  In recent years, the increasing need for high-performance controllers in
applications like autonomous driving has motivated the development of
optimization routines tailored to specific control problems. In this paper, we
propose an efficient inexact model predictive control (MPC) strategy for
autonomous miniature racing with inherent robustness properties. We rely on a
feasible sequential quadratic programming (SQP) algorithm capable of generating
feasible intermediate iterates such that the solver can be stopped after any
number of iterations, without jeopardizing recursive feasibility. In this way,
we provide a strategy that computes suboptimal and yet feasible solutions with
a computational footprint that is much lower than state-of-the-art methods
based on the computation of locally optimal solutions. Under suitable
assumptions on the terminal set and on the controllability properties of the
system, we can state that, for any sufficiently small disturbance affecting the
system's dynamics, recursive feasibility can be guaranteed. We validate the
effectiveness of the proposed strategy in simulation and by deploying it onto a
physical experiment with autonomous miniature race cars. Both the simulation
and experimental results demonstrate that, using the feasible SQP method, a
feasible solution can be obtained with moderate additional computational effort
compared to strategies that resort to early termination without providing a
feasible solution. At the same time, the proposed method is significantly
faster than the state-of-the-art solver Ipopt.
