Differential flatness is a property of certain nonlinear systems widely used in controller design, trajectory generation and computing solutions to optimal control problems. For systems that are differentially flat, the states and controls can be expressed as a function of flat outputs and their derivatives. In this work we evaluate (computationally) the performance of a trajectory generation and tracking problem for a 6-DOF aircraft model which is differentially flat. Towards this, we consider an unmanned aerial vehicle in dynamic soaring. Dynamic soaring is an energy efficient flight where wind gradients are exploited to minimize (or even zero) power and are observed in birds like albatross.

Reformulation of the optimal control problem (OCP) in flat output space using differential flatness reduces the number of constraints and decision variables in the resulting optimization problem. However, such a reduction in decision variables need not provide any benefit in terms of computational time while solving the OCP. The evaluation performed here delineates the computational time for different components that are used while solving the OCP. A pseudospectral collocation approach using Legendre-Gauss-Lobatto collocation points is adopted to solve the OCP and evaluation is restricted to that scheme.

The open loop trajectories generated for dynamic soaring are unstable and atmospheric disturbances can cause loss of aircraft altitude leading to failures. To stabilize the aircraft, feedback is introduced via two model-based control techniques: finite-horizon linear quadratic regulator (LQR) and linear model predictive control (MPC). A linear time-varying model is obtained by linearizing about the open loop trajectories and simulations are performed. To enable real-time tracking, differential flatness is invoked while solving MPC and it leads to reduction in computational time by an order of magnitude.