David S. Bayard

New class of control laws for robotic manipulators Part 1. Non–adaptive case

A new class of exponentially stabilizing control laws for joint level control of robot arms is introduced. It has recently been recognized that the non-linear dynamics associated with robotic manip...

Model-based, goal-oriented, individualised drug therapy : Linkage of population modelling, new 'multiple model' dosage design, Bayesian feedback and individualised target goals

SummaryThis article examines the use of population pharmacokinetic models to store experiences about drugs in patients and to apply that experience to the care of new patients. Population models are the Bayesian prior. For truly individualised therapy, it is necessary first to select a specific target goal, such as a desired serum or peripheral compartment concentration, and then to develop the dosage regimen individualised to best hit that target in that patient.One must monitor the behaviour of the drug by measuring serum concentrations or other responses, hopefully obtained at optimally chosen times, not only to see the raw results, but to also make an individualised (Bayesian posterior) model of how the drug is behaving in that patient. Only then can one see the relationship between the dose and the absorption, distribution, effect and elimination of the drug, and the patient’s clinical sensitivity to it; one must always look at the patient. Only by looking at both the patient and the model can it be judged whether the target goal was correct or needs to be changed. The adjusted dosage regimen is again developed to hit that target most precisely starting with the very next dose, not just for some future steady state.Nonparametric population models have discrete, not continuous, parameter distributions. These lead naturally into the multiple model method of dosage design, specifically to hit a desired target with the greatest possible precision for whatever past experience and present data are available on that drug — a new feature for this goal-oriented, model-based, individualised drug therapy. As clinical versions of this new approach become available from several centres, it should lead to further improvements in patient care, especially for bacterial and viral infections, cardiovascular therapy, and cancer and transplant situations.

A criterion for joint optimization of identification and robust control

A criterion for system identification is developed that is consistent with the intended use of the fitted model for modern robust control synthesis. Specifically, a joint optimization problem is posed which simultaneously solves the plant model estimate and control design, so as to optimize robust performance over the set of plants consistent with a specified experimental data set. >

Drag-Based Predictive Tracking Guidance for Mars Precision Landing

Future Mars missions require precision landing capability. An entry guidance law is developed for a lander with flying capabilities consistent with those expected for the lander in the 2001 mission. The lander flight path is controlled by bank angle adjustments. The guidance law belongs to the class of drag-based predictive tracking guidance laws which includes the entry guidance law for the Space Shuttle Orbiter. Modifications relative to the Shuttle entry guidance law are introduced to accommodate the very low lift capability and the combination of a low bandwidth attitude control system and a fixed trim angle of attack. Monte Carlo results show that even with a maximum lift-to-drag ratio of only 0.12 a specified parachute deployment latitude/longitude point can be achieved with 99% certainty to within 13.2 km under the assumed worst case dispersions. The dynamic pressure and Mach number constraints for parachute deployment are also satisfied with 99% certainty.

High-order multivariable transfer function curve fitting: algorithms, sparse matrix methods and experimental results

Abstract This paper develops a computational approach to multivariable frequency domain curve fitting, based on two-norm minimization. The algorithm is specifically tailored to the identification of complex systems having a large number of parameters, and includes a sparse matrix method for reducing computation and memory requirements on large problems. The algorithm is also well-suited for identification of lightly damped systems such as flexible structures. The overall approach is successfully demonstrated on a high-order multivariable flexible structure experiment requiring the estimation of 780 parameters over a 100 Hz band width.

Achieving target goals most precisely using nonparametric compartmental models and "multiple model" design of dosage regimens.

Multiple model (MM) design and stochastic control of dosage regimens permit essentially full use of all the information contained in either a Bayesian prior nonparametric EM (NPEM) population pharmacokinetic model or in an MM Bayesian posterior updated parameter set, to achieve and maintain selected therapeutic goals with optimal precision (least predicted weighted squared error). The regimens are visibly more precise in the achievement of desired target goals than are current methods using mean or median population parameter values. Bayesian feedback has now also been incorporated into the MM software. An evaluation of MM dosage design using an NPEM population model versus dosage design based on conventional mean population parameter values is presented, using a population model of vancomycin. Further feedback control was also evaluated, incorporating realistic simulated uncertainties in the clinical environment such as those in the preparation and administration of doses.

