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The paper revisits a Lyapunov-based feedback control to implement spacecraft orbital transfer maneuvers. The spacecraft equations of motion in the form of Gauss Variational Equations (GVEs) are used. By shaping the Lyapunov function using barrier functions, we demonstrate that state and control constraints during orbital maneuvers can be enforced. Simulation results from orbital maneuvering scenarios are reported. The synergistic use of the reference governor in conjunction with the barrier functions is proposed to ensure convergence to the target orbit (liveness) while satisfying the imposed constraints., Comment: This is the author's original manuscript (pre-print) of the paper AAS 23-292 presented at 33rd AAS/AIAA Space Flight Mechanics Meeting, Austin, Texas, January 15-19 2023, https://www.space-flight.org/docs/2023_winter/33rdSFFM-Full_Program_Abstracts.pdf

The applications of reference governors to systems with unmeasured set-bounded disturbances can lead to conservative solutions. This conservatism can be reduced by estimating the disturbance from output measurements and canceling it in the nominal control law. In this paper, a reference governor based on such an approach is considered and time-varying, disturbance and state estimation errors bounding sets are derived. Consequently, the traditional implementation of a reference governor, which exploits a constraint admissible positively-invariant set of constant commands and initial states, is replaced by one which utilizes a time-dependent sequence of similar sets (which are not necessary nested). Examples are reported which include two applications to longitudinal control of aircraft that illustrate handling of elevator uncertainty and wing icing., Comment: 20 pages

When robots are able to see and respond to their surroundings, a whole new world of possibilities opens up. To bring these possibilities to life, the robotics industry is increasingly adopting camera-based vision systems, especially when a robotic system needs to interact with a dynamic environment or moving target. However, this kind of vision system is known to have low data transmission rates, packet loss during communication and noisy measurements as major disadvantages. These problems can perturb the control performance and the quality of the robot-environment interaction. To improve the quality of visual information, in this paper, we propose to model the dynamics of the motion of a target object and use this model to implement an Extended Kalman Filter based on Intermittent Observations of the vision system. The effectiveness of the proposed approach was tested through experiments with a robotic arm, a camera device in an eye-to-hand configuration, and an oscillating suspended block as a target to follow., Comment: 6pages, 11 figures

The paper considers the application of feedback control to orbital transfer maneuvers subject to constraints on the spacecraft thrust and on avoiding the collision with the primary body. Incremental reference governor (IRG) strategies are developed to complement the nominal Lyapunov controller, derived based on Gauss Variational Equations, and enforce the constraints. Simulation results are reported that demonstrate the successful constrained orbital transfer maneuvers with the proposed approach. A Lyapunov function based IRG and a prediction-based IRG are compared. While both implementations successfully enforce the constraints, a prediction-based IRG is shown to result in faster maneuvers., Comment: 17 pages, 14 figures, submitted to Advanced Control for Applications

Reference and command governors are add-on schemes that augment nominal closed-loop systems with the capability to enforce state and control constraints. They do this by monitoring and modifying, when necessary, the reference command. Existing command governors do this by solving at each sampling time a quadratic programming problem to find a modified reference closest to the original command such that the current state and the modified reference pair are constraint admissible. In this paper, we show that a simple modification of the basic command governor enables it to operate with inexact optimization and even without requiring invariance of the constraint admissible set. Thus this modification significantly extends the applicability of the reference and command governors to practical problems where finding invariant sets may be problematic and where exact optimization may not be feasible due to reliability of the optimizers or limited computing power. Numerical examples are reported which illustrate the approach.

Boom cranes are among the most used cranes to lift heavy loads. Although fairly simple mechanically, from the control viewpoint this kind of crane is a nonlinear underactuated system which presents several challenges, especially when con-trolled in the presence of constraints. To solve this problem, we propose an approach based on the Explicit Reference Governor (ERG), which does not require any online optimization, thus making it computationally inexpensive. The proposed control scheme is able to steer the crane to a desired position ensuring the respect of limited joint ranges, maximum oscillation angle, and the avoidance of static obstacles., Comment: The paper was published in 37th International Symposium on Automation and Robotics in Construction (ISARC 2020)

