  We show that 10D spinor helicity formalism can be understood as spinor moving
frame approach to supersymmetric particles extended to the description of
amplitudes. This allows us to develop the spinor helicity formalism for 11D
supergravity and a new constrained superfield formalism for 10D SYM and 11D
SUGRA amplitudes. We show how the constrained on-shell superfields,
one-particle counterparts of the superamplitudes, can be obtained by
quantization of massless superparticle mechanics.
  We make some stages towards the calculation of amplitudes of 10D SYM and 11D
SUGRA in this framework. In particular we have found supersymmetric Ward
identities for constrained amplitudes and an especially convenient gauge, fixed
on the spinor frame variables corresponding to scattered particles, which
promises to be an extremely useful tool for further development of our
approach.
  We also discuss a candidate for generalization of the BCFW recurrent
relations for the constrained tree superamplitudes, indicate and discuss a
problem of dependence of the expressions obtained with it on a deformation
vector, which is not fixed uniquely in higher dimensional $D>4$ cases.
