Dynamic Smoothing, Filtering and Differentiation of Signals Defining the Path of the UAV

Abstract

On the example of a control system for an unmanned aerial vehicle, we consider the problems of filtering, smoothing and restoring derivatives of reference action signals. These signals determine the desired spatial path of the plant at the first approximation. As a rule, researchers have considered these problems separately and have used different methods to solve each of them. The paper aims to develop a unified approach that provides a comprehensive solution to mentioned problems. We propose a dynamic admissible path generator. It is constructed as a copy of the canonical control plant model with smooth and bounded sigmoid corrective actions. For the deterministic case, a synthesis procedure has been developed, which ensures that the output variables of the generator track a non-smooth reference signal. Moreover, it considers the constraints on the velocity and acceleration of the plant. As a result, the generator variables produce a naturally smoothed spatial curve and its derivatives, which are realizable reference actions for the plant. The construction of the generator does not require exact knowledge of the plant parameters. Its dynamic order is less than that of the standard differentiators. We confirm the effectiveness of the approach by the results of numerical simulation.

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

“…To smooth the primitive trajectory signals, we use a tracking dynamic differentiator with sigmoid correcting actions. Instead of following [16,17], in this paper, we will increase the order of the dynamic model used. It is to enable us to additionally enforce the design constraints on the third and fourth derivatives of the reference actions, as well as to reduce the outliers of the second derivative at special points (joints of polyline ( 16)).…”

“….. χ 1 (t). To satisfy given constraints (18) in the design of corrective actions w we will also, as in [16,17,20,21,38], use non-linear odd sigma-functions σ(x) = −th(−x/2), σ(−x) = −σ(x) in the local feedback. In order to set up the required features, we have introduced two scaling parameters k, m = const > 0 into the sigma function, namely…”

“…Next, we demonstrate the developed procedure for the design of sigmoid corrective actions in system (17) consisting of three 3rd-order blocks. It is a logical continuation of the design procedure for the system consisting of two blocks [16,17], so here we give it without strict proof.…”

“…Instead of the above methods of analytical smoothing of the reference trajectory, we propose dynamic smoothing that does not require complex geometric calculations, an exact analytical description of the trajectory segments, and the calculation of the appropriate polynomial factors. In our previous papers [16,17], we designed a dynamic generator of admissible trajectories for aircraft-type UAVs. This is an autonomous sixth-order dynamic virtual model, which is constructed as a replica of the input-output canonical model describing the motion of the UAV's center of mass.…”

“…It is also shown that unlike the sixth-order dynamic generator [16,17], in this case, we can additionally ensure that the constraints on the third and fourth derivatives are satisfied, obtain a smoother signal for the second derivative, and reduce the algorithm's counting time. The novelty of the proposed approach lies in the fact that the tracking differentiator generates smooth signals and their derivatives of the required order (which is quite sufficient for the design of standard tracking systems) with automatic implementation of design constraints.…”