Dynamic Models with Sigmoid Corrections to Generation of an Achievable 4D-Trajectory for a UAV and Estimating Wind Disturbances

Abstract

For an unmanned aerial vehicle (UAV) of an aircraft type, the problems of planning achievable trajectories as well as robust control under wind disturbances are considered. A computationally simple method for compiling a primary non-smooth 4D trajectory is proposed. Its segments connect the given waypoints and determine the desired average velocity in various sections. Instead of time-consuming methods of analytical smoothing of broken path joints using polynomials, a tracking differentiator with S-shaped smooth and limited sigmoid corrective actions is developed. This virtual dynamic model provides natural smoothing of the primary trajectory considering the design constraints on the velocity, acceleration, and thrust of the UAV. The tracking differentiator variables create an achievable trajectory and are used to synthesize the UAV tracking system. To compensate for the action of wind disturbances on the UAV, a disturbance observer is developed. It is a replica of the equations of the control plant model, which are directly affected by external uncontrolled disturbances. These algorithms also use sigmoid corrections. Unlike standard disturbances observers, this approach does not require the development of a dynamic model of external disturbances and does not assume their smoothness. The effectiveness of the developed algorithms was confirmed by numerical simulation.

Generation of Achievable Three-Dimensional Trajectories for Autonomous Wheeled Vehicles via Tracking Differentiators

“…Now, let us introduce constraints on the state variables of the tracking differentiator (18), its corrective influences, and the rate of their change. Considering (25) and the inverse Equation (20), namely z 2 = e 2 − p 1 σ(l 1 e 1 ), z 3 = e 3 − p 2 σ(l 2 e 2 ), we obtain a system of dual inequalities.…”

“…Under the assumption of non-smoothness of the external signal χ 1 (t), the accuracy of stabilization of the variables e 2 (t), e 3 (t) (25) is not important. The tracking error at special points is bounded e 1 (t) ≤ 2.2/l 1 .…”

“…Second, by changing the dimensionality of the tracking differentiator blocks, it is possible to automatically generate smoothed trajectories with defined constraints in phase spaces of different dimensionalities. For example, the system (32) at ∀z i ∈ R generates an achievable trajectory for a single-channel control plant (e.g., a single-link manipulator), and at ∀z i ∈ R 3 it generates a spatial trajectory for a UAV [25].…”

“…In our previous paper [25], this method was tested to generate achievable 4D trajectories for an aircraft-type unmanned aerial vehicle (UAV) center of mass and showed excellent performance. In this paper, we extend this method to a set of motion-planning problems for a wheeled robot.…”