3D Force Control of a Quadrotor subject to 2D Non-holonomic Contact with an Spherical Tip

Quadrotor navigation has been studied mainly in a free-flight regime, and a multitude of modeling and control schemes have been proposed, but fewer schemes have been proposed for engaging purposely contact. The flight regime of contact tasks is needed, for instance, to polish a surface or turn on a switch, where simultaneous force-position is required. Since quadrotor rotors induce a high frequency at contact, from the lightweight structure of the aircraft, schemes have been explored to mitigate energy transfer at contact with impedance or admittance filters but, nevertheless, leading to tracking errors. Inspired by our previous result for 1D contact, we propose in this paper a 2D rolling (non-holonomic Pffafian constraint) to establish force-position control of a quadrotor. To this end, the quadrotor is equipped with a sphere in its tip. 2D tangent forces are asymptotically stabilized, with a model-free chatterless sliding mode controller. Stability in the sense of Lyapunov, with local exponential convergence, is presented. Representative simulations are discussed, and conclusions are provided.