along prescribed directions. When the number of translations is bounded in advance, then the corresponding path finding problem can be modelled and solved as a linear quantifier elimination problem. Moreover the problem to find a shortest or almost shortest admissible path can be modelled as a special quadratic quantifier elimination problem. We give upper complexity bounds on these problems, report experimental results using the elimination facilities of the REDLOG package of REDUCE, and indicate a possible application.
Erika Cetindag, Martin Griebl