Empirical Model Reduction of Controlled Nonlinear Systems

In this paper we introduce a new method of model reduction for nonlinear systems with inputs and outputs. The method requires only standard matrix computations, and when applied to linear systems results in the usual balanced truncation. For nonlinear systems, the method makes used of the Karhunen-Lo`eve decomposition of the state-space, and is an extension of the method of empirical eigenfunctions used in fluid dynamics. We show that the new method is equivalent to balanced-truncation in the linear case, and perform an example reduction for a nonlinear mechanical system

Challenges in Controllers on UAV Aircraft: Theory and Practice

This review explores the theoretical foundations and experimental dynamics of modern tiltrotor aircraft. Emphasizing feedback linearization, the study delves into the distinctive constraints and angular velocity ranges shaping tiltrotor behavior. Experimental findings highlight challenges in tracking circular trajectories, with color-coded representations illustrating the impact of angular velocity. Practical implications for applications like unmanned aerial vehicles are discussed, alongside identified challenges and avenues for future research. This work contributes to both theoretical understanding and practical considerations in the evolving field of tiltrotor control

Robust nonlinear control of vectored thrust aircraft

An interdisciplinary program in robust control for nonlinear systems with applications to a variety of engineering problems is outlined. Major emphasis will be placed on flight control, with both experimental and analytical studies. This program builds on recent new results in control theory for stability, stabilization, robust stability, robust performance, synthesis, and model reduction in a unified framework using Linear Fractional Transformations (LFT's), Linear Matrix Inequalities (LMI's), and the structured singular value micron. Most of these new advances have been accomplished by the Caltech controls group independently or in collaboration with researchers in other institutions. These recent results offer a new and remarkably unified framework for all aspects of robust control, but what is particularly important for this program is that they also have important implications for system identification and control of nonlinear systems. This combines well with Caltech's expertise in nonlinear control theory, both in geometric methods and methods for systems with constraints and saturations

Shape of an elastica under growth restricted by friction

We investigate the quasi-static growth of elastic fibers in the presence of dry or viscous friction. An unusual form of destabilization beyond a critical length is described. In order to characterize this phenomenon, a new definition of stability against infinitesimal perturbations over finite time intervals is proposed and a semi-analytical method for the determination of the critical length is developed. The post-critical behavior of the system is studied by using an appropriate numerical scheme based on variational methods. We find post-critical shapes for uniformly distributed as well as for concentrated growth and demonstrate convergence to a figure-8 shape for large lengths when self-crossing is allowed. Comparison with simple physical experiments yields reasonable accuracy of the theoretical predictions

Unscented Bayesian Optimization for Safe Robot Grasping

We address the robot grasp optimization problem of unknown objects considering uncertainty in the input space. Grasping unknown objects can be achieved by using a trial and error exploration strategy. Bayesian optimization is a sample efficient optimization algorithm that is especially suitable for this setups as it actively reduces the number of trials for learning about the function to optimize. In fact, this active object exploration is the same strategy that infants do to learn optimal grasps. One problem that arises while learning grasping policies is that some configurations of grasp parameters may be very sensitive to error in the relative pose between the object and robot end-effector. We call these configurations unsafe because small errors during grasp execution may turn good grasps into bad grasps. Therefore, to reduce the risk of grasp failure, grasps should be planned in safe areas. We propose a new algorithm, Unscented Bayesian optimization that is able to perform sample efficient optimization while taking into consideration input noise to find safe optima. The contribution of Unscented Bayesian optimization is twofold as if provides a new decision process that drives exploration to safe regions and a new selection procedure that chooses the optimal in terms of its safety without extra analysis or computational cost. Both contributions are rooted on the strong theory behind the unscented transformation, a popular nonlinear approximation method. We show its advantages with respect to the classical Bayesian optimization both in synthetic problems and in realistic robot grasp simulations. The results highlights that our method achieves optimal and robust grasping policies after few trials while the selected grasps remain in safe regions.Comment: conference pape

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

The Time Invariance Principle, Ecological (Non)Chaos, and A Fundamental Pitfall of Discrete Modeling

This paper is to show that most discrete models used for population dynamics in ecology are inherently pathological that their predications cannot be independently verified by experiments because they violate a fundamental principle of physics. The result is used to tackle an on-going controversy regarding ecological chaos. Another implication of the result is that all continuous dynamical systems must be modeled by differential equations. As a result it suggests that researches based on discrete modeling must be closely scrutinized and the teaching of calculus and differential equations must be emphasized for students of biology