D-dimensional massless particle with extended gauge invariance

We propose the model of $D-$dimensional massless particle whose Lagrangian is given by the $N-$th extrinsic curvature of world-line. The system has $N+1$ gauge degrees of freedom constituting $W-$like algebra; the classical trajectories of the model are space-like curves which obey the conditions $k_{N+a}=k_{N-a}$, $k_{2N}=0$, $a=1,\mathrm{.}\mathrm{.}\mathrm{.},N-1$, $N\le [(D-2)\mathrm{/}2]$, while the first $N$ curvatures $k_i$ remain arbitrary. We show that the model admits consistent formulation on the anti-De Sitter space. The solutions of the system are the massless irreducible representations of Poincar'e group with $N$ nonzero helicities, which are equal to each other.