a simple solution for most cases is: if the path has maximum curvature less than or equal to the maximum force divided by mass times the maximum velocity squared, than the speed is constant at the maximum speed, and the force is perpendicular to the motion of travel, with a magnitude proportional to the curvature. This is derived by setting the speed to the maximum allowed speed, and than using the osculating circle as a second order approximation for the path, and because acceleration(and therefore force) is locally independent of o(t^3) terms this approximation is exact. To generalize to higher dimensions one would have to take into account torsion, but the same concept applies.