Suspended load path tracking control using a tilt-rotor UAV based on zonotopic state estimation

Abstract

This work addresses the problem of path tracking control of a suspended load using a tilt-rotor UAV. The main challenge in controlling this kind of system arises from the dynamic behavior imposed by the load, which is usually coupled to the UAV by means of a rope, adding unactuated degrees of freedom to the whole system. Furthermore, to perform the load transportation it is often needed the knowledge of the load position to accomplish the task. Since available sensors are commonly embedded in the mobile platform, information on the load position may not be directly available. To solve this problem in this work, initially, the kinematics of the multi-body mechanical system are formulated from the load's perspective, from which a detailed dynamic model is derived using the Euler-Lagrange approach, yielding a highly coupled, nonlinear state-space representation of the system, affine in the inputs, with the load's position and orientation directly represented by state variables. A zonotopic state estimator is proposed to solve the problem of estimating the load position and orientation, which is formulated based on sensors located at the aircraft, with different sampling times, and unknown-but-bounded measurement noise. To solve the path tracking problem, a discrete-time mixed H 2 /H ∞ controller with pole-placement constraints is designed with guaranteed time-response properties and robust to unmodeled dynamics, parametric uncertainties, and external disturbances. Results from numerical experiments, performed in a platform based on the Gazebo simulator and on a Computer Aided Design (CAD) model of the system, are presented to corroborate the performance of the zonotopic state estimator along with the designed controller.

Guaranteed methods based on constrained zonotopes for set-valued state estimation of nonlinear discrete-time systems

“…11 The conversion from CG-rep to H-rep (see [25]) for the purposes of exact drawing is intractable for the constrained zonotopes in this example. 12 The increased complexity of the constrained zonotopes provided by C4 proved to be intractable for this example. from CZMV and CZFO were again very similar, with CZMV providing marginally better results (the CZMV-to-CZFO ARR was 99.93%).…”

“…where c (n c ) = c x − h. Therefore, c (0) = 0 iff h is given by (18), thus m = 0, and diam(m) = 0. Note that in (12),M G (0) is invariant with respect to h, and since J ⊇ ∇ T x µ(X, W), then J is also invariant with respect to h. Consequently, the second term in (12) is not a function of h. Therefore, PB n ∞ ⊆PB n ∞ = (1/2)diag(diam(m))B n ∞ ⊕ PB n ∞ , withm computed usingĥ ∈ X. The result then follows from (13).…”

“…If stochastic descriptions of the process and measurement uncertainties are available, then Bayesian state estimation methods such as Kalman filtering or particle filtering are typically employed. On the other hand, if only bounds on the uncertainties are known, then set-valued state estimation methods are applied [3,9,10,11,12]. Recent approaches also consider the presence of both kinds of uncertainties in the system [13].…”

Nonlinear optimal control for UAVs with tilting rotors

“…), one has to modify the turn speed of the rotors so as to generate torques and thrust forces that will allow the drone's state variables converge to their setpoints and will make the drone follow the specified reference trajectories (Zhou et al ., 2021; Thirumaleshwar Hedge et al ., 2020, 2021; Zhang et al ., 2020; Xian and Hao, 2019). However, in tilt-rotor UAVs, one can primarily modify the tilting angles of the rotors and can use these angles as control inputs so as to make the drone follow the designated paths and accomplish its flight plans (Reyo and Raffo, 2019; Prach and Kayacan, 2018; Park et al ., 2013; Ricardo and Santos, 2022; Zheng et al ., 2020; Su et al ., 2022b). Unlike fixed-angle rotor UAVs where the associated dynamic model is characterized by underactuation, tilt-rotor UAVs can be fully actuated (Tadakoro et al ., 2018, 2019; Ding and Lu, 2018; Ryll et al ., 2015; Ji et al ., 2020; Liu et al ., 2021; Xu et al ., 2022).…”

Energy-Based Control and LMI-Based Control for a Quadrotor Transporting a Payload

“…A nonlinear attitude controller is developed in [11] to stabilize the altitude, and the translational dynamics control law is introduced by converting the vehicle velocity and position error into rotation control. Rego and Raffo [12] address trajectory tracking for a two-dimensional aerial robot transporting a payload. A discrete-time mixed H2/H∞ linear control strategy is presented.…”