Motion Planning of Uncertain Ordinary Differential Equation Systems

This work presents a novel motion planning framework, rooted in nonlinear programming theory, that treats uncertain fully and under-actuated dynamical systems described by ordinary differential equations. Uncertainty in multibody dynamical systems comes from various sources, such as: system parameters, initial conditions, sensor and actuator noise, and external forcing. Treatment of uncertainty in design is of paramount practical importance because all real-life systems are affected by it, and poor robustness and suboptimal performance result if it’s not accounted for in a given design. In this work uncertainties are modeled using Generalized Polynomial Chaos and are solved quantitatively using a least-square collocation method. The computational efficiency of this approach enables the inclusion of uncertainty statistics in the nonlinear programming optimization process. As such, the proposed framework allows the user to pose, and answer, new design questions related to uncertain dynamical systems. Specifically, the new framework is explained in the context of forward, inverse, and hybrid dynamics formulations. The forward dynamics formulation, applicable to both fully and under-actuated systems, prescribes deterministic actuator inputs which yield uncertain state trajectories. The inverse dynamics formulation is the dual to the forward dynamic, and is only applicable to fully-actuated systems; deterministic state trajectories are prescribed and yield uncertain actuator inputs. The inverse dynamics formulation is more computationally efficient as it requires only algebraic evaluations and completely avoids numerical integration. Finally, the hybrid dynamics formulation is applicable to under-actuated systems where it leverages the benefits of inverse dynamics for actuated joints and forward dynamics for unactuated joints; it prescribes actuated state and unactuated input trajectories which yield uncertain unactuated states and actuated inputs. The benefits of the ability to quantify uncertainty when planning the motion of multibody dynamic systems are illustrated through several case-studies. The resulting designs determine optimal motion plans—subject to deterministic and statistical constraints—for all possible systems within the probability space

Simultaneous Optimal Uncertainty Apportionment and Robust Design Optimization of Systems Governed by Ordinary Differential Equations

The inclusion of uncertainty in design is of paramount practical importance because all real-life systems are affected by it. Designs that ignore uncertainty often lead to poor robustness, suboptimal performance, and higher build costs. Treatment of small geometric uncertainty in the context of manufacturing tolerances is a well studied topic. Traditional sequential design methodologies have recently been replaced by concurrent optimal design methodologies where optimal system parameters are simultaneously determined along with optimally allocated tolerances; this allows to reduce manufacturing costs while increasing performance. However, the state of the art approaches remain limited in that they can only treat geometric related uncertainties restricted to be small in magnitude. This work proposes a novel framework to perform robust design optimization concurrently with optimal uncertainty apportionment for dynamical systems governed by ordinary differential equations. The proposed framework considerably expands the capabilities of contemporary methods by enabling the treatment of both geometric and non-geometric uncertainties in a unified manner. Additionally, uncertainties are allowed to be large in magnitude and the governing constitutive relations may be highly nonlinear. In the proposed framework, uncertainties are modeled using Generalized Polynomial Chaos and are solved quantitatively using a least-square collocation method. The computational efficiency of this approach allows statistical moments of the uncertain system to be explicitly included in the optimization-based design process. The framework formulates design problems as constrained multi-objective optimization problems, thus enabling the characterization of a Pareto optimal trade-off curve that is off-set from the traditional deterministic optimal trade-off curve. The Pareto off-set is shown to be a result of the additional statistical moment information formulated in the objective and constraint relations that account for the system uncertainties. Therefore, the Pareto trade-off curve from the new framework characterizes the entire family of systems within the probability space; consequently, designers are able to produce robust and optimally performing systems at an optimal manufacturing cost. A kinematic tolerance analysis case-study is presented first to illustrate how the proposed methodology can be applied to treat geometric tolerances. A nonlinear vehicle suspension design problem, subject to parametric uncertainty, illustrates the capability of the new framework to produce an optimal design at an optimal manufacturing cost, accounting for the entire family of systems within the associated probability space. This case-study highlights the general nature of the new framework which is capable of optimally allocating uncertainties of multiple types and with large magnitudes in a single calculation

Synaptic motor adaptation: A three-factor learning rule for adaptive robotic control in spiking neural networks

Legged robots operating in real-world environments must possess the ability to rapidly adapt to unexpected conditions, such as changing terrains and varying payloads. This paper introduces the Synaptic Motor Adaptation (SMA) algorithm, a novel approach to achieving real-time online adaptation in quadruped robots through the utilization of neuroscience-derived rules of synaptic plasticity with three-factor learning. To facilitate rapid adaptation, we meta-optimize a three-factor learning rule via gradient descent to adapt to uncertainty by approximating an embedding produced by privileged information using only locally accessible onboard sensing data. Our algorithm performs similarly to state-of-the-art motor adaptation algorithms and presents a clear path toward achieving adaptive robotics with neuromorphic hardware

A Web-Shareable Real-World Imaging Problem for Enhancing an Image-Processing Curriculum

