Design of state-feedback controllers for linear parameter varying systems subject to time-varying input saturation

All real-world systems are affected by the saturation phenomenon due to inherent physical limitations of actuators. These limitations should be taken into account in the controller’s design to prevent a possibly severe deterioration of the system’s performance, and may even lead to instability of the closed-loop system. Contrarily to most of the control strategies, which assume that the saturation limits are constant in time, this paper considers the problem of designing a state-feedback controller for a system affected by time-varying saturation limits with the objective to improve the performance. In order to tie variations of the saturation function to changes in the performance of the closed-loop system, the shifting paradigm is used, that is, some parameters scheduled by the time-varying saturations are introduced to schedule the performance criterion, which is considered to be the instantaneous guaranteed decay rate. The design conditions are obtained within the framework of linear parameter varying (LPV) systems using quadratic Lyapunov functions with constant Lyapunov matrices and they consist in a linear matrix inequality (LMI)-based feasibility problem, which can be solved efficiently using available solvers. Simulation results obtained using an illustrative example demonstrate the validity and the main characteristics of the proposed approach.Peer ReviewedPostprint (published version

Design of shifting output-feedback controllers for LPV systems subject to time-varying saturations

This paper considers the problem of designing a shifting output-feedback controller for polytopic linear parameter-varying (LPV) systems subject to time-varying saturations. By means of the LPV framework and the use of the Lyapunov theory, the shifting paradigm concept, and the ellipsoidal invariant theory, a linear matrix inequality (LMI)-based methodology for the controller's design is proposed. The resulting gain-scheduled controller holds the control action in the linearity region of the actuators and regulates online the closed-loop convergence taking into account the instantaneous saturation limit values. The proposed approach is validated by means of an illustrative example.This work has been partially funded by the Spanish State Research Agency (AEI) and the European Regional Development Fund (ERFD) through the project SaCoAV (ref. PID2020-114244RB-I00). This work has also been partially funded by AGAUR of Generalitat de Catalunya through the Advanced Control Systems (SAC) group grant (2017 SGR 482) and by the University of Stavanger through the project IN-12267. A. Ruiz is also supported by the Secretaria d’Universitats i Recerca de la Generalitat de Catalunya, the European Social Fund (ESF) and AGAUR under a FI SDUR grant (ref. 2020 FI-SDUR 00097).Peer ReviewedPostprint (published version

Quadrotor path following and reactive obstacle avoidance with deep reinforcement learning

A deep reinforcement learning approach for solving the quadrotor path following and obstacle avoidance problem is proposed in this paper. The problem is solved with two agents: one for the path following task and another one for the obstacle avoidance task. A novel structure is proposed, where the action computed by the obstacle avoidance agent becomes the state of the path following agent. Compared to traditional deep reinforcement learning approaches, the proposed method allows to interpret the training process outcomes, is faster and can be safely trained on the real quadrotor. Both agents implement the Deep Deterministic Policy Gradient algorithm. The path following agent was developed in a previous work. The obstacle avoidance agent uses the information provided by a low-cost LIDAR to detect obstacles around the vehicle. Since LIDAR has a narrow field-of-view, an approach for providing the agent with a memory of the previously seen obstacles is developed. A detailed description of the process of defining the state vector, the reward function and the action of this agent is given. The agents are programmed in python/tensorflow and are trained and tested in the RotorS/gazebo platform. Simulations results prove the validity of the proposed approach.This work has been partially funded by the Spanish Government (MINECO) through the project CICYT (ref. DPI2017-88403-R).Peer ReviewedPostprint (published version

A deep reinforcement learning approach for path following on a quadrotor

© 2020 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.This paper proposes the Deep Deterministic Policy Grandient (DDPG) reinforcement learning algorithm to solve the path following problem in a quadrotor vehicle. This agent is implemented using a separated control and guidance structure with an autopilot tracking the attitude and velocity commands. The DDPG agent is implemented in python and it is trained and tested in the RotorS-Gazebo environment, a realistic multirotor simulator integrated in ROS. Performance is compared with Adaptive NLGL, a geometric algorithm that implements an equivalent control structure. Results show how the DDPG agent is able to outperform the Adaptive NLGL approach while reducing its complexity.This work has been partially funded by the Spanish State Research Agency (AEI) and the European Regional Development Fund (ERDF) through the SCAV project (ref. MINECO DPI2017-88403-R), and by SMART project (ref. EFA 153/16 Interreg Cooperation Program POCTEFA 2014- 2020). Bartomeu Rubí is also supported by the Secretaria d’Universitats i Recerca de la Generalitat de Catalunya, the European Social Fund (ESF) and AGAUR under a FI grant (ref. 2017FI B 00212).Peer ReviewedPostprint (author's final draft