Boom cranes are among the most common material handling systems due to their simple design. Some boom cranes also have an auxiliary jib connected to the boom with a flexible joint to enhance the maneuverability and increase the workspace of the crane. Such boom cranes are commonly called knuckle boom cranes. Due to their underactuated properties, it is fairly challenging to control knuckle boom cranes. To the best of our knowledge, only a few techniques are present in the literature to control this type of cranes using approximate models of the crane. In this paper we present for the first time a complete mathematical model for this crane where it is possible to control the three rotations of the crane (known as luff, slew, and jib movement), and the cable length. One of the main challenges to control this system is how to reduce the oscillations in an effective way. In this paper we propose a nonlinear control based on energy considerations capable of guiding the crane to desired sets points while effectively reducing load oscillations. The corresponding stability and convergence analysis is proved using the LaSalle's invariance principle. Simulation results are provided to demonstrate the effectiveness and feasibility of the proposed method., Comment: This paper was published in 37th International Symposium on Automation and Robotics in Construction (ISARC 2020)

Automation of cranes can have a direct impact on the productivity of construction projects. In this paper, we focus on the control of one of the most used cranes, the boom crane. Tower cranes and overhead cranes have been widely studied in the literature, whereas the control of boom cranes has been investigated only by a few works. Typically, these works make use of simple models making use of a large number of simplifying assumptions (e.g. fixed length cable, assuming certain dynamics are uncoupled, etc.) A first result of this paper is to present a fairly complete nonlinear dynamic model of a boom crane taking into account all coupling dynamics and where the only simplifying assumption is that the cable is considered as rigid. The boom crane involves pitching and rotational movements, which generate complicated centrifugal forces, and consequently, equations of motion highly nonlinear. On the basis of this model, a control law has been developed able to perform position control of the crane while actively damping the oscillations of the load. The effectiveness of the approach has been tested in simulation with realistic physical parameters and tested in the presence of wind disturbances., Comment: the paper was published in 37th International Symposium on Automation and Robotics in Construction (ISARC 2020)

The P-difference between two sets $\mathcal{A}$ and $\mathcal{B}$ is the set of all points, $\mathcal{C}$, such that the addition of $\mathcal{B}$ to any of the points in $\mathcal{C}$ is contained in $\mathcal{A}$. Such a set difference plays an important role in robust model predictive control and in set-theoretic control. In the paper we demonstrate that an inner approximation of the P-difference between two semialgebraic sets can be computed using the Sums of Squares Programming, and we illustrate the procedure using several computational examples.

This paper is based on the observation that, during Covid-19 epidemic, the choice of which individuals should be tested has an important impact on the effectiveness of selective confinement measures. This decision problem is closely related to the problem of optimal sensor selection, which is a very active research subject in control engineering. The goal of this paper is to propose a policy to smartly select the individuals to be tested. The main idea is to model the epidemics as a stochastic dynamic system and to select the individual to be tested accordingly to some optimality criteria, e.g. to minimize the probability of undetected asymptomatic cases. Every day, the probability of infection of the different individuals is updated making use of the stochastic model of the phenomenon and of the information collected in the previous days. Simulations for a closed community of 10000 individuals show that the proposed technique, coupled with a selective confinement policy, can reduce the spread of the disease while limiting the number of individuals confined if compared to the simple contact tracing of positive and to an off-line test selection strategy based on the number of contacts., Comment: Preprint submitted to Annual Reviews in Control. Updated on 22 December 2020

This paper presents an extension to the nonlinear Model Predictive Control for Tracking scheme able to guarantee convergence even in cases of non-convex output admissible sets. This is achieved by incorporating a convexifying homeomorphism in the optimization problem, allowing it to be solved in the convex space. A novel class of non-convex sets is also defined for which a systematic procedure to construct a convexifying homeomorphism is provided. This homeomorphism is then embedded in the Model Predictive Control optimization problem in such a way that the homeomorphism is no longer required in closed form. Finally, the effectiveness of the proposed method is showcased through an illustrative example.

The goal of this paper is to present a systematic method to compute reference dependent positively invariant sets for systems subject to constraints. To this end, we first characterize these sets as level sets of reference dependent Lyapunov functions. Based on this characterization and using Sum of Squares (SOS) theory, we provide a polynomial certificate for the existence of such sets. Subsequently, through some algebraic manipulations, we express this certificate in terms of a Semi-Definite Programming (SDP) problem which maximizes the size of the resulting reference dependent invariant sets. We then present the results of implementing the proposed method to an example system and propose some variations of the proposed method that may help in reducing the numerical issues of the method. Finally, the proposed method is employed in the Model Predictive Control (MPC) for Tracking scheme to compute the terminal set, and in the Explicit Reference Governor (ERG) scheme to compute the so-called Dynamic Safety Margin (DSM). The effectiveness of the proposed method in each of the schemes is demonstrated through a simulation study.

