Modeling Complex Biological and Mechanical Movements: Applications to Animal Locomotion and Gesture Classification in Robotic Surgery

Mutual interaction between biology and robots can significantly benefit both fields. The richness and diversity in animal locomotion and movement provides an extensive resource for inspiration in engineering design of robots. On the other hand, bio-mimetic and bio-inspired robots play a critical role in testing hypotheses in biology and neuromechanics. Modeling complex biological and mechanical movements is at the core of this mutual interaction. Models and analytical tools are required for decoding and analysis of behavior in biological and mechanical systems, both at low level (sensory systems and control) and high level (activity recognition). This dissertation is focused on modeling approaches for biological and mechanical movements. We first primarily focus on physics-based template modeling to answer a long-standing question in animal locomotion: why do animals often produce substantial forces in directions that do not directly contribute to movement? We examine the weakly electric knifefish, a well-suited model system to investigate the relationship between mutually opposing forces and locomotor control. We use slow-motion videography to study the ribbon-fin motion and develop a physics-based template model at the task-level for tracking behavior. Using the developed physics-based model integrated with experiments with a biomimetic robot, we demonstrate that the production and differential control of mutually opposing forces is a strategy that generates passive stabilization while simultaneously enhancing maneuverability, thereby simplifies neural control. The second part of this work aims to propose a more general data-driven system-theoretic framework for decoding complex behaviors. Specifically we introduce a new class of linear time-invariant dynamical systems with sparse inputs (LDS-SI). In the proposed framework, at each time instant, the input to the system is sparse with respect to a dictionary of inputs. In the context of complex behaviors, the dictionary may represent the dictionary of inputs for all possible simple behaviors. We propose a convex optimization formulation for the state estimation with unknown inputs in LDS-SI. We derive sufficient conditions for the perfect joint recovery and explore the results with simulation. We demonstrate the power of the proposed framework in the analysis of complex gestures in robotic surgery. Results are better than state-of-the-art methods in joint segmentation and classification of surgical gestures in a dataset of suturing task trials performed by different surgeons

Walking dynamics are symmetric (enough)

Many biological phenomena such as locomotion, circadian cycles, and breathing are rhythmic in nature and can be modeled as rhythmic dynamical systems. Dynamical systems modeling often involves neglecting certain characteristics of a physical system as a modeling convenience. For example, human locomotion is frequently treated as symmetric about the sagittal plane. In this work, we test this assumption by examining human walking dynamics around the steady-state (limit-cycle). Here we adapt statistical cross validation in order to examine whether there are statistically significant asymmetries, and even if so, test the consequences of assuming bilateral symmetry anyway. Indeed, we identify significant asymmetries in the dynamics of human walking, but nevertheless show that ignoring these asymmetries results in a more consistent and predictive model. In general, neglecting evident characteristics of a system can be more than a modeling convenience---it can produce a better model.Comment: Draft submitted to Journal of the Royal Society Interfac

Feedback Control as a Framework for Understanding Tradeoffs in Biology

Control theory arose from a need to control synthetic systems. From regulating steam engines to tuning radios to devices capable of autonomous movement, it provided a formal mathematical basis for understanding the role of feedback in the stability (or change) of dynamical systems. It provides a framework for understanding any system with feedback regulation, including biological ones such as regulatory gene networks, cellular metabolic systems, sensorimotor dynamics of moving animals, and even ecological or evolutionary dynamics of organisms and populations. Here we focus on four case studies of the sensorimotor dynamics of animals, each of which involves the application of principles from control theory to probe stability and feedback in an organism's response to perturbations. We use examples from aquatic (electric fish station keeping and jamming avoidance), terrestrial (cockroach wall following) and aerial environments (flight control in moths) to highlight how one can use control theory to understand how feedback mechanisms interact with the physical dynamics of animals to determine their stability and response to sensory inputs and perturbations. Each case study is cast as a control problem with sensory input, neural processing, and motor dynamics, the output of which feeds back to the sensory inputs. Collectively, the interaction of these systems in a closed loop determines the behavior of the entire system.Comment: Submitted to Integr Comp Bio

Fitting low-order transfer function models to messy biological data

Biological systems are not low order, linear, nor time invariant. But it is often useful to model them as such. Given the significant variability in biological systems, we want to fit models that are robust to biological “noise”—such as trial-totrial variability, differences between individuals, sex differences, and parameter drift that may occur over time—but that nevertheless capture the system behavior in a parsimonious manner. Here, we present a straightforward approach for fitting low-order parametric transfer functions to frequency-domain data. Our goal is to produce a user-friendly set of tools based on model selection (e.g. AIC, BIC, cross validation) that will enable biologists to generate simple analytical expressions from necessarily nonlinear, time-varying, and infinite dimensional biological phenomena. Application to problems in sensorimotor control systems illustrate the approach