A real-world laboratory exercise is presented for image processing and related curricula. The exercise is a traffic-monitoring problem in which a truck must be tracked as it moves across a bridge and its velocity measured. Sequential images are taken from a dedicated Web camera that views the Smart Composite Bridge on the University of Missouri-Rolla campus. The prototype bridge is a field laboratory for several interdisciplinary courses, including a Machine Vision elective. The Machine Vision image-processing elective uses the traffic-monitoring exercise to give students experience with processing complex images, tracking image markers, and applying theoretical orthographic concepts. The laboratory exercise uses an image sequence acquired during the springtime with multiple potential markers available on the truck for assignment flexibility. A wintertime image sequence with snowy conditions is also available for assignment flexibility. This paper discusses the bridge and camera resources, the traffic-monitoring laboratory exercise description, and the Machine Vision course implementation and evaluation. Two versions of the traffic-monitoring exercise, including two image sequences and orthographic MATLAB code, are available on the bridge Website

Fuzzy Color Clustering for Melanoma Diagnosis in Dermoscopy Images

A fuzzy logic-based color histogram analysis technique is presented for discriminating benign skin lesions from malignant melanomas in dermoscopy images. The approach extends previous research for utilizing a fuzzy set for skin lesion color for a specified class of skin lesions, using alpha-cut and support set cardinality for quantifying a fuzzy ratio skin lesion color feature. Skin lesion discrimination results are reported for the fuzzy clustering ratio over different regions of the lesion over a data set of 517 dermoscopy images consisting of 175 invasive melanomas and 342 benign lesions. Experimental results show that the fuzzy clustering ratio applied over an eight-connected neighborhood on the outer 25% of the skin lesion with an alpha-cut of 0.08 can recognize 92.6% of melanomas with approximately 13.5% false positive lesions. These results show the critical importance of colors in the lesion periphery. Our fuzzy logic-based description of lesion colors offers relevance to clinical descriptions of malignant melanoma

Effects of Late Castration and Zeranol on Growth Rate, Feed Efficiency, and Carcass and Meat Traits of Bovine Males

It is generally recognized that intact bovine males gain weight faster and require less feed per unit of gain than castrate bovine males. Further, carcasses from intact bovine males have a higher percentage of retail or edible product, but meat from intact males is generally evaluated slightly lower on palatability characteristics, particularly tenderness, than carcasses from castrate bovine males. It has been suggested that much of the advantage of intact vs castrate for rate of gain, efficiency of gain, and composition of gain may be expressed by an age of about 1 year and the disadvantages, including aggressive male behavior, that result in reduced rate and efficiency of gain, begin at about 1 year of age (at or immediately after puberty). Thus, there was need to determine the effects of castration at about 1 year on rate of gain, efficiency of gain, composition of gain, meat characteristics, and behavioral characteristics. Reports have shown that, when the anabolic agent zeranol [6-(6,10-dyhydroxyundecyl)-B-resorcyclic acid-d-lactone] is implanted in intact male calves at or before weaning, rate of gain is increased and rate of testicular growth is decreased. These experiments were conducted to determine the effects of castration and zeranol implants at 13 months of age on rate of gain, efficiency of gain, behavioral characteristics, and carcass and meat traits of bovine males

Automatic Detection of Critical Dermoscopy Features for Malignant Melanoma Diagnosis

Improved methods for computer-aided analysis of identifying features of skin lesions from digital images of the lesions are provided. Improved preprocessing of the image that 1) eliminates artifacts that occlude or distort skin lesion features and 2) identifies groups of pixels within the skin lesion that represent features and/or facilitate the quantification of features are provided including improved digital hair removal algorithms. Improved methods for analyzing lesion features are also provided

Analysis of Globule Types in Malignant Melanoma

Objective: To identify and analyze subtypes of globules based on size, shape, network connectedness, pigmentation, and distribution to determine which globule types and globule distributions are most frequently associated with a diagnosis of malignant melanoma. Design: Retrospective case series of dermoscopy images with globules. Setting: Private dermatology practices. Participants: Patients in dermatology practices. Intervention: Observation only. Main Outcome Measure: Association of globule types with malignant melanoma. Results: The presence of large globules (odds ratio [OR], 5.25) and globules varying in size (4.72) or shape (5.37) had the highest ORs for malignant melanoma among all globule types and combinations studied. Classical globules (dark, discrete, convex, and 0.10-0.20 mm) had a higher risk (OR, 4.20) than irregularly shaped globules (dark, discrete, and not generally convex) (2.89). Globules connected to other structures were not significant in the diagnosis of malignant melanoma. Of the different configurations studied, asymmetric clusters have the highest risk (OR, 3.02). Conclusions: The presence of globules of varying size or shape seems to be more associated with a diagnosis of malignant melanoma than any other globule type or distribution in this study. Large globules are of particular importance in the diagnosis of malignant melanoma