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Noah J. Cowan

Publications and source records attributed to Noah J. Cowan.

15 recordsLinked to original sources

Active Sensing Subserves Task-Level Control

Active sensing is traditionally defined as the expenditure of energy, typically in