A passive velocity field for navigation of quadrotors with model-free integral sliding mode control

Velocity field (VF) control has proved effective for mobile robots and robot arms, aiming essentially at navigation and obstacle avoidance under position and velocity control in cluttered environment, however additional features are required for quadrotors due to its underactuated flight dynamics. The design of a VF control then comprises of two aspects, the design of the desired trajectories based on the VF and the design of the controller that guarantees tracking of such trajectories. In this paper, we propose a constructive method to design a passive VF for desired underactuated translational velocities; for desired orientation trajectories and due to the underactuation, those depend on the VF and the position controller from the analytical solution of the derivative of the rotation matrix. The controller uses model-free and chattering-free integral sliding modes for position and for attitude dynamics without requiring derivative of the VF nor assumption on boundedness on the integral of the VF nor the quadrotor dynamic model to withstand robustness against parametric and model uncertainties. It is shown that the controller steers the quadrotor onto the VF for all time and any initial conditions so as to the quadrotor behaves accordingly to the properties of the VF, such as exponential convergence toward the time-invariant nominal spatial contour for a robust and fast, yet smooth, approaching for easy manoeuvring. Simulations are discussed, and remarks address the viability of the proposed approach.