Philippe Müllhaupt

Velocity-Scheduling Control for a Unicycle Mobile Robot: Theory and Experiments

Improvement over classical dynamic feedback linearization for a unicycle mobile robots is proposed. Compared to classical extension, the technique uses a higher-dimensional state extension, which allows rejecting a constant disturbance on the robot rotational axis. The proposed dynamic extension acts as a velocity scheduler that specifies, at each time instant, the ideal translational velocity that the robot should have. By using a higher-order extension, both the magnitude and the orientation of the velocity vector can be generated, which introduces robustness in the control scheme. Stability for both asymptotic convergence to a point and trajectory tracking is proven. The theoretical results are illustrated first in simulation, and then experimentally on the autonomous mobile robot Fouzy III.

A musculoskeletal shoulder model based on pseudo-inverse and null-space optimization

The goal of the present work was assess the feasibility of using a pseudo-inverse and null-space optimization approach in the modeling of the shoulder biomechanics. The method was applied to a simplified musculoskeletal shoulder model. The mechanical system consisted in the arm, and the external forces were the arm weight, 6 scapulo-humeral muscles and the reaction at the glenohumeral joint, which was considered as a spherical joint. The muscle wrapping was considered around the humeral head assumed spherical. The dynamical equations were solved in a Lagrangian approach. The mathematical redundancy of the mechanical system was solved in two steps: a pseudo-inverse optimization to minimize the square of the muscle stress and a null-space optimization to restrict the muscle force to physiological limits. Several movements were simulated. The mathematical and numerical aspects of the constrained redundancy problem were efficiently solved by the proposed method. The prediction of muscle moment arms was consistent with cadaveric measurements and the joint reaction force was consistent with in vivo measurements. This preliminary work demonstrated that the developed algorithm has a great potential for more complex musculoskeletal modeling of the shoulder joint. In particular it could be further applied to a non-spherical joint model, allowing for the natural translation of the humeral head in the glenoid fossa.

Brief paper: A numerical sufficiency test for the asymptotic stability of linear time-varying systems

A numerical sufficiency test for the asymptotic stability of linear time-varying Hurwitz systems is proposed. The algorithmic procedure constructs a bounding tube in which the state is guaranteed to stay. The continuous-time system is evaluated at discrete time instants, for which successive quadratic Lyapunov functions are generated. The tube is constructed based on: (i) a conservative estimate of the state evolution, from a discrete time instant to the next, obtained from the corresponding Lyapunov function, and (ii) re-evaluation of the tube diameter at each discrete time instant to account for variations in the plant matrix. The numerical test is illustrated in simulation via both a stable and an unstable system.

Quotient Submanifolds for Static Feedback Linearization

A procedure for finding locally the linearizing output of a single input nonlinear affine system is proposed. It relies on successive integrations of one-dimensional distributions and projections along these submanifolds. The algorithm proceeds recursively reducing the dimension one by one of both the number of coordinates and the number of vector fields, until the solution is obtained. A variant of the algorithm is also proposed, which does not require the computation of the full initial distribution. The proof of convergence of this second algorithm shows the importance of a new anti-symmetrical product. Besides providing a new insight into the involutivity condition, the algorithm can lead to a simple way of integrating the system of partial differential equations defining the linearizing output.

Quotient method for controlling the acrobot

This paper describes a two-sweep control design method to stabilize the acrobot, an input-affine under-actuated system, at the upper equilibrium point. In the forward sweep, the system is successively reduced, one dimension at a time, until a two-dimensional system is obtained. At each step of the reduction process, a quotient is taken along one-dimensional integral manifolds of the input vector field. This decomposes the current manifold into classes of equivalence that constitute a quotient manifold of reduced dimension. The input to a given step becomes the representative of the previous-step equivalence class, and a new input vector field can be defined on the tangent of the quotient manifold. The representatives remain undefined throughout the forward sweep. During the backward sweep, the controller is designed recursively, starting with the two-dimensional system. At each step of the recursion, a well-chosen representative of the equivalence class ahead of the current level of recursion is chosen, so as to guarantee stability of the current step. Therefore, this stabilizes the global system once the backward sweep is complete. Although stability can only be guaranteed locally around the upper equilibrium point, the domain of attraction can be enlarged to include the lower-equilibrium point, thereby allowing a swing-up implementation. As a result, the controller does not require switching, which is illustrated in simulation. The controller has four tuning parameters, which helps shape the closed-loop behavior.

