Henryk Flashner

Mechanics and Control

Two dozen papers promote the use of the advanced mechanics method in control theory, emphasizing the control of nonlinear mechanical systems subject to uncertainty. They cover control methodology, applications to aerospace systems, and the control of mechanical systems. Reproduced from typescript. A

Robust fuzzy logic control of mechanical systems

An approach for the design of fuzzy control laws for tracking control of a large class of mechanical systems is proposed. The approach employs the framework of Lyapunovs stability theory to formulate a class of control laws that guarantee convergence of the tracking errors to within specification limits in presence of bounded parameter uncertainties and input disturbances. The proposed control laws possess a large number of parameters and functional relationships to be chosen by the designer according to a methodology developed in the paper. The large number of design degrees of freedom makes the approach suitable for fuzzy logic implementation. A number of fuzzy implementations of the proposed control methodology are provided. All implementations guarantee tracking error convergence to within prespecified performance limits. An extensive simulation study using a model of a two-degree-of-freedom robot manipulator was conducted. Fuzzy and non-fuzzy implementations of the proposed methodology were compared to control laws designed using other design methods. Simulation study results indicate a superiority of the proposed control methodology compared to other approaches. The study also demonstrates better performance of the fuzzy control implementation compared to its non-fuzzy counterpart.

Model sensitivity and use of the comparative finite element method in mammalian jaw mechanics: mandible performance in the gray wolf.

Finite Element Analysis (FEA) is a powerful tool gaining use in studies of biological form and function. This method is particularly conducive to studies of extinct and fossilized organisms, as models can be assigned properties that approximate living tissues. In disciplines where model validation is difficult or impossible, the choice of model parameters and their effects on the results become increasingly important, especially in comparing outputs to infer function. To evaluate the extent to which performance measures are affected by initial model input, we tested the sensitivity of bite force, strain energy, and stress to changes in seven parameters that are required in testing craniodental function with FEA. Simulations were performed on FE models of a Gray Wolf (Canis lupus) mandible. Results showed that unilateral bite force outputs are least affected by the relative ratios of the balancing and working muscles, but only ratios above 0.5 provided balancing-working side joint reaction force relationships that are consistent with experimental data. The constraints modeled at the bite point had the greatest effect on bite force output, but the most appropriate constraint may depend on the study question. Strain energy is least affected by variation in bite point constraint, but larger variations in strain energy values are observed in models with different number of tetrahedral elements, masticatory muscle ratios and muscle subgroups present, and number of material properties. These findings indicate that performance measures are differentially affected by variation in initial model parameters. In the absence of validated input values, FE models can nevertheless provide robust comparisons if these parameters are standardized within a given study to minimize variation that arise during the model-building process. Sensitivity tests incorporated into the study design not only aid in the interpretation of simulation results, but can also provide additional insights on form and function.

Modeling of control and learning in a stepping motion

In a previous study (Beuter et al. 1986) the authors modeled a stepping motion using a three-body linkage with four degrees of freedom. Stepping was simulated by using three task parameters (i.e., step height, length, and duration) and sinusoidal joint angular velocity profiles. The results supported the concept of a hierarchical control structure with open-loop control during normal operation. In this study we refine the dynamic model and improve the simulation technique by incorporating the dynamics of the leg after landing, adding a foot segment to the model, and preprogramming the complete step motion using cycloids. The equations of the forces and torques developed on the ground by the foot during the landing phase are derived using the Lagrangian method. Simulation results are compared to experimental data collected on a subject stepping four times over an obstacle using a Selspot motion analysis system. A hierarchical control model that incorporates a learning process is proposed. The model allows an efficient combination of open and closed loop control strategies and involves hardwired movement segments. We also test the hypothesis of cycloidal velocity profiles in the joint programs against experimental data using a novel curve-fitting procedure based on analytical rather than numerical differentiation. The results suggest multiob-jective optimization of the joints motion. The control and learning model proposed here will help the understanding of the mechanisms responsible for assembling selected movement segments into goaldirected movement sequences in humans.

Spacecraft momentum unloading - The cell mapping approach

An approach for developing spacecraft angular momentum unloading control algorithms based on the cell mapping formulation is presented. Representations of periodic dynamic systems in terms of point mappings are discussed and their discretizations to form cell mappings derived. An optimal control technique exploiting the cell approach is presented and applied to the problem of momentum unloading. A number of unloading schemes by means of magnetic torquers are derived using this cell state space optimal control approach. The unloading schemes entail off-line control sequence generation, enabling the attitude control system to achieve unloading by a table lookup of magnetic torquer settings once per orbit. Simulation study results for two model spacecraft in low Earth orbit indicate closely bounded momentum performance from the control laws developed by the proposed approach.

