International conference papers with proceedings

Abstract:This paper presents a controller tuning strategy for a quadrotor MAV carrying a cable-suspended load. In our study, no measurement nor estimation of the load's position is used in the control strategy and only the quadrotor attitude and position are controlled. The tuning of the controllers has been done in order to satisfy mixed H_inf requirements and a pole-location requirement. The resolution is made with an available tool based on non-smooth optimization. The proposed methodology, allowing to find a good trade-off between fast displacements of the MAV and well damped oscillations of the load, is validated in simulation.

Abstract:This paper presents the development of a collaborative event-based control applied to the problem of 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 neighbours. The asymptotic convergence to average consensus or desired formation is depicted via a real-time implementation.

Abstract:This 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 Take-off 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.

Abstract:This 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.

Abstract:Although periodicity simplifies design and analysis in control theory, it results in a conservative usage of resources (because the control signal is computed and updated at the same rate regardless whether is really required or not). The event-triggered paradigm is proposed as a solution to reduce the control updates (and, consequently, the resource utilization) for similar final performance. An event-based digital PID controller is proposed in this paper, where events are enforced on level detection mechanism. Both tracking and regulation problems are discussed. Furthermore, contrary to the original approaches, the controller and control parameters are directly designed in the discrete-time domain. Both continuous- and discrete-time approaches are compared in simulation in terms of frequency of control updates and performance.

Abstract:In this paper, a discrete state feedback Linear Quadratic Regulator (LQR) for event-triggered control is presented. To ensure zero steady state error in the case of such controllers, one normally extends the states with an integral action. Instead of using integral action, the idea is to estimate the disturbance causing the steady state error and use this to extend the states. A Lyapunov-based event triggering function is proposed. Practical results using a gyroscope actuator are presented and compared to a classical time-triggered controller. The obtained results demonstrate the simplicity and efficiency of the proposed approach.

Abstract:This 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.

Abstract:This paper proposes a simple solution for global stabilization of a quadrotor carrying a manipulator arm. The manipulator arm is attached to the lower part of the fuselage of a quadrotor to increase the type of missions achievable. The motion of the arm induces torques and disturbances to the quadrotor causing the loss of stability. This work deals with the stabilization of the quadrotor under such disturbances, by means of a bounded quaternion-based feedback. A set of nonlinear control laws are obtained. First, the attitude control stabilizes the quadrotor to a desired position and angular velocities. Then, the translational dynamics (three independent chains integrators) allow the formulation of a nonlinear control. Both controls consist in saturation functions and allow the stabilization of the quadrotor. Simulations in closed loop show the effectiveness of the proposed algorithm.

Abstract:Event-triggered control is a resource-aware sampling strategy that updates the control value only when a certain condition is satisfied, which denotes event instants. Such a technique allows a reduction of the control's computational cost and communications demand. In this paper, an asynchronous feedback is developed for event-triggered stabilization of a PVTOL (Planar Vertical Take-Off and Landing) system wherein the control loop is closed through an Internet connection. The proposed feedback ensures asymptotic stability to the desired position. Real-time experiments are carried out in order to show the convergence of the PVTOL to the desired position as well as robustness with respect to external disturbances. Results show that the proposed strategy can reduce the number of control updates and consequently reduce the communication traffic over the network without sacrificing performance of the whole system.

Abstract:In this paper, a state-feedback linear-quadratic regulator (LQR) is proposed for event-based control of a linear system. An interesting property of LQRs is that an optimal response of the system can be obtained in accordance to some specifications, like the actuator limits. An integral action is also added in order to not only restrict the study to null stabilization but also to tracking. The idea is to consider an external control loop and stabilize the integral of the error between the measurement and a desired setpoint to track. However, an event-triggered integral can lead to important overshoots when the interval between two successive events becomes large. Therefore, an exponential forgetting factor of the sampling interval is proposed as a solution to avoid such problems. The whole proposal is tested on a real-time system (a gyroscope) in order to highlight its ability, the reduction of control updates and the respect to the actuator limits.