Step by step robust nonlinear PI for attitude stabilisation of a four-rotor mini-aircraft

Based on the Euler angles parameterization, a new approach for the attitude control of a vertical take-off and landing (VTOL) quadrotor aircraft is proposed. It rests on the combination of the backstepping technique and a nonlinear robust PI controller. The integral action gain is nonlinear and based on a switching function that ensures a robust behaviour for the overall control law. One of the strengths of the proposed approach is its robustness with respect to plant parameters uncertainties. The proposed approach has been tested in simulation and shows good performance.

Strategy for the Control of a Dual-stage Nano-positioning System with a Single Metrology

A double-stage feedback control structure for a double-stage mechanical system, with a single optical metrology is developed to reach nanometer accuracy at high bandwidth over large displacements. A piezoelectric stack actuator is used for fine positioning, while a permanent magnet (PM) stepper motor handles the coarse positioning. Two different control approaches are compared for driving the PM stepper motor, while a classical PID controller is designed to drive the piezoelectric actuator. Since only a single measurement device is used, the references for both control loops (fine and coarse) must be appropriately obtained. An adequate control structure including a partial observer is designed so as to take into account the influence of the fine actuator on the position estimation of the coarse actuator. The complete control mechanism and strategy ensure the tracking of the real reference with sufficient accuracy and bandwidth

Improving tokamak vertical position control in the presence of power supply voltage saturation

The control of the current, position and shape of an elongated cross-section tokamak plasma is complicated by the so-called instability of the current vertical position. Linearized models all share the feature of a single unstable eigenmode, attributable to this vertical instability of the plasma equilibrium movement, and a large number of stable or marginally stable eigenmodes, attributable to zero or positive resistance in all other model circuit equations. Due to the size and therefore cost of the ITER tokamak, there will naturally be smaller margins in the poloidal field coil power supplies, implying that the feedback control will experience actuator saturation during large transients due to a variety of plasma disturbances. Current saturation is relatively benign, due to the integrating nature of the tokamak, resulting in a reasonable time horizon for strategically handling the approach to saturation which leads to the loss of one degree of freedom in the feedback control for each saturated coil. On the other hand, voltage saturation is produced by the feedback controller itself, with no intrinsic delay. This paper presents a feedback controller design approach which explicitly takes saturation of the power supply voltage into account when producing the power supply demand signals. We consider the vertically stabilizing part of the ITER controller (fast controller) with one power supply and therefore a single saturated input. We consider an existing ITER controller and enlarge its region of attraction to the full null controllable region by adding a continuous nonlinearity into the control. In a system with a single unstable eigenmode and a single stable eigenmode we have already provided a proof of the asymptotical stability of the closed loop system, and we have examined the performance of this new continuous nonlinear controller. We have subsequently extended this analysis to a system with a single eigenmode and multiple stable eigenmodes. The method requires state feedback control, and therefore a reconstruction of the states is indispensable. We discuss the feasibility of extracting these states from the available diagnostic information as well as other implementation details. As a complement to our ITER simulations we confirm the enlargement of the region of attraction by the new controller by a JET simulation.

Interactive 3D Simulation of Flat Systems: The SpiderCrane as a Case Study

In order to display the main characteristics of a well-known flat system, an interactive 3D simulation of SpiderCrane has been developed using Ejs(Easy Java Simulations) and Matlab/Simulink. The application allows users to set up different trajectories and introduce disturbances in a very visual and attractive way.

End-to-end adaptation scheme for ubiquitous remote experimentation

Remote experimentation is an effective e-learning paradigm for supporting hands-on education using laboratory equipment at distance. The current trend is to enable remote experimentation in mobile and ubiquitous learning. In such a context, the remote experimentation software should enable effective telemonitoring and teleoperation, no matter the kind of device used to access the equipment. It should also be sufficiently lenient so as to handle the rapidly evolving wireless and mobile communication environment. While the current Internet bandwidth allows remote experimentation to work flawlessly on fixed connections such as LANs, mobile users suffer from both the versatile nature of wireless communications and the limitation of the mobile devices. These conditions impose that the remote experimentation software should integrate adaptation features. For effective ubiquitous remote experimentation, it should ideally be guaranteed that the information representing the state of the remote equipment is rendered (to the end user) at the same pace at which it has been acquired, yet possibly at the cost of a somewhat minimal time delay between the acquisition and rendering phases. In this respect, an end-to-end adaptation scheme is proposed that explicitly handles the inherent variability of the connection and the versatility of the mobile devices considered in ubiquitous remote experimentation. Instead of relying on a stochastic approach, the proposed adaptation scheme relies on a deterministic mass-balance equivalence model. The effectiveness of the proposed adaptation scheme is demonstrated in critical conditions corresponding to remote experimentation carried out using a PDA over a Bluetooth link.