Suspended Load Path Tracking Control Using a Tilt-rotor UAV Based on Zonotopic State Estimation

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 $\mathcal{H}_2/\mathcal{H}_\infty$ 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

Set-Point Tracking MPC with Avoidance Features

This work proposes a finite-horizon optimal control strategy to solve the tracking problem while providing avoidance features to the closed-loop system. Inspired by the set-point tracking model predictive control (MPC) framework, the central idea of including artificial variables into the optimal control problem is considered. This approach allows us to add avoidance features into the set-point tracking MPC strategy without losing the properties of an enlarged domain of attraction and feasibility insurances in the face of any changing reference. Besides, the artificial variables are considered together with an avoidance cost functional to establish the basis of the strategy, maintaining the recursive feasibility property in the presence of a previously unknown number of regions to be avoided. It is shown that the closed-loop system is recursively feasible and input-to-state-stable under the mild assumption that the avoidance cost is uniformly bounded over time. Finally, two numerical examples illustrate the controller behavior

Set-based state estimation and fault diagnosis of linear discrete-time descriptor systems using constrained zonotopes

This paper presents new methods for set-valued state estimation and active fault diagnosis of linear descriptor systems. The algorithms are based on constrained zonotopes, a generalization of zonotopes capable of describing strongly asymmetric convex sets, while retaining the computational advantages of zonotopes. Additionally, unlike other set representations like intervals, zonotopes, ellipsoids, paralletopes, among others, linear static constraints on the state variables, typical of descriptor systems, can be directly incorporated in the mathematical description of constrained zonotopes. Therefore, the proposed methods lead to more accurate results in state estimation in comparison to existing methods based on the previous sets without requiring rank assumptions on the structure of the descriptor system and with a fair trade-off between accuracy and efficiency. These advantages are highlighted in two numerical examples.Comment: This paper was accepted and presented in the 1st IFAC Virtual World Congress, 202

Joint state and parameter estimation based on constrained zonotopes

This note presents a new method for set-based joint state and parameter estimation of discrete-time systems using constrained zonotopes. This is done by extending previous set-based state estimation methods to include parameter identification in a unified framework. Unlike in interval-based methods, the existing dependencies between states and model parameters are maintained from one time step to the next, thus providing a more accurate estimation scheme. In addition, the enclosure of states and parameters is refined using measurements through generalized intersections, which are properly captured by constrained zonotopes. The advantages of the new approach are highlighted in two numerical examples

Nonlinear Model Predictive Path Following Controller with Obstacle Avoidance

In the control systems community, path-following refers to the problem of tracking an output reference curve. This work presents a novel model predictive path-following control formulation for nonlinear systems with constraints, extended with an obstacle avoidance strategy. The method proposed in this work simultaneously provides an optimizing solution for both, path-following and obstacle avoidance tasks in a single optimization problem, using Nonlinear Model Predictive Control (NMPC). The main idea consists in extending the existing NMPC controllers by the introduction of an additional auxiliary trajectory that maintains the feasibility of the successive optimization problems even when the reference curve is unfeasible, possibly discontinuous, relaxing assumptions required in previous works. The obstacle avoidance is fulfilled by introducing additional terms in the value functional, rather than imposing state space constraints, with the aim of maintaining the convexity of the state and output spaces. Simulations results considering an autonomous vehicle subject to input and state constraints are carried out to illustrate the performance of the proposed control strategy.Fil: Sánchez, Ignacio Julián Rodolfo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; ArgentinaFil: D'jorge, Agustina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo Tecnológico para la Industria Química. Universidad Nacional del Litoral. Instituto de Desarrollo Tecnológico para la Industria Química; ArgentinaFil: Raffo, Guilherme V.. Universidade Federal de Minas Gerais; BrasilFil: González, Alejandro Hernán. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo Tecnológico para la Industria Química. Universidad Nacional del Litoral. Instituto de Desarrollo Tecnológico para la Industria Química; ArgentinaFil: Ferramosca, Antonio. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin

Stability Constraints for Robust Model Predictive Control

This paper proposes an approach for the robust stabilization of systems controlled by MPC strategies. Uncertain SISO linear systems with box-bounded parametric uncertainties are considered. The proposed approach delivers some constraints on the control inputs which impose sufficient conditions for the convergence of the system output. These stability constraints can be included in the set of constraints dealt with by existing MPC design strategies, in this way leading to the “robustification” of the MPC

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

This paper presents new methods for set-valued state estimation of nonlinear discrete-time systems with unknown-but-bounded uncertainties. A single time step involves propagating an enclosure of the system states through the nonlinear dynamics (prediction), and then enclosing the intersection of this set with a bounded-error measurement (update). When these enclosures are represented by simple sets such as intervals, ellipsoids, parallelotopes, and zonotopes, certain set operations can be very conservative. Yet, using general convex polytopes is much more computationally demanding. To address this, this paper presents two new methods, a mean value extension and a first-order Taylor extension, for efficiently propagating constrained zonotopes through nonlinear mappings. These extend existing methods for zonotopes in a consistent way. Examples show that these extensions yield tighter prediction enclosures than zonotopic estimation methods, while largely retaining the computational benefits of zonotopes. Moreover, they enable tighter update enclosures because constrained zonotopes can represent intersections much more accurately than zonotopes.Comment: This includes the supplement "Supplementary material for: Guaranteed methods based on constrained zonotopes for set-valued state estimation of nonlinear discrete-time systems

A Load Transportation Nonlinear Control Strategy Using a Tilt-Rotor UAV

This paper proposes a nonlinear control strategy to solve the trajectory tracking problem of a tilt-rotor Unmanned Aerial Vehicle (UAV) when transporting a suspended load. For the present study, the aim of the control system is to track a desired trajectory of the aircraft with load’s swing-free, even in the presence of external disturbances, parametric uncertainties, unmodeled dynamics, and noisy position measurements with lower sampling frequency than the controller. The whole system modeling is obtained through the Euler-Lagrange formulation considering the dynamics of the tilt-rotor UAV coupled to the suspended load. As for the nonlinear control strategy, an inner-loop control is designed based on input-output feedback linearization combined with the dynamic extension approach to stabilize the attitude and altitude of the UAV assuming nonlinearities, while an outer-loop control law is designed for guiding the aircraft with reduced load swing. The linearized dynamics are controlled using linear mixed H2/H∞ controllers with pole placement constraints. The solution is compared to two simpler control systems: the first one considers the load as a disturbance to the system but does not avoid its swing; the second one is a previous academic result with a three-level cascade strategy. Finally, in order to deal with the problem of position estimation in presence of unknown disturbances and noisy measurements with low sampling frequency, a Linear Kalman Filter with Unknown Inputs is designed for estimating both the aircraft’s translational position and translational disturbances. Simulation results are carried out to corroborate the proposed control strategy

Tube-based MPC with Nonlinear Control for Load Transportation using a UAV

This paper presents a two-stage cascade control framework to solve hierarchically the trajectory tracking problem of a Tilt-rotor Unmanned Aerial Vehicle (UAV) carrying a suspended load. Initially, a nonlinear dynamic model is presented, which is after decoupled into two subsystems. The outer control system is designed by means of a robust tube-based Model Predictive Control (MPC) strategy, which is used to control the UAV´s planar motion and stabilize the suspended load. For the inner control system, the input-output feedback linearization (IOFL) technique combined with the dynamic extension approach and a discrete mixed H2/H∞ controller is considered to control the UAV´s altitude and attitude. Simulations results are carried out to corroborate the proposed control strategy.Fil: Santos, Marcelo A.. Universidade Federal de Minas Gerais; BrasilFil: Ferramosca, Antonio. Universidad Tecnológica Nacional. Facultad Reg.reconquista. Departamento de Electromecanica; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe; ArgentinaFil: Raffo, Guilherme V.. Universidade Federal de Minas Gerais; Brasi