Abstract:In this paper, a universal formula is proposed for event-based stabilization of nonlinear time-delay systems affine in the control. The feedback is derived from the original one proposed by E. Sontag (1989) and previously extended to event-based control of nonlinear non-delay systems. Under the assumption of the existence of a Control Lyapunov-Krasovsky functional (an extension of Control Lyapunov functions for time-delay systems), it enables smooth (except at the origin) asymptotic stabilization while ensuring that the sampling intervals do not contract to zero. Global asymptotic stability is obtain under the small control property assumption. Moreover, the control can be proved to be smooth anywhere under certain conditions. Some simulation results highlight the ability of the proposals.

Abstract:In this paper, an original framework is proposed for the stabilization of a linear system with delays in the measurements: i) an observer estimates the full state information of the plant from a partial measurement, ii) an event-based control technique computes and updates the control signal only when a certain condition is satisfied and iii) an event-based corrector updates the model used to calculate the control law when it deviates from the estimated state. It is notably proved that such a proposal renders the closed-loop system stable for larger delays in the measurements than in the classical continuous-time control case. Simulation results are provided.

Abstract:Although periodicity simplifies design and analysis in control theory, it is no more adapted for embedded and networked cyber-physical systems because it results in a conservative usage of resources. Indeed, the control signal is computed and updated at the same rate regardless whether is really required or not, and is periodically sent on the communication link. On the other hand, event-driven sampling calls for resources whenever they are indeed necessary. An event-based controller is proposed in this paper as a solution to reduce the updates from the controller to the plant. An event-based corrector is also added to reduce the communications from the plant to the controller. The approach is tested for controlling the position of a real-time mini quadrotor helicopter using a motion capture system with deported controller. A reduction of the computing/communication resources utilization is highly demonstrated for similar final performance.

Abstract:Event-triggered control is a sampling strategy that updates the control value only when when some event occurs. This event is usually generated by an event-function that indicates if the control signal must be updated or not. If one excepts self-triggered implementation, event-triggered control requires the evaluation of the event function at each time instant. Unfortunately, in the literature of nonlinear system event-based control, computing the event function is more resource consuming than computing the control itself. Moreover, it requires the knowledge of the Lyapunov function that is not necessarily available. The purpose of this paper is to propose for affine nonlinear systems a new event function that only requires the computation of the control. This reduces the complexity of computing the event and avoids to have the Lyapunov function.

Abstract:Embedded devices using highly integrated circuits must cope with conflicting constraints. They have become more sensitive to variabilities with technology scaling while requiring computational efficiency under even more limited energy storage. Power management techniques, mainly based on Dynamic Voltage and Frequency Scaling (DVFS) algorithms, are hence of great interest. Also, temperature increase/decrease is directly related to the power consumption and platform characteristics highly depend on the temperature. As a result, temperature must be controlled, at least limited. In the present paper, the nonlinearity between power and temperature is analyzed and a thermal-aware DVFS control technique is discussed. The proposed strategy implements a chopped scheme on top of a robust DVFS approach in order to limit the temperature increase. The nonlinearity notably leads to an asymmetry in the temperature behavior, which makes the final attained temperature is higher than in the linear case.

Abstract:In this paper, we propose an original framework for the stabilization of a linear system with delays in the measurements: i) an event-based control technique computes and updates the control signal only when a certain condition is satisfied and ii) an event-based corrector updates the model used to calculate the control law when it deviates from the real measurement (that is when a perturbation occurs). Such a proposal allows a low computational cost as well as a robust behavior. We also prove that it renders the closed-loop system stable for larger delays in the measurements than in the classical continuous-time control case.

Abstract:Many Processor Systems on Chip (MPSoCs) have become tremendously complex systems and more sensitive to variabilities with technology scaling. Globally Asynchronous Locally Synchronous (GALS) designs alleviate such problems by having multiple clocks, each one being distributed on a small area of the chip. Also, power constraints are of great interest for mobile platforms powered by battery and power management techniques, mainly based on Dynamic Voltage and Frequency Scaling (DVFS) algorithms, are hence required. Whereas a closed-loop feedback has been shown as an efficient solution in the monoprocessor case, the present paper is dedicated to a multiprocessor architecture where a decentralized global controller manages the different voltage/frequency domains into a chip. The main innovation of the proposal is the use of event-based methods, where the control updates are event driven. Thus, the communicating instants are decided w.r.t. the dynamics of the system to control. The proposed framework is tested in simulation. It notably highlights a strong reduction in the sampling and communication instants and, consequently, in the energy consumption since the communication consumes a lot in such a MPSoC configuration.