The reduction of constraints to obtain minimal representations of sets is a very common problem in many engineering applications. While well-established methodologies exist for the case of linear constraints, the problem of how to detect redundant non-linear constraints is an open problem. In this paper we present a novel methodology based on Sum of Squares for the elimination of redundant polynomial constraints. The paper also presents some relevant applications of the presented method to constrained control problems. In particular, we show how the proposed method can be used in the Model Predictive Control and in the Reference Governor frameworks to reduce the computational burden of the online algorithms. Furthermore, this method can also be used to eliminate the terminal constraints in MPC in a simple way that is independent from the cost function.

This paper presents a novel information-based mission planner for a drone tasked to monitor a spatially distributed dynamical phenomenon. For the sake of simplicity, the area to be monitored is discretized. The insight behind the proposed approach is that, thanks to the spatio-temporal dependencies of the observed phenomenon, one does not need to collect data on the entire area. In fact, unmeasured states can be estimated using an estimator, such as a Kalman filter. In this context the planning problem becomes the one of generating a flight path that maximizes the quality of the state estimation while satisfying the flight constraints (e.g. flight time). The first result of this paper is to formulate this problem as a special Orienteering Problem where the cost function is a measure of the quality of the estimation. This approach provides a Mixed-Integer Semi-Definite formulation to the problem which can be optimally solved for small instances. For larger instances, two heuristics are proposed which provide good sub-optimal results. To conclude, numerical simulations are shown to prove the capabilities and efficiency of the proposed path planning strategy. We believe this approach has the potential to increase dramatically the area that a drone can monitor, thus increasing the number of applications where monitoring with drones can become economically convenient., Comment: Submitted to "IEEE Transactions on Automation Science and Engineering"

This technical note focuses on the control of a quadrotor unmanned aerial vehicle (UAV) tethered to the ground. The control objective is to stabilize the UAV to the desired position while ensuring that the cable remains taut at all times. A cascade control scheme is proposed. The inner loop controls the attitude of the UAV. The outer loop gives the attitude reference to the inner loop, and is designed so that (i) the gravity force is compensated, (ii) the cable is taut at all times, and (iii) the trajectory of the UAV follows the geodesic path. To prove asymptotic stability, small gain arguments are used. The control scheme is augmented with a reference governor to enforce constraints.

This paper proposes a constrained control scheme for the control of the depth of hypnosis during induction phase in clinical anesthesia. In contrast with existing control schemes for propofol delivery, the proposed scheme guarantees overdosing prevention while ensuring good performance. The core idea is to reformulate overdosing prevention as a constraint, and then use the recently introduced Explicit Reference Governor to enforce the constraint satisfaction at all times. The proposed scheme is evaluated in comparison with a robust PID controller on a simulated surgical procedure for 44 patients whose Pharmacokinetic-Pharmacodynamic models have been identified using clinical data. The results demonstrate that the proposed constrained control scheme can deliver propofol to yield good induction phase response while preventing overdosing in patients; whereas other existing schemes might cause overdosing in some patients. Simulations show that mean rise time, mean settling time, and mean overshoot of less than 5 [min], 8 [min], and 10%, respectively, are achieved, which meet typical anesthesiologists' response specifications.

This paper focuses on the control of a cooperative system composed of an Unmanned Aerial Vehicle (UAV) and an Unmanned Ground Vehicle (UGV) manipulating an object. The two units are subject to input saturations and collaborate to move the object to a desired pose characterized by its position and inclination. The dynamics are derived using Euler-Lagrange method. A pre-stabilizing control law is proposed where the UGV is tasked to deploy the object to a certain position whereas the UAV adjusts its inclination. In particular, a proportional-derivative control law is proposed for the UGV, and a cascade control approach is used for the UAV, where the inner loop controls the attitude of the UAV and the outer loop stabilizes the inclination of the object. Then, we prove the stability of the points of equilibrium using small gain arguments. To ensure constraints satisfaction at all times, a reference governor unit is added to the pre-stabilizing control scheme. Finally, numerical results combined with experimental results are provided to validate the effectiveness of the proposed control scheme in practice., Comment: 16 pages, 7 figures

In this note we provide an algorithm for the computation of the steady-state input able to achieve the steady-state output tracking of any desired output signal representable as a rational transfer function.

