Autonomous Exploration of Small Bodies Toward Greater Autonomy for Deep Space Missions.

Autonomy is becoming increasingly important for the robotic exploration of unpredictable environments. One such example is the approach, proximity operation, and surface exploration of small bodies. In this article, we present an overview of an estimation framework to approach and land on small bodies as a key functional capability for an autonomous small-body explorer. We use a multi-phase perception/estimation pipeline with interconnected and overlapping measurements and algorithms to characterize and reach the body, from millions of kilometers down to its surface. We consider a notional spacecraft design that operates across all phases from approach to landing and to maneuvering on the surface of the microgravity body. This SmallSat design makes accommodations to simplify autonomous surface operations. The estimation pipeline combines state-of-the-art techniques with new approaches to estimating the target's unknown properties across all phases. Centroid and light-curve algorithms estimate the body-spacecraft relative trajectory and rotation, respectively, using a priori knowledge of the initial relative orbit. A new shape-from-silhouette algorithm estimates the pole (i.e., rotation axis) and the initial visual hull that seeds subsequent feature tracking as the body gets more resolved in the narrow field-of-view imager. Feature tracking refines the pole orientation and shape of the body for estimating initial gravity to enable safe close approach. A coarse-shape reconstruction algorithm is used to identify initial landable regions whose hazardous nature would subsequently be assessed by dense 3D reconstruction. Slope stability, thermal, occlusion, and terra-mechanical hazards would be assessed on densely reconstructed regions and continually refined prior to landing. We simulated a mission scenario for approaching a hypothetical small body whose motion and shape were unknown a priori, starting from thousands of kilometers down to 20 km. Results indicate the feasibility of recovering the relative body motion and shape solely relying on onboard measurements and estimates with their associated uncertainties and without human input. Current work continues to mature and characterize the algorithms for the last phases of the estimation framework to land on the surface.

An Algorithm for Nonparametric Estimation of a Multivariate Mixing Distribution with Applications to Population Pharmacokinetics.

Population pharmacokinetic (PK) modeling has become a cornerstone of drug development and optimal patient dosing. This approach offers great benefits for datasets with sparse sampling, such as in pediatric patients, and can describe between-patient variability. While most current algorithms assume normal or log-normal distributions for PK parameters, we present a mathematically consistent nonparametric maximum likelihood (NPML) method for estimating multivariate mixing distributions without any assumption about the shape of the distribution. This approach can handle distributions with any shape for all PK parameters. It is shown in convexity theory that the NPML estimator is discrete, meaning that it has finite number of points with nonzero probability. In fact, there are at most N points where N is the number of observed subjects. The original infinite NPML problem then becomes the finite dimensional problem of finding the location and probability of the support points. In the simplest case, each point essentially represents the set of PK parameters for one patient. The probability of the points is found by a primal-dual interior-point method; the location of the support points is found by an adaptive grid method. Our method is able to handle high-dimensional and complex multivariate mixture models. An important application is discussed for the problem of population pharmacokinetics and a nontrivial example is treated. Our algorithm has been successfully applied in hundreds of published pharmacometric studies. In addition to population pharmacokinetics, this research also applies to empirical Bayes estimation and many other areas of applied mathematics. Thereby, this approach presents an important addition to the pharmacometric toolbox for drug development and optimal patient dosing.

Experiment design for nonparametric models based on minimizing Bayes Risk: application to voriconazole¹.

An experimental design approach is presented for individualized therapy in the special case where the prior information is specified by a nonparametric (NP) population model. Here, a NP model refers to a discrete probability model characterized by a finite set of support points and their associated weights. An important question arises as to how to best design experiments for this type of model. Many experimental design methods are based on Fisher information or other approaches originally developed for parametric models. While such approaches have been used with some success across various applications, it is interesting to note that they largely fail to address the fundamentally discrete nature of the NP model. Specifically, the problem of identifying an individual from a NP prior is more naturally treated as a problem of classification, i.e., to find a support point that best matches the patient's behavior. This paper studies the discrete nature of the NP experiment design problem from a classification point of view. Several new insights are provided including the use of Bayes Risk as an information measure, and new alternative methods for experiment design. One particular method, denoted as MMopt (multiple-model optimal), will be examined in detail and shown to require minimal computation while having distinct advantages compared to existing approaches. Several simulated examples, including a case study involving oral voriconazole in children, are given to demonstrate the usefulness of MMopt in pharmacokinetics applications.

IMPLICIT DUAL CONTROL BASED ON PARTICLE FILTERING AND FORWARD DYNAMIC PROGRAMMING.

