Control of Flight Vehicles From the Perspective of Non-Holonomic Constraint Manifold Dynamics: Quadrotor Application

Abstract

In this paper, we address the problem of flight path planning and control. We approach the problem from the perspective of non-holonomic generalized momenta. We first build a desired minimum Jerk trajectory that we use as a momentum manifold constraint for the vehicle. We then develop a trajectory reference model of the flight vehicle that evolves exactly on the flight path as a constraint, as if the vehicle were a bead on a wire in the generalized coordinate configuration space. This model uses non-holonomic generalized momenta and position and orientation variables as states, the model is of order 2N – M, where N is the full dimension of the vehicle model and M is the number of manifold constraints imposed. These momenta models are canonical without Lagrange Multipliers. Next, we build a full 2N order model of the flight vehicle and design an LQR controller linearized about nominal path independent flight. We then implement this control in the full flight model and use as the reference state trajectory the constrained momentum states computed on the desired flight path. We allow inflight disturbances. We demonstrate that this approach provides good performance for a Quadrotor flight vehicle.