Aymeric Kron

Evaluation of the lambda model for human postural control during ankle strategy

Abstract.An accurate modeling of human stance might be helpful in assessing postural deficit. The objective of this article is to validate a mathematical postural control model for quiet standing posture. The postural dynamics is modeled in the sagittal plane as an inverted pendulum with torque applied at the ankle joint. The torque control system is represented by the physiological lambda model. Two neurophysiological command variables of the central nervous system, designated λ and μ, establish the dynamic threshold muscle at which motoneuron recruitment begins. Kinematic data and electromyographic signals were collected on four young males in order to measure small voluntary sway and quiet standing posture. Validation of the mathematical model was achieved through comparison of the experimental and simulated results. The mathematical model allows computation of the unmeasurable neurophysiological commands λ and μ that control the equilibrium position and stability. Furthermore, with the model it is possible to conclude that low-amplitude body sway during quiet stance is commanded by the central nervous system.

Robust Guidance and Control Algorithms using Constant Flight Path Angle for Precision Landing on Mars

This paper proposes four guidance laws aimed at reducing the most significant sources of landing dispersion during atmospheric entry at Mars. The autonomous guidance algorithms rely on simple analytic and semi-analytic solutions that prescribe segments of constantflightpath angles (FPAs) that match the trajectory constraints in terms of desired final altitude, velocity and downrange. Two one-segment solutions and two two-segment solutions are presented. A nonlinear dynamic inversion of the translational dynamics and a robust attitude controller, designed with the Robust Modal Control technique, complete the guidance and control system whose performance is demonstrated through numerical simulations of a Mars entry scenario.

Robust synthesis of static output feedback controller for Mars entry

Abstract This paper addresses the 6 degrees-of-freedom (DOF) control of a Mars Lander Module (LM) during its aerodynamic entry phase. It focuses on the robust synthesis of a static output feedback for the attitude dynamics. It presents a systematic way to design the controller using a robust modal control technique: the feedback gain tuning. The robustness is obtained by constraining pole placement over three models selected to represent the different flying conditions. Monte-Carlo simulations are performed to demonstrate the robust performance of the controller. The simulator includes realistic model of the atmosphere (European Mars Climate Database) and Mars gravity (J2).

CONTROL OF MARS GUIDED ENTRY (PART II): ROBUST NONLINEAR DYNAMICS INVERSION

Abstract This paper addresses the 6 degrees-of-freedom control of a Mars Lander Module during its aerodynamic entry phase. It focuses on Robust Nonlinear Dynamics Inversion (RDI) technique. On one hand, RDI is shown to be efficient for translation controller synthesis. On the other hand, this technique is shown to be inappropriate for attitude control except for the gyroscopic torque cancellation which could be coupled with a robust static controller. Monte-Carlo simulations are performed to demonstrate the robust performance of the 6 DOF control software. The nonlinear simulator includes a realistic model of the atmosphere (European Mars Climate Database) and Mars gravity (J2).

A Matlab toolbox for LMI-based analysis and synthesis of LPV/LFT self-scheduled H ∞ control systems

When controlling a Linear Parameter Varying (LPV) system, a LPV regulator is advisable, since it ensures better performance than a simple Linear Time Invariant actually does. In fact, real-time scheduling to the variations of the system allows the achievement of stability and performance requirements for a number of operating points. Within this setting, this paper discusses a Matlab toolbox achieving a self-scheduled LPV controller for an LPV model of the plant, robust in an H∞ sense in the face of uncertainties affecting the systems dynamics, through a Linear Matrix Inequality approach. The resulting algorithm alternatively implements synthesis and analysis steps, until the desired closed-loop performance level has been reached or no improvement between two successive steps arises.

Mu-analysis Based Verification and Validation of Autonomous Satellite Rendezvous Systems

Abstract This paper presents a Verification and Validation (VV) framework that integrates Linear Fractional Transformation (LFT) and mu-analysis with simulation based VV. This innovative VV framework is developed for the terminal phase of Mars Sample Return autonomous orbital rendezvous around Mars. The concept consists in steering a global nonlinear time simulations environment in function of linear robustness analysis in order to establish the global system properties more efficiently than with a traditional Monte-Carlo simulations-based framework. This paper presents the technique with a proof of concept that compares the traditional approach with this new VV framework. The analysis of the results highlights the efficiency of the technique.

