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, N - 1,..., N less than or equal to [(D - 2)/2], while the first N curvatures ki remain arbitrary. We show that the model admits consistent formulation on the anti-DeSitter space. The solutions of the system are the massless irreducible representations of Poincare group with N nonzero helicities, which are equal to each other.