Lyapunov function-based control laws for revolute robot arms: tracking control, robustness, and adaptive control

A new class of joint level control laws for all-revolute robot arms is introduced. The analysis is similar to an energy-like Lyapunov function approach, except that the closed-loop potential function is shaped in accordance with the underlying joint space topology. This approach gives way to a much simpler analysis and leads to a new class of control designs which guarantee both global asymptotic stability and local exponential stability. When Coulomb and viscous friction and parameter uncertainty are present as model perturbations, a sliding mode-like modification of the control law results in a robustness-enhancing outer loop. Adaptive control is formulated within the same framework. A linear-in-the-parameters formulation is adopted and globally asymptotically stable adaptive control laws are derived by simply replacing unknown model parameters by their estimates. >

Adaptive Kalman filtering, failure detection and identification for spacecraft attitude estimation

Future space missions call for unprecedented levels of autonomy, reliability and precision, thereby increasing the demands on spacecraft failure detection, identification and compensation (FDIC) systems. We address the problems of spacecraft attitude determination (AD) and FDI for sensors and actuators by developing: 1) a nonlinear extended Kalman filter (EKF) which does not require a small angle approximation; 2) a method for online tuning of noise covariances; and 3) a multi-hypothesis extended Kalman filter (MEKF) for detection and identification of sensor (gyro, Star tracker) and actuator (thruster) failures. A nonlinear EKF is designed for AD using angular rates, quaternions and the gyro biases as state variables. It is shown to provide more accurate estimates of the attitude angles and can be used for the detection and removal of bad gyro and Star-tracker measurements. The MEKF approach is used for the detection and identification of gyro, Star-tracker and thruster failures. Gyro failures are the quickest to detect and identify, followed by thruster and star tracker failures.

Two general methods for population pharmacokinetic modeling: non-parametric adaptive grid and non-parametric Bayesian

Population pharmacokinetic (PK) modeling methods can be statistically classified as either parametric or nonparametric (NP). Each classification can be divided into maximum likelihood (ML) or Bayesian (B) approaches. In this paper we discuss the nonparametric case using both maximum likelihood and Bayesian approaches. We present two nonparametric methods for estimating the unknown joint population distribution of model parameter values in a pharmacokinetic/pharmacodynamic (PK/PD) dataset. The first method is the NP Adaptive Grid (NPAG). The second is the NP Bayesian (NPB) algorithm with a stick-breaking process to construct a Dirichlet prior. Our objective is to compare the performance of these two methods using a simulated PK/PD dataset. Our results showed excellent performance of NPAG and NPB in a realistically simulated PK study. This simulation allowed us to have benchmarks in the form of the true population parameters to compare with the estimates produced by the two methods, while incorporating challenges like unbalanced sample times and sample numbers as well as the ability to include the covariate of patient weight. We conclude that both NPML and NPB can be used in realistic PK/PD population analysis problems. The advantages of one versus the other are discussed in the paper. NPAG and NPB are implemented in R and freely available for download within the Pmetrics package from www.lapk.org.

Swarm Keeping Strategies for Spacecraft under J2 and Atmospheric Drag Perturbations

This paper presents several new open-loop guidance methods for spacecraft swarms comprised of hundreds to thousands of agents with each spacecraft having modest capabilities. These methods have three main goals: preventing relative drift of the swarm, preventing collisions within the swarm, and minimizing the fuel used throughout the mission. The development of these methods progresses by eliminating drift using the Hill-ClohessyWiltshire equations, removing drift due to nonlinearity, and minimizing the J2 drift. In order to verify these guidance methods, a new dynamic model for the relative motion of spacecraft is developed. These dynamics are exact and include the two main disturbances for spacecraft in Low Earth Orbit (LEO), J2 and atmospheric drag. Using this dynamic model, numerical simulations are provided at each step to show the eectiveness of each method and to see where improvements can be made. The main result is a set of initial conditions for each spacecraft in the swarm which provides hundreds of collision-free orbits in the presence of J2. Finally, a multi-burn strategy is developed in order to provide hundreds of collision free orbits under the inuence of atmospheric drag. This last method works by enforcing the initial conditions multiple times throughout the mission thereby providing collision free motion for the duration of the mission.