A Survey of path following control strategies for UAVs focused on quadrotors

The trajectory control problem, defined as making a vehicle follow a pre-established path in space, can be solved by means of trajectory tracking or path following. In the trajectory tracking problem a timed reference position is tracked. The path following approach removes any time dependence of the problem, resulting in many advantages on the control performance and design. An exhaustive review of path following algorithms applied to quadrotor vehicles has been carried out, the most relevant are studied in this paper. Then, four of these algorithms have been implemented and compared in a quadrotor simulation platform: Backstepping and Feedback Linearisation control-oriented algorithms and NLGL and Carrot-Chasing geometric algorithms.Peer ReviewedPostprint (author's final draft

Adaptive nonlinear guidance law using neural networks applied to a quadrotor

© 2019IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.The NonLinear Guidance Law (NLGL) is a geometric algorithm commonly employed to solve the path following problem on different unmanned vehicles. NLGL is simple (does no depend on the model of the vehicle), effective and has only one tunning parameter. Its control parameter (L) depends on various factors, such as the velocity of the vehicle, the shape of the reference path and the dynamics of the vehicle. This paper analyses the effect of parameter L on the performance of NLGL when it is applied to a quadrotor vehicle. An Adaptive NLGL, which includes a velocity reduction term, is proposed. Stability proofs are given. Simulation results show that the proposed algorithm enhances the performance of the standard NLGL. Furthermore, it has no parameters to tune.Peer ReviewedPostprint (author's final draft

Tail motion model identification for control design of an unmanned helicopter

This paper explains the methodology developed to design the yaw control system (heading control system) of the α-SAC UAV. The problem of modeling and controlling the tail motion of this UAV along a desired trajectory is considered. First, the response data of the system are collected during special flight test and a linear time invariant model is extracted by identification techniques. Then, the control system is designed and implemented using a PID feedback/feedforward control method. The technique is tested in simulation and validated in the autonomous flight of the small scale helicopter.Peer ReviewedPostprint (published version

Backstepping with virtual filtered command: Application to a 2D autonomous Vehicle

Through this work a deep understanding of the backstepping control technique is sought when applied over non-affine systems. It is shown that in this case appears the necessity to bound the value of internal states and that a modification over standard backstepping is mandatory. The principal goal of this study is to evaluate the effects of finite frequency filters, and the effects of saturation affecting intermediate states and control actions, in the tracking performance when using the command filtered backstepping. Some relations that bind the controller gains to maintain performance appear naturally. Finally simulations over a 2D steering robot model are given to illustrate the found results.Peer ReviewedPostprint (author’s final draft

Impedance control of a planar quadrotor with an extended Kalman filter external wrench estimator

In this work we deal with the non-linear control of aerial vehicles under external disturbances. We develop a non-linear velocity controller able to accommodate estimations of the external disturbing forces and moments. To estimate the external actions and at the same time provide improvements on the state estimation we make use of the EKF approach. Finally, we present simulations comparing close loop performance of a system with the proposed methodology implemented against close loop performance of the same controller but without the estimation of the external forces.Postprint (published version

Optimal state observation using quadratic boundedness: application to UAV disturbance estimation

This paper presents the design of a state observer which guarantees quadratic boundedness of the estimation error. By using quadratic Lyapunov stability analysis, the convergence rate and the ultimate (steady-state) error bounding ellipsoid are identified as the parameters that define the behaviour of the estimation. Then, it is shown that these objectives can be merged in a scalarised objective function with one design parameter, making the design problem convex. In the second part of the article, a UAV model is presented which can be made linear by considering a particular state and frame of reference. The UAV model is extended to incorporate a disturbance model of variable size. The joint model matches the structure required to derive an observer, following the lines of the proposed design approach. An observer for disturbances acting on the UAV is derived and the analysis of the performances with respect to the design parameters is presented. The effectiveness and main characteristics of the proposed approach are shown using simulation results.Peer ReviewedPostprint (author's final draft