Abstract:Embedded devices using highly integrated circuits must cope with conflicting constraints. They have become more sensitive to variabilities with technology scaling while requiring computational efficiency under even more limited energy storage. Power management techniques, mainly based on Dynamic Voltage and Frequency Scaling (DVFS) algorithms, are hence of great interest. Also, temperature increase/decrease is directly related to the power consumption and platform characteristics highly depend on the temperature. As a result, temperature must be controlled, at least limited. In the present paper, asynchronous thermal-aware DVFS control techniques are discussed. The proposed strategies implement a chopped scheme on top of a robust DVFS approach in order to limit the temperature increase. The asynchronous paradigm comes from the original idea in triggering the periods of oscillation from the monitoring of the internal temperature of the chip.

Abstract:Event-triggered control is a resource-aware sampling strategy that updates the control value only when a certain condition is satisfied, 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 event-triggered stabilization of general nonlinear systems affine 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 sacrificing performance of the whole system. To the best of the authors' knowledge, this is the first time that a nonlinear event-triggered controller is experimentally applied to the attitude stabilization of an unmanned aircraft system.

Abstract:The present work deals with the control and localization problem of wheeled-mobile robots with nonholonomic constraints. In the proposed method a simple nonlinear control law, composed of a position and heading direction controller, is designed to asymptotically stabilize the position error. The control law takes into account the constraints on the control signals in order to avoid saturation of the actuators. Furthermore, this paper considers a method of using the dynamic vehicle model and vehicle's nonholonomic constraints in order to aid position and attitude estimates provided by an Inertial Navigation System (INS). It is shown that dynamic model and vehicle's nonholonomic constraints can reduce the error growth in robot position estimates. Simulations are included to confirm the effectiveness of the proposed scheme.

Abstract:In this paper, an event-based LQR control strategy is proposed and tested on a real-time system, that is a quadrotor mini-helicopter. Contrary to the classical periodic fashion which computes and updates the control law regardless it is really required or not, an event-driven setup allows a resource-aware implementation of the control law - using event-based sampling - while still ensuring equivalent performance. In this paper, we develop an event-based LQR control where two tuning parameters allow to scale both the frequency of events and how quickly respond the algorithm. They notably demonstrate that such an event-based scheme is a valuable solution to reduce the number of samples even in the case of highly unstable systems where the actuators have to be actively controlled.

Abstract:Contrary to the classical (time-triggered) principle that samples the control signal in a periodic fashion, an event-driven control is computed and updated only when the closed-loop system trajectory "sufficiently" changes. This notably enables to save computations while ensuring equivalent performance, but a continuous monitoring is still required to detect events. On the other hand, self-triggered strategy eliminates such a resource utilization in predicting the next activation time. In return, it operates in open loop between updates and robustness is therefore highly concerned. To overcome such a trade-off, we propose in this paper to combine together the self-triggered scheme (for its low computational cost) with the event-based one (for its robustness properties). The study is restricted to linear systems. Some simulations are presented comparing the different proposals.

Abstract:Contrary 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.

Abstract:In this paper, a universal formula is proposed for event-based stabilization of general nonlinear systems affine in the control. The feedback is derived from the original one proposed by Sontag. Under the assumption of the existence of a smooth Control Lyapunov Function, it enables smooth (except at the origin) global asymptotic stabilization of the origin while ensuring that the sampling interval do not contract to zero. Indeed, for any initial condition within any given closed set the minimal sampling interval is proved to be strictly positive. Under homogeneity assumptions the control can be proved to be smooth anywhere and the sampling intervals bounded below for any initial condition.

Abstract:The main contribution of this paper is to develop an experimental platform in order to test some event-based control strategies. Contrary to the time-triggered fashion which calculates the control signal at each sampling time, an event-driven controller updates the control signal only when required. This theoretically allows to reduce the computational cost. In this paper, we propose to firstly test an asynchronous cruise control mechanism. Some first results clearly show a noticeable reduction of the mean control computation cost, which is really encouraging for developing such a platform.