Attitude Guidance and Control for Synchronized Maneuvers About a Fixed Rotation Axis

The attitude guidance and control problem of rotating in synchronization two rigid bodies from their current attitude to their desired attitude is addressed, where the instantaneous axis of rotation must be aligned as closely as possible with an externally defined desired axis of rotation that is fixed in the inertial frame. The approach presented in this paper is based on the fact that the angular rate vector is collinear with the axis of rotation. Therefore, by controlling the direction of the angular rate, the axis of rotation is also controlled. A sliding mode control strategy is designed to minimize the quaternion error while at the same time to track a reference angular rate direction defined by the commanded fixed axis. Simulation results are provided to demonstrate the performance of the proposed guidance and control approach in a realistic scenario that considers parameter uncertainties, measurement noises, and actuation limits.

Control of mars guided entry (part I): Robust self-scheduling modal control

Abstract Robust Modal Control theory can be extended in order to design Self-Scheduling controllers. In this paper, the technique is applied to the control of a Lander Module attitude dynamics during Mars atmospheric Entry. The extra degrees-of-freedom brought by self-scheduling controllers with respect to non scheduled ones makes it possible to improve some structural aspects of the designed controller which is able to adapt itself to the flight conditions: reduced gain level to limit actuators sollicitation, or reduced order to simplify the on-board implementation of the controller.

Integrated Structure/Control Optimisation Applied to the BIOMASS Earth Observation Mission

A new approach of an integrated structure/control co-design methodology is developed based on the recognition that a high degree of coupling exists between the control and structural disciplines in the control of flexible space structures. A unified computational framework is developed gathering methodologies and tools coming from robust control theory and advanced worst case analysis techniques together with mechanical modelling engineering tools. Within this environment, design iterations consist in updating critical control and structure design variables by assessing controlled performance while minimizing structural mass. The optimisation process utilises a Differential Evolution algorithm. Multiobjective optimisation is also supported highlighting the compromise between mechanical and control objectives. The Linear Fractional Transformation formalism provides an uncertain representation of the spacecraft dynamics which is considered during the controller synthesis and analysis processes together, managed in the H∞/μ setting. Traditional Monte-Carlo simulations evaluate the robust performance of the controller design whilst optimisation-based worst-case analysis has been implemented to increase the efficiency of the worst-case extraction. This paper presents the work supported by the European Space Agency in the scope of the robust AOCS technology program initiated to support the BIOMASS mission; a candidate for the Earth Explorer Core 7 missions.

An Integrated Analytical/Numerical Framework for Verication and Validation of Attitude Control Systems for Flexible Satellites

Modern geostationary telecommunication satellites typically employ large antenna and solar arrays which can generate flexible modes close to the bandwidth of the attitude control system. Combined with uncertainties in mass and inertias and effects such as fuel sloshing in large tanks without membranes, such dynamics represent a particular problem for accurate attitude control. This paper describes a framework for assessing the effects of these uncertain dynamics on the stability and performance of attitude control systems, using a combination of analytical and numerical tools. We develop detailed Linear Fractional Transformation (LFT)-based models of the uncertainties present in a modern telecom satellite and apply -analysis to these models in order to generate robustness guarantees. We validate these models and results by cross-checking them against worst-case analysis results produced by global optimisation algorithms applied to the original system model. The proposed integrated analytical/numerical framework is shown to provide more reliable results, and to be significantly more efficient, than standard Monte-Carlo simulations. I. Introduction A key challenge in the design of modern telecom satellites is the assessment of the effects of flexible modes generated by large appendages on the satellite’s attitude control system. Both the frequency and damping of these flexible modes are very difficult to predict accurately, and are typically only specified to lie within certain minimum and maximum bounds. The problem is compounded by the possibility of interactions with other sources of uncertainty in the system, in particular the effects of fuel sloshing in large tanks that are required in order to reach and maintain geostationary orbits. Attitude control systems for telecom satellites are generally designed using simplified models which do not include all sources of uncertainty and variation present in the system. This necessitates a formal process of verification and validation which assess the stability and performance properties of the controller when implemented on a high-fidelity simulation model. The standard approach to this problem adopted by satellite manufacturers is to combine tests on configurations that (based on engineering judgement) are considered likely to be problematic, with extensive Monte Carlo simulation campaigns in order to accumulate statistical confidence in the robustness properties of the controller. Such campaigns can have significant computational and cost overheads for manufacturers, since very large numbers of simulations are required in order to provide strong statistical guarantees of robustness. 1 In addition, there is now accumulating evidence that such campaigns can fail to reliably assess worst-case behaviour, especially for systems which are subject to flexible dynamics. 2–5