Geometric control theory is a branch of mathematical control that utilizes tools from differential geometry to tackle fundamental problems in nonlinear control analysis and synthesis, such as controllability, motion planning, stability and stabilization. We revisit motion planning techniques for control affine systems with drift. When a Lie Algebraic Rank Condition (LARC) is satisfied by the family of control vector fields, the motion planning problem is simplified into an easier one whose solution can be used to solve the original problem in a universal way. Utilizing these techniques, we propose a time varying feedback control law that asymptotically stabilizes the origin for systems satisfying the LARC. In particular, the proposed control law asymptotically stabilizes a class of control affine systems that are known to have no continuous stabilizing feedback laws. Potential applications to stall recovery systems in airplanes due to loss of controllability are discussed.

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