This paper develops a sampling-based approach to implicit dual control. Implicit dual control methods synthesize stochastic control policies by systematically approximating the stochastic dynamic programming equations of Bellman, in contrast to explicit dual control methods that artificially induce probing into the control law by modifying the cost function to include a term that rewards learning. The proposed implicit dual control approach is novel in that it combines a particle filter with a policy-iteration method for forward dynamic programming. The integration of the two methods provides a complete sampling-based approach to the problem. Implementation of the approach is simplified by making use of a specific architecture denoted as an H-block. Practical suggestions are given for reducing computational loads within the H-block for real-time applications. As an example, the method is applied to the control of a stochastic pendulum model having unknown mass, length, initial position and velocity, and unknown sign of its dc gain. Simulation results indicate that active controllers based on the described method can systematically improve closed-loop performance with respect to other more common stochastic control approaches.

Outcome prediction by a mathematical model based on noninvasive hemodynamic monitoring.

BACKGROUND: The aims are to apply a mathematical search and display model based on noninvasive hemodynamic monitoring, to predict outcome early in a consecutively monitored series of 661 severely injured patients. METHODS: A prospective observational study by a previously designed protocol in a Level I trauma service in a university-run inner city public hospital was conducted. The survival probabilities were calculated at the initial resuscitation on admission and at subsequent intervals during their hospitalization beginning shortly after admission to the emergency department. Cardiac function was evaluated by cardiac output (CI), heart rate (HR), and mean arterial blood pressure (MAP), pulmonary function by pulse oximetry (SapO2), and tissue perfusion function by transcutaneous oxygen indexed to FiO2, (PtcO2/FiO2), and carbon dioxide (PtcCO2) tension. RESULTS: The survival probability (SP) averaged 89 +/- 0.4% for survivors and 75.7 +/- 1.6% (p < 0.001) for nonsurvivors in the first 24-hour period of resuscitation. The CI, MAP, SapO2, PtcO2, and PtcO2/FiO2 were significantly higher in survivors than in nonsurvivors in initial resuscitation, whereas HR and PtcCO2 were higher in nonsurvivors. CONCLUSIONS: During the initial resuscitation period, misclassifications were 102 of 661 or 15%. The SP provided early objective criteria to evaluate hospital outcome and to track changes throughout the hospital course based on a large database of patients with similar clinical-hemodynamic states.

Stochastic model for outcome prediction in acute illness.

The aims were to apply a stochastic model to predict outcome early in acute emergencies and to evaluate the effectiveness of various therapies in a consecutively monitored series of severely injured patients with noninvasive hemodynamic monitoring. The survival probabilities were calculated beginning shortly after admission to the emergency department (ED) and at subsequent intervals during their hospitalization. Cardiac function was evaluated by cardiac output (CI), heart rate (HR), and mean arterial blood pressure (MAP), pulmonary function by pulse oximetry (SapO(2)), and tissue perfusion function by transcutaneous oxygen indexed to FiO(2),(PtcO(2)/FiO(2)), and carbon dioxide (PtcCO(2)) tension. The survival probability (SP) of survivors averaged 81.5+/-1.1% (SEM) and for nonsurvivors 57.7+/-2.3% (p<0.001) in the first 24-hour period of resuscitation and subsequent management. The CI, SapO(2),PtcO(2)/FiO(2) and MAP were significantly higher in survivors than in nonsurvivors during the initial resuscitation, while HR and PtcCO(2) tensions were higher in the nonsurvivors. Predictions made during the initial resuscitation period in the first 24-hours after admission were compared with the actual outcome at hospital discharge, which were usually several weeks later; misclassifications were 9.6% (16/167). The therapeutic decision support system objectively evaluated the responses of alternative therapies based on responses of patients with similar clinical-hemodynamic states.

A stochastic control program to predict outcome and to support therapeutic decisions: a preliminary report.

BACKGROUND AND OBJECTIVES: Early noninvasive hemodynamic monitoring with an outcome predictor and a therapeutic decision support system may be useful to identify and correct hemodynamic deficiencies in emergency patients. The first aim was to apply a stochastic (probability) search and display model to predict outcome as early as possible. The second aim was to explore the usefulness of a therapeutic decision support system to evaluate the relative effectiveness of various therapies. METHODS: A stochastic control and display program based on noninvasive hemodynamic monitoring was applied in 100 consecutive critically ill patients admitted to the emergency department of an inner city public hospital. The program continuously displayed the noninvasive hemodynamic data and the patient's predicted survival probability (SP) that was based on the patient's diagnosis, covariates, and hemodynamic data. The accuracy of the SP at the initial resuscitation on admission to the emergency department (ED) was evaluated by the actual outcome at hospital discharge. The therapeutic decision support program evaluated the relative effectiveness of various therapies on based on their hemodynamic and SP responses and outcome of patients with similar clinical-hemodynamic states. RESULTS: The cardiac index, mean arterial pressure, arterial saturation, transcutaneous oxygen and carbon dioxide tensions were appreciably higher in survivors than in nonsurvivors in the initial resuscitation. Heart rate was higher in the nonsurvivors. The calculated Survival Probability (SP) of survivors averaged 81 +/- 1.4% in the first 24-hour observation period. It was 58 +/- 2.2% for nonsurvivors during this period. Misclassifications were 10/100 or 10%.

