  In this paper, we propose a Feasible Sequential Linear Programming (FSLP)
algorithm applied to time-optimal control problems (TOCP) obtained through
direct multiple shooting discretization. This method is motivated by TOCP with
nonlinear constraints which arise in motion planning of mechatronic systems.
The algorithm applies a trust-region globalization strategy ensuring global
convergence. For fully determined problems our algorithm provides locally
quadratic convergence. Moreover, the algorithm keeps all iterates feasible
enabling early termination at suboptimal, feasible solutions. This additional
feasibility is achieved by an efficient iterative strategy using evaluations of
constraints, i.e., zero-order information. Convergence of the feasibility
iterations can be enforced by reduction of the trust-region radius. These
feasibility iterations maintain feasibility for general Nonlinear Programs
(NLP). Therefore, the algorithm is applicable to general NLPs. We demonstrate
our algorithm's efficiency and the feasibility update strategy on a TOCP of an
overhead crane motion planning simulation case.
