General Formula for Event-Based Stabilization of Nonlinear Systems with Delays in the State

International audienceIn this chapter, a universal formula is proposed for event-based stabilization of nonlinear systems affine in the control and with delays in the state. The feedback is derived from the seminal law proposed by E. Sontag (1989) and then extended to event-based control of affine nonlinear undelayed systems. Under the assumption of the existence of a control Lyapunov-Krasovskii functional (CLKF), the proposal enables smooth (except at the origin) asymptotic stabilization while ensuring that the sampling intervals do not contract to zero. Global asymptotic stability is obtained under the small control property assumption. Moreover, the control can be proved to be smooth anywhere under certain conditions. Simulation results highlight the ability of the proposed formula. The particular linear case is also discussed

Simple Lyapunov Sampling for Event-Driven Control

International audienceIn this paper, a simple Lyapunov sampling is proposed. Contrary to a periodic fashion which samples the system uniformly in time, an event-based scheme updates the control signal only when the system trajectory sufficiently changes. Furthermore, the present triggering mechanism is based on a Lyapunov function in order to enforce the events only when required from a stability point of view. Nevertheless, whereas the Lyapunov sampling mechanism initially introduced in Velasco et al. (2009) requires to execute a computationally heavy off-line algorithm, a fully on-line version is developed in this paper. The different approaches are tested (in simulation and practice) to show the efficiency of such an event-based control and, eventually, the performance remains ensured even if the constraint on the stability is relaxed

Event-triggered attitude control for flying robots using an event approach based on the control

International audienceThis paper presents the development of a quaternion-based nonlinear event-triggered control for the attitude stabilization of Flying robots. Firstly, it is proved the existence of a Control Lyapunov Function. Unlike some previously proposed schemes, the aim of this paper is to propose a new and simpler event function. The control law ensures the asymptotic stability of the closed-loop system to the desired attitude. The approach is validated in real-time using a quadrotor mini-helicopter. The experiments show that the event driven controller reduces the control update without deteriorating the closed-loop system performance

Event-triggered attitude control for flying robots using an event approach based on the control

International audienceThis paper presents the development of a quaternion-based nonlinear event-triggered control for the attitude stabilization of Flying robots. Firstly, it is proved the existence of a Control Lyapunov Function. Unlike some previously proposed schemes, the aim of this paper is to propose a new and simpler event function. The control law ensures the asymptotic stability of the closed-loop system to the desired attitude. The approach is validated in real-time using a quadrotor mini-helicopter. The experiments show that the event driven controller reduces the control update without deteriorating the closed-loop system performance

Biomimetic-Based Output Feedback for Attitude Stabilization of Rigid Bodies: Real-Time Experimentation on a Quadrotor

International audienceThe present paper deals with the development of bounded feedback control laws mimicking the strategy adopted by flapping flyers to stabilize the attitude of systems falling within the framework of rigid bodies. Flapping flyers are able to orient their trajectory without any knowledge of their current attitude and without any attitude computation. They rely on the measurements of some sensitive organs: halteres, leg sensilla and magnetic sense, which give information about their angular velocity and the orientation of gravity and magnetic field vectors. Therefore, the proposed feedback laws are computed using direct inertial sensors measurements, that is vector observations with/without angular velocity measurements. Hence, the attitude is not explicitly required. This biomimetic approach is very simple, requires little computational power and is suitable for embedded applications on small control units. The boundedness of the control signal is taken into consideration through the design of the control laws by saturation of the actuators' input. The asymptotic stability Micromachines 2015, 6 994 of the closed loop system is proven by Lyapunov analysis. Real-time experiments are carried out on a quadrotor using MEMS inertial sensors in order to emphasize the efficiency of this biomimetic strategy by showing the convergence of the body's states in hovering mode, as well as the robustness with respect to external disturbances

Event-based control strategy for consensus of a group of VTOL-UAVs

International audienceThis paper presents the development of a collaborative event-based control applied to the problem of consensus and formation of a group of VTOL-UAVs (Vertical Takeoff and Landing, Unmanned Aerial Vehicles). Each VTOL-UAV decides, based on the difference of its current state (linear position and velocity) and its latest broadcast state, when it has to send a new value to its neighbors. The asymptotic convergence to average consensus or desired formation is depicted via numerical simulations

Attitude Stabilization of a Quadrotor by Means of Event-Triggered Nonlinear Control

International audienceEvent-triggered control is a resource-aware sampling strategy that updates the control value only when a certain condition is satis ed, which denotes event instants. Such a technique allows to reduce the control computational cost and communications. In this paper, a quaternion-based feedback is developed for event-triggered attitude stabilization of a quadrotor mini-helicopter. The feedback is derived from the universal formula for eventtriggered stabilization of general nonlinear systems a ne in the control. The proposed feedback ensures the asymptotic stability to the desired attitude. Real-time experiments are carried out in order to show the convergence of the quadrotor states to the desired attitude as well as the robustness with respect to external disturbances. Results show that the proposed control can reduce by 80 % the communications of the embedded system without sacri cing performance of the whole system. To the best of the authors' knowledge, this is the rst time that a nonlinear event-triggered controller is experimentally applied to the attitude stabilization of an unmanned aircraft system

Nonlinear control of a nano-hexacopter carrying a manipulator arm

International audienceThis paper proposes a simple solution for stabilization of a nano-hexacopter carrying a manipulator arm in order to increase the type of missions achievable by these types of systems. The manipulator arm is attached to the lower part of the hexacopter. The motion of the arm induces a change of the center of mass of the whole body, which induces torques which can produce the loss of stability. The present work deals with the stabilization of the whole system-that is hexacopter and arm-by means of a set of nonlinear control laws. First, an attitude control, stabilizes the hexacopter to a desired attitude taking into account the movement of the arm. Then, a suitable virtual control and the translational dynamics allow the formulation of a nonlinear controller, which drives the aerial vehicle to a desired position. Both controls consist in saturation functions. Experimental results validate the proposed control strategy and compares the results when the motion of the arm is taken into account or not

Self-triggered control for the stabilization of linear systems

International audienceContrary to the classical (time-triggered) principle that samples the system states and calculates the control signal in a periodic fashion, a self-triggered control predicts the next time at which the states must be sampled and the control signal updated and applied. The main advantage of self-triggered control implementation is that it eliminates the resource utilization for continuously monitoring the states. In this paper, a new self-triggered control strategy is proposed. We propose to emulate the universal event-based formula - developed in previous work - to calculate the feedback law and the next activation time. We claim that our proposal behaves better than the existing self-triggered approaches due to the universal formula properties. The study is restricted to the stabilization of linear systems. Some simulations are presented comparing the proposal with existing techniques

Simple Lyapunov Sampling for Event-Driven Control

International audienceIn this paper, a simple Lyapunov sampling is proposed. Contrary to a periodic fashion which samples the system uniformly in time, an event-based scheme updates the control signal only when the system trajectory sufficiently changes. Furthermore, the present triggering mechanism is based on a Lyapunov function in order to enforce the events only when required from a stability point of view. Nevertheless, whereas the Lyapunov sampling mechanism initially introduced in Velasco et al. (2009) requires to execute a computationally heavy off-line algorithm, a fully on-line version is developed in this paper. The different approaches are tested (in simulation and practice) to show the efficiency of such an event-based control and, eventually, the performance remains ensured even if the constraint on the stability is relaxed