This paper introduces an explicit reference governor approach for controlling time delay linear systems subject to state and input constraints. The proposed framework relies on suitable invariant sets that can be built using both Lyapunov-Razumikhin and Lyapunov-Krasovskii arguments. The proposed method is validated both numerically and experimentally using several alternative formulations.

This paper focuses on a passivity-based distributed reference governor (RG) applied to a pre-stabilized mobile robotic network. The novelty of this paper lies in the method used to solve the RG problem, where a passivity-based distributed optimization scheme is proposed. In particular, the gradient descent method minimizes the global objective function while the dual ascent method maximizes the Hamiltonian. To make the agents converge to the agreed optimal solution, a proportional-integral consensus estimator is used. This paper proves the convergence of the state estimates of the RG to the optimal solution through passivity arguments, considering the physical system static. Then, the effectiveness of the scheme considering the dynamics of the physical system is demonstrated through simulations and experiments., Comment: 8 pages, International Federation of Automatic Conference 2017, 8 figures

In this paper, we address a general eigenstructure assignment problem where the objective is to distribute the closed-loop modes over the components of the system outputs in such a way that, if a certain mode appears in a given output, it is unobservable from any of the other output components. By linking classical geometric control results with the theory of combinatorics, we provide necessary and sufficient conditions for the solvability of this problem, herein referred to as state-to-output decoupling, under very mild assumptions. We propose solvability conditions expressed in terms of the dimensions of suitably defined controlled invariant subspaces of the system. In this way, the solvability of the problem can be evaluated a priori, in the sense that it is given in terms of the problem/system data. Finally, it is worth mentioning that the proposed approach is constructive, so that when a controller that solves the problem indeed exists, it can be readily computed by using the machinery developed in this paper., Comment: 47 pages

This paper focuses on the control of a system composed of an Unmanned Aerial Vehicle (UAV) and an Unmanned Ground Vehicle (UGV) which cooperate to manipulate an object. The two units are subject to actuator saturations and cooperate to move the object to a desired pose, characterized by its position and inclination. The paper proposes a control strategy where the ground vehicle is tasked to deploy the object to a certain position, whereas the aerial vehicle adjusts its inclination. The ground vehicle is governed by a saturated proportional-derivative control law. The aerial vehicle is regulated by means of a cascade control specifically designed for this problem that is able to exploit the mechanical interconnection. The stability of the overall system is proved through Input-to-State Stability and Small Gain theorem arguments. To solve the problem of constraints satisfaction, a nonlinear Reference Governor scheme is implemented. Numerical simulations are provided to demonstrate the effectiveness of the proposed method., Comment: 8 pages, 5 figures, American Control Conference (ACC) 2016

This paper introduces a novel closed-form strategy that dynamically modifies the reference of a pre-compensated nonlinear system to ensure the satisfaction of a set of convex constraints. The main idea consists of translating constraints in the state space into constraints on the Lyapunov function and then modulating the reference velocity so as to limit the value of the Lyapunov function. The theory is introduced for general nonlinear systems subject to convex constraints. In the case of polyhedric constraints, an explicit solution is provided for the large and highly relevant class of nonlinear systems whose Lyapunov function is lower-bounded by a quadratic form. In view of improving performances, further specializations are provided for the relevant cases of linear systems and robotic manipulators., Comment: Submitted to: IEEE Transactions on Automatic Control

Wireless Sensor Networks (WSNs) enable a wealth of new applications where remote estimation is essential. Individual sensors simultaneously sense a dynamic process and transmit measured information over a shared channel to a central fusion center. The fusion center computes an estimate of the process state by means of a Kalman filter. In this paper we assume that the WSN admits a tree topology with fusion center at the root. At each time step only a subset of sensors can be selected to transmit observations to the fusion center due to a limited energy budget. We propose a stochastic sensor selection algorithm that randomly selects a subset of sensors according to certain probability distribution, which is opportunely designed to minimize the asymptotic expected estimation error covariance matrix. We show that the optimal stochastic sensor selection problem can be relaxed into a convex optimization problem and thus solved efficiently. We also provide a possible implementation of our algorithm which does not introduce any communication overhead. The paper ends with some numerical examples that show the effectiveness of the proposed approach., Comment: 7 pages, 2 figures, complete version of a technical note for the IEEE transactions on automatic control