Control of bimanual rhythmic movements: Trading efficiency for robustness depending on the context

This paper investigates how the efficiency and robustness of a skilled rhythmic task compete against each other in the control of a bimanual movement. Human subjects juggled a puck in 2D through impacts with two metallic arms, requiring rhythmic bimanual actuation. The arms kinematics were only constrained by the position, velocity and time of impacts while the rest of the trajectory did not influence the movement of the puck. In order to expose the task robustness, we manipulated the task context in two distinct manners: the task tempo was assigned at four different values (hence manipulating the time available to plan and execute each impact movement individually); and vision was withdrawn during half of the trials (hence reducing the sensory inflows). We show that when the tempo was fast, the actuation was rhythmic (no pause in the trajectory) while at slow tempo, the actuation was discrete (with pause intervals between individual movements). Moreover, the withdrawal of visual information encouraged the rhythmic behavior at the four tested tempi. The discrete versus rhythmic behavior give different answers to the efficiency/robustness trade-off: discrete movements result in energy efficient movements, while rhythmic movements impact the puck with negative acceleration, a property preserving robustness. Moreover, we report that in all conditions the impact velocity of the arms was negatively correlated with the energy of the puck. This correlation tended to stabilize the task and was influenced by vision, revealing again different control strategies. In conclusion, this task involves different modes of control that balance efficiency and robustness, depending on the context. © 2008 Springer-Verlag.

Time-optimal control of a 3-level quantum system and its generalization to an n-level system

We solve the problem of steering a three-level quantum system from one eigen-state to another in minimum time and study its possible extension to the time-optimal control problem for a general n-level quantum system. For the three-level system we find all optimal controls by finding two types of symmetry in the problem: ℤ2 × S3 discrete symmetry and S1 continuous symmetry, and exploiting them to solve the problem through discrete reduction and symplectic reduction. We then study the geometry, in the same framework, which occurs in the time-optimal control of a general n-level quantum system. © 2007 IEEE.

Rhythmic feedback control of a blind planar juggler

The paper considers the feedback stabilization of periodic orbits in a planar juggler. The juggler is "blind," i.e, he has no other sensing capabilities than the detection of impact times. The robustness analysis of the proposed control suggests that the arms acceleration at impact is a crucial design parameter even though it plays no role in the stability analysis. Analytical results and convergence proofs are provided for a simplified model of the juggler. The control law is then adapted to a more accurate model and validated in an experimental setup. © 2007 IEEE.

Time-optimal control of a 3-level quantum system and its generalization

We solve the problem of steering a three-level quantum system from one eigen-state to another in minimum time and study its possible extension to the time-optimal control problem for a general n-level quantum system. For the three-level system we find all optimal controls by finding two types of symmetry in the problems: ℤ × S3 discrete symmetry and 51 continuous symmetry, and exploiting them to solve the problem through discrete reduction and symplectic reduction. We then study the geometry, in the same framework, which occurs in the time-optimal control of a general n-level quantum system. Copyright ©2007 Watam Press.

Group coordination and cooperative control of steered particles in the plane

The paper overviews recent and ongoing efforts by the authors to develop a design methodology to stabilize isolated relative equilibria in a kinematic model of identical particles moving in the plane at unit speed. Isolated relative equilibria correspond to either parallel motion of all particles with fixed relative spacing or to circular motion of all particles about the same center with fixed relative headings. © Springer-Verlag Berlin Heidelberg 2006.

Feedback control of impact dynamics: The bouncing ball revisited

We study the the design of a tracking controller for the popular bouncing ball model: the continuous-time actuation of a table is used to control the impacts of the table with a bouncing ball. The proposed control law uses the impact times as the sole feedback information. We show that the acceleration of the table at impact plays no role in the stability analysis but is an important parameter for the robustness of the feedback system to model uncertainty, in particular to the uncertainty on the coefficient of restitution. © 2006 IEEE.

Timing feedback control of a rhythmic system

This paper addresses the question relative to the role of sensory feedback in rhythmic tasks. We study the properties of a sinusoidally vibrating wedge-billiard as a model for 2-D bounce juggling. If this wedge is actuated with an harmonic sinusoidal input, it has been shown that some periodic orbits are exponentially stable. This paper explores an intuitive method to enlarge the parametric stability region of the simplest of these orbits. Accurate processing of timing is proven to be an important key to achieve frequency-locking in rhythmic tasks. © 2005 IEEE.

Improving the performance of low-gain designs for bounded control of linear systems

An online scheduling of the parameter ensuring in addition to closed loop stability was presented. Attention was given to saturated linear low-gain control laws. Null controllability of the considered linear systems was assumed. The family of low gain control laws achieved semiglobal stabilization.

Delayed control of a Moore-Greitzer axial compressor model

Several feedback control laws have appeared in the literature concerning the stabilization of the nonlinear Moore-Greitzer axial compression model. Motivated by magnitude and rate limitations imposed by the physical implementation of the control law, Larsen et al. studied a dynamic implementation of the S-controller suggested by Sepulchre and Kokotović. They showed the potential benefit of implementing the S-controller through a first-order lag: while the location of the closed-loop equilibrium achieved with the static control law was sensitive to poorly known parameters, the dynamic implementation resulted in a small limit cycle at a very desirable location, insensitive to parameter variations. In this paper, we investigate the more general case when the control is applied with a time delay. This can be seen as an extension of the model with a first-order lag. The delay can either be a result of system constraints or be deliberately implemented to achieve better system behavior. The resulting closed-loop system is a set of parameter-dependent delay differential equations. Numerical bifurcation analysis is used to study this model and investigate whether the positive results obtained for the first-order model persist, even for larger values of the delay.

Shape signifiers for control of a low-order compressor model

Rotating stall and surge, two instability mechanisms limiting the performance of aeroengines compressors, are studied on the third-order Moore-Greitzer model. The skewness of the compressor characteristic, a single parameter shape signifier, is shown to determine the key qualitative properties of feedback control.

Base Isolation of Buildings for Control of Ground-borne Vibration

These works, edited by Malcolm Crocker, positioned Wiley as a major player in the acoustics reference market.