Parametrised collision-free optimal motion planning algorithms in Euclidean spaces

We describe parametrised motion planning algorithms for systems controlling\nobjects represented by points that move without collisions in an even\ndimensional Euclidean space and in the presence of up to three obstacles with\n\\emph{a priori} unknown positions. Our algorithms are optimal in the sense that\nthe parametrised local planners have minimal posible size.\n