Robust digital autopilot design for spacecraft equipped with pulse-operated thrusters

The analysis and design of attitude control systems for spacecraft employing pulse-operated (on-off) thrusters is usually accomplished through a combination of modeling approximations and empirical techniques. A new thruster pulse-modulation theory for pointing and tracking applications is developed from nonlinear control theory. This theory provides the framework for an autopilot suitable for use in digital computers whose performance and robustness properties are characterized analytically, in the design process. Given bounds on the anticipated dynamical modeling errors and sensor errors, it is shown that design specifications can be established and acceptable performance ensured in the presence of these error sources. Spacecraft with time-varying inertia properties can be accommodated, as well as clustered thruster configurations that provide multiple discrete torque levels about one or more spacecraft axes. A realistic application of the theory is illustrated via detailed computer simulation of a digital autopilot designed for midcourse guidance of a hypothetical interplanetary spacecraft.

Fitting mathematical functions to joint kinematics during stepping: Implications for motor control

The present study extends past work on modeling and control of stepping. The relationship between joint space kinematic data and routine motor control (i.e., open loop) during human stepping is investigated. A model of open loop stepping control using joint kinematics is described. Different functional approximations are employed to simulate experimental joint kinematic data collected on a subject stepping repeatedly over an obstacle. Results indicate that joint kinematics can be characterized by a small number of functions yielding a simple analytical description of open loop motor control. The different basis functions used and their associated coefficients reflected the qualitative behavior of joint trajectories thus allowing flexibility in the formulation of system kinematics. This approach provides a tool to study movement pathologies and movement development by identifying the basis functions governing the kinematics of motion and their associated coefficients. The model presented here is helpful in studying the segmentation of multiarticular movements into their elementary components by analytically modeling the discrete organization of motor behavior.

Modification of landing conditions at contact via flight

Abstract.Weight-bearing tasks performed by humans consist of a series of phases with multiple objectives. Analysis of the relationship between control and dynamics during successive phases of the tasks is essential for improving performance without sustaining injury. Experimental evidence regarding foot landings suggests that the distribution of momentum among segments at contact influences stability during interaction with the landing surface. In this study, we hypothesized that modification of control in one subsystem, in our case shoulder torque, during the flight phase of an aerial task would enable the performer to maintain behavior of other subsystems (e.g.lower extremity kinematics) and initiate contact with momentum conditions consistent with successful task performance. To test this hypothesis, an experimentally validated multilink dynamic model that incorporated modifications in shoulder torque was used to simulate the flight phase dynamics of overrotated landings. The simulation results indicate that modification in shoulder torque during the flight phase enables gymnasts to maintain lower extremity kinematics and initiate contact with trunk angular velocities consistent with those observed during successful landings. These results suggest that modifications in the control logic of one subsystem may be sufficient for achieving both global and local task objectives of landing.

Regulation of reaction forces during the golf swing

During the golf swing, the reaction forces applied at the feet control translation and rotation of the body–club system. In this study, we hypothesized that skilled players using a 6-iron would regulate shot distance by scaling the magnitude of the resultant horizontal reaction force applied to the each foot with minimal modifications in force direction. Skilled players (n = 12) hit golf balls using a 6-iron. Shot distance was varied by hitting the ball as they would normally and when reducing shot distance using the same club. During each swing, reaction forces were measured using dual force plates (1200 Hz) and three-dimensional kinematics were simultaneously captured (110 Hz). The results indicate that, on average, the peak resultant horizontal reaction forces of the target leg were significantly less than normal (5%, p < 0.05) when reducing shot distance. No significant differences in the orientation of the peak resultant horizontal reaction forces were observed. Resultant horizontal reaction force–angle relationships within leg and temporal relationships between target and rear legs during the swing were consistent within player across shot conditions. Regulation of force magnitude with minimal modification in force direction is expected to provide advantages from muscle activation, coordination, and performance points of view.

Multijoint Control Strategies Transfer Between Tasks

In this paper, the hypothesis that multijoint control strategies are transferred between similar tasks was tested. To test this hypothesis, we studied the take-off phase of two types of backward somersault dives: one while translating backwards (Back), the other while translating forward (Reverse). An experimentally based dynamic model of the musculoskeletal system was employed to simulate the measured kinematics and reaction force data and to study the sensitivity of take-off performance to initial kinematic conditions. It was found that the horizontal velocity of the total body center of mass (CM) was most sensitive to modifications in the initial shank conditions. Consequently, the initial shank kinematics of the Back dive was modified in the optimization procedure while maintaining the joint coordination of the Back in order to generate the CM trajectory and reaction forces of a Reverse. Similarly, the initial shank kinematics of the Reverse dive was modified to simulate the CM trajectory and reaction force of the Back. It was found that small modifications in the initial shank kinematics led to change in direction of horizontal CM velocity at take-off; resulting in a switch from Back to Reverse and vice versa. In both cases, the simulated momentum conditions at departure and the bimodal shape of the reaction force-time curve were consistent with those experimentally observed. The results of this study support the hypothesis that transfer of control strategies between similar tasks is a viable option in multijoint control. This transfer of control strategy is explained using a hierarchical model of the motion control system.