Emma Delgado

Generic Approach to Stability Under Time-Varying Delay in Teleoperation: Application to the Position-Error Control of a Gantry Crane

In this paper, we develop a generic approach for modeling a teleoperation setup, as a negative single feedback loop containing a linear time-invariant block and an uncertain time-varying delay. It is not based on specific dynamics of masters and slaves, neither on any control architecture. The main added value of the proposed approach is the possibility of deriving frequency-domain conditions for robust stability in the presence of time-varying delays and parametric uncertainties. To address stability, we choose a primitive result providing a bound of certain delay subsystem. We combine this, with input-output stability criteria and μ-analysis and synthesis techniques, to reach a procedure based on the structured singular value providing less conservative results. Finally, our approach is presented within a suggested flowchart that helps the designer to manage the control parameter ranges and facilitates the gradual achievement of stability, robust stability, and performance properties. As a case study, we consider the Internet-based teleoperation of a gantry crane by means of the position-error control architecture. We have also obtained actual delay bounds appearing with UDP protocol for different Internet locations. Simulation and experimental results confirm the robust performance of the teleoperation system in terms of stability and tracking behavior.

Stability of Teleoperation Systems for Time-Varying Delays by Neutral LMI Techniques

This paper investigates the delay-dependent stability of a teleoperation system based on the transparent Generalized Four-Channel control (G-4C) scheme under time-varying communication delays. To address stability we choose here a primitive result providing a Linear Matrix Inequalities (LMIs) approach based on Lyapunov-Krasovskii functionals. Firstly, the scheme is modeled as the neutral-type differential-delayed equation; that is, the delay affects not only the state but also the state derivative. Secondly, we apply a less conservative stability criteria based on LMIs that are delay dependent and delays time-derivative dependent. The reason is that, for better performance in the case of small delays, we must accept the possibility that stability is lost for large delays. The approach is applied to an example, and its advantages are discussed. As a result, we propose to modify the values of standard controllers in G-4C defining the -4C scheme, which introduces a tuning factor to increase in practical conditions the stable region fixing the desired bounds on time-varying delay, with the particularity of maintaining the tracking properties provided by this transparent control scheme. The simulation results justify the proposed control architecture and confirm robust stability and performance.

Brief Sonar-based robot navigation using nonlinear robust observers

This paper addresses the sonar-based navigation of mobile robots. The extended Kalman filtering (EKF) technique is considered, but from a deterministic, nonstochastic, point of view. For this problem, new results are presented on the robustness of the nonlinear observation scheme. The original feature is that the region-of-convergence question is posed in its complete nonlinear framework, that is, considering the dynamics not only of the estimation error @z(t), but also of the covariance matrix P(t). In this way the approach followed makes less conservative the treatment and improves the convergence analysis. The proposed ideas were tested successfully on simulation experiments of a mobile platform.

Basic Send-on-Delta Sampling for Signal Tracking-Error Reduction

This paper investigates the dynamic selection of an appropriate threshold for basic Send-on-Delta (SoD) sampling strategies, given an available transmission rate to reduce the signal tracking-error. The paper formulates the error-reduction principle and proposes an algorithm that calculates, in real time, the amplitude threshold value (also called delta value) for a desired mean transmission rate. The algorithm is implemented to be computed in a Send-on-Delta driver and is tested with three signals that match the step response of a second order control system. Comparison results with a conformant periodic transmission strategy reveals that it improves deeply the tracking-error while maintaining the desired average throughput.

Network Adaptive Deadband: NCS data flow control for shared networks.

This paper proposes a new middleware solution called Network Adaptive Deadband (NAD) for long time operation of Networked Control Systems (NCS) through the Internet or any shared network based on IP technology. The proposed middleware takes into account the network status and the NCS status, to improve the global system performance and to share more effectively the network by several NCS and sensor/actuator data flows. Relationship between network status and NCS status is solved with a TCP-friendly transport flow control protocol and the deadband concept, relating deadband value and transmission throughput. This creates a deadband-based flow control solution. Simulation and experiments in shared networks show that the implemented network adaptive deadband has better performance than an optimal constant deadband solution in the same circumstances.

Stability of Teleoperation Systems by Delay-dependent Neutral LMI Techniques

In this work we study the stability of several standard teleoperation schemes. This problem is usually addressed by frequency domain Laplace techniques or by passivity techniques. We use an LMI approach based on Lyapunov-Krasovskii functionals. Firstly, the schemes are modelled as differential-delayed equations which are of the neutral type, that is, the delay affects not only the state but also the state derivative. Secondly, we apply stability results that are delay-dependent, the reason is that for better performance for small delays, we must accept the possibility that stability is lost for large delays. The proposed approach is applied to an example, and advantages are discussed

Stability of teleoperation systems for time-varying delays by Lyapunov-Krasovskii and frequencial techniques

This work presents a stability analysis for an architecture for teleoperating a laboratory crane using haptic devices. The teleoperation scheme chosen is the 2-channel position error (PE) architecture. This scheme is modeled first by state-space equations testing that the system is Hurwitz stable for zero delay and calculating the maximum constant value of the delay hmax > 0 for which the nominal system (constant delay) is asymptotically stable. Then, by frequencial Laplace techniques, the delay system to be analyzed is transformed in such a way that it becomes a feedback interconnection of a linear time-invariant plant and a time-delay operator. In this way, we obtain the upper bound on the time-varying delay for each nominal value in the interval 0 < h ≤ hmax. Final discussions are provided regarding expected tracking capabilities and agreement of the theory and simulation results, which are satisfactory.

Four-Channel Teleoperation with Time-Varying Delays and Disturbance Observers

This paper addresses the robust stability of teleoperated systems under the four-channel architecture, affected by time-varying communication delays and using disturbance observers. It is based on our previous work which provides a framework for robust stability against delays with bounded variation and a bounded time-derivative, using structured singular values (SSV). The main new feature here is the inclusion of disturbance observers (DOBs). The DOB concept is well-documented and relevant to many applications, since only position (but not force) measurements are usually available. In this paper, we adapt two DOBs (master and slave) to our generic framework, by representing them as stable, fast filters affected by the uncertainty in the plant modelling. Our main result is an SSV test to verify robust stability. The simulation results confirm the usefulness of this approach.

Passivity framework and traffic reduction for the teleoperation of a gantry crane

Teleoperation over shared networks like Internet can take advantage of the deadband approach to reduce data traffic. In this work a passivity-based framework to teleoperate a three-dimensional force-feedback system with deadband control is designed and implemented. The teleoperated slave is a gantry crane and the teleoperation master is a haptic device controlled by a human operator. A deadband reconstruction algorithm based on energy supervision is presented, which preserves passivity of the deadband controlled communication for arbitrary time delays. Experiments to determine the framework parameters are made, and they shows that the passivity of the whole system is preserved, even with variable delays.

Stability of teleoperation systems under time-varying delays by using Lyapunov-Krasovskii techniques

Abstract This paper investigates the stability of a teleoperation system under time-varying communication delays. The system is a laboratory platform consisting on a scale model of a gantry crane, teleoperated by means of a haptic device. This paper focuses on the problems arising from the time-varying nature of the UDP communication delay. First, the actual delay is investigated and bounds on its magnitude and on its time-derivative are estimated, emulating different geographical connections. Second, a recent Lyapunov-Krasovkii technique taken from the literature (Zhao et al. 2007) is applied to the model of the system and stability bounds are obtained for the position error (PE) architecture. The method is applied for different controller parameters and delay bounds, and it is compared to a frequency-domain technique (Kao and Rantzer, 2007), showing reasonably non-conservative results.