Abstract:This paper deals with the development and implementation of a cheap Micro Attitude and Heading Reference System (AHRS) using low-cost inertial and magnetic sensors. The orientation is parameterized with unit quaternion and the data fusion is done unifying a quaternion linear formulation of Wahba\'s problem with a Multiplicative Extended Kalman Filter. It includes the gyro bias model. The estimation methodology proposed in this work is implemented and evaluated in real time, in order to assess its effectiveness. Special attention was paid to the low power consumption, speed and weight requirements, leading to the selection of a 16-bit microcontroller. The sensor suite is based on a tri-axis accelerometer, a dual axis gyro, a single axis gyro and a tri-axis magnetometer. Furthermore, the system is equipped with a Bluetooth module, which provides wireless capabilities. The total system supply voltage is 3.3 V. The dimension and weight are 60x40x15 mm and 60 g, respectively. The attitude rate estimation is 55.5 Hz.

Abstract:A voltage scalable device is known to be interesting for energy saving. It enables to reduce the general speed of the device and, therefore, its consumption. We already proposed a fast predictive control strategy to deal with this power-performance tradeoff in an electronic device supplied by two voltage levels and a continuously varying frequency. In this paper, the approach is extended to a fully discrete scheme with M possible voltage levels and N frequency levels. The proposed approach clearly gives an important reduction of the energy consumption with a very low control computational cost. Moreover, the control strategy is highly robust to tackle variability since it is not based on any parameters of the system.

Abstract:In 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 by Velasco et al. in CDC (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.

Abstract:With the upcoming nanometric technologies, integrated system performances after fabrication will not be fully predictable. Indeed, the process variations really become huge at the chip scale. This implies to consider global management strategies in order to respect energetic and real-time constraints. Therefore performance estimation and management are today key points in new integrated systems. New strategies for energy management have to be used to meet the energy and real-time constraints. Solutions such as dynamic voltage and frequency scaling (DVFS) have to be considered, they have been explored and have shown significant energy savings while meeting performance requirements. This paper starts with a survey on different solutions for the new problems that arise with the nanometric era. Then, it proposes an energy/performance feedback control algorithm in order to reduce the impact of process variability. Finally, a case study is shown that applies this kind of feedback control algorithm for an embedded application on deep submicron technology. The proposed performance/energy controller is shown to have strong robustness against process variability.

Abstract:A two voltage level electronic device is interesting because the clock frequency and the supply voltage level could be reduced (respecting certain rules) in order to decrease the energy consumption. We proposed in a previous paper a robust control architecture to deal with this power-performance tradeoff and we are now interested in extending this principle for several devices which works together since they are all supplied with the same voltage and clock frequency. Thus, an intuitive multicore control strategy which duplicates the whole monocore architecture as much as devices is compared with a second strategy where the duplication is reduced as much as possible. It appears that the proposal clearly gives a low control computational needs with the same reduction of the energy consumption.

Abstract:A two voltage level electronic device is interesting because the clock frequency and the supply voltage level could be reduced in order to decrease the energy consumption. However, these two quantities have to be controlled respecting certain rules, and decreasing them leads to a reduced computational speed. In this paper a control architecture is proposed to deal with this power-performance tradeoff. First, a fast predictive control technic gives the best computational speed set point to minimize the penalizing high voltage running time. Then, the frequency and the supply voltage are controlled together in order that the measured speed tracks this set point. Finally, the proposal clearly gives an important reduction of the energy consumption. Moreover, the control strategy is robust to process variability and therefore suitable for 45nm, 32nm or smaller implementations.

Abstract:In this paper, some improvements of event-based PID controllers are proposed. These controllers, contrary to a time-triggered one which calculates the control signal at each sampling time, calculate the new control signal only when the measurement signal sufficiently changes. The contribution of this paper is a low computational cost scheme thanks to a minimum sampling interval condition. Moreover, we propose to reduce much more the error margin during the steady state intervals by adding some extra samples just after transients. A cruise control mechanism is used for simulations and a noticeable reduction of the mean control computation cost is finally achieved with similar closed-loop performances to the conventional time-triggered ones.

Abstract:In this paper, some improvements of the simple event-based PID controller presented by K-E Arzen in IFAC WC (1999) are proposed. This controller, contrary to a time-triggered controller which calculates the control signal at each sampling time, calculates the new control signal only when the measurement signal sufficiently changes. In the original work of Arzen, a safety maximum period is added forcing the control to be recomputed even if the measurement signal remains unchanged. The contribution of this paper is to propose a scheme to avoid this re-computation. Besides a noticeable reduction of the mean control computation cost, the performance of the closed loop system is also improved.