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

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