  We introduce variational problems on Riemannian manifolds with constrained
acceleration and derive necessary conditions for normal extremals in the
constrained variational problem. The problem consists on minimizing a
higher-order energy functional, among a set of admissible curves defined by a
constraint on the covariant acceleration. In addition, we use this framework to
address the elastic splines problem with obstacle avoidance in the presence of
this type of contraints.
