Abstract: A trajectory is generated using non-uniform rational B-splines. A feasible corridor is approximated with at least one convex polytope. The at least one convex polytope is defined by a plurality of vertices. The feasible corridor comprises a region in a trajectory space that satisfies a plurality of trajectory constraints for a vehicle to pass through the trajectory space. The vehicle comprises a plurality of vehicle constraints. A non-uniform rational B-spline (NURBS) definition is constructed that comprises: a plurality of NURBS basis functions, a plurality of control points that comprise the plurality of vertices, and a plurality of weight points. The plurality of vehicle constraints are parameterized with the plurality of NURBS basis functions. At least one trajectory is generated for the vehicle through the trajectory space where the at least on trajectory lies within the feasible corridor to satisfy the plurality of trajectory constraints.