Outcome prediction in chest injury by a mathematical search and display program.

OBJECTIVE: This study applies a stochastic or probability search and display model to prospectively predict outcome and to evaluate therapeutic effects in a consecutively monitored series of 396 patients with severe thoracic and thoracoabdominal injuries. STUDY DESIGN: Prospective observational study of outcome prediction using noninvasive hemodynamic monitoring by previously designed protocols and tested against actual outcome at hospital discharge in a level 1 trauma service of a university-run, inner-city public hospital. METHODS: Cardiac index (CI), heart rate (HR), mean arterial pressure (MAP), arterial oxygen saturation measured by pulse oximetry (Sp(O2)), transcutaneous oxygen tension (PtC(O2)), and transcutaneous carbon dioxide tension (Ptc(CO2)) were monitored beginning shortly after admission to the emergency department. The stochastic search and display model with a decision support program based on noninvasive hemodynamic monitoring was applied to 396 severely ill patients with major thoracic and thoracoabdominal trauma. The survival probability (SP) was calculated during initial resuscitation continuously until patients were stabilized, and compared with the actual outcome when the patient was discharged from the hospital usually a week or more later. RESULTS: The CI, Sp(O2), Ptc(O2), and MAP were appreciably higher in survivors than in nonsurvivors. HR and Ptc(CO2) were higher in the nonsurvivors. The calculated SP in the first 24-h observation period of survivors of chest wounds averaged 83 +/- 18% (+/- SD) and 62 +/- 19% for nonsurvivors. Misclassifications were 9.6%. The relative effects of alternative therapies were evaluated before and after therapy, using hemodynamic monitoring and SP as criteria. CONCLUSIONS: Noninvasive hemodynamic monitoring with an information system provided a feasible approach to early outcome predictions and therapeutic decision support.

Mathematical program for outcome prediction and therapeutic support for trauma beginning within 1 hr of admission: a preliminary report.

OBJECTIVES: The aims were a) to noninvasively monitor acute emergency trauma patients beginning within 1 hr after admission to the emergency department; b) to prospectively predict outcome; and c) to evaluate the relative effectiveness of various modes of therapy. DESIGN: Prospective outcome prediction study using a mathematical search and display model based on noninvasive hemodynamic monitoring. SETTING: A level I trauma service in a large university-run inner-city public hospital. PATIENTS: We studied 185 consecutively noninvasively monitored emergency patients. INTERVENTIONS: We noninvasively monitored cardiac index, mean arterial blood pressure, heart rate, pulse oximetry, and transcutaneous oxygen and carbon dioxide tensions beginning within 1-hr after emergency admission. MEASUREMENTS AND MAIN RESULTS: The cardiac index, pulse oximetry, transcutaneous oxygen tension, transcutaneous carbon dioxide tension, and mean arterial blood pressure were higher in survivors than in nonsurvivors in the initial resuscitation period and at the hemodynamic nadir. Heart rate and transcutaneous carbon dioxide tension were higher in the nonsurvivors. The calculated survival probability in the first hour observation period of survivors averaged 85 +/- 14% vs. 69 +/- 16% for nonsurvivors (p = .0001). Misclassifications of the series as a whole were 11.3%; after excluding brain death from severe head injury, there were 6.4% misclassifications. A decision support system evaluated the effects of various therapies based on responses of patients with similar clinical-hemodynamic states. CONCLUSION: Noninvasive hemodynamic monitoring and an information system provided a feasible approach to predict outcome early and to evaluate prospectively the efficacy of various therapies.

A Bayesian approach to tracking patients having changing pharmacokinetic parameters.

This paper considers the updating of Bayesian posterior densities for pharmacokinetic models associated with patients having changing parameter values. For estimation purposes it is proposed to use the Interacting Multiple Model (IMM) estimation algorithm, which is currently a popular algorithm in the aerospace community for tracking maneuvering targets. The IMM algorithm is described, and compared to the multiple model (MM) and Maximum A-Posteriori (MAP) Bayesian estimation methods, which are presently used for posterior updating when pharmacokinetic parameters do not change. Both the MM and MAP Bayesian estimation methods are used in their sequential forms, to facilitate tracking of changing parameters. Results indicate that the IMM algorithm is well suited for tracking time-varying pharmacokinetic parameters in acutely ill and unstable patients, incurring only about half of the integrated error compared to the sequential MM and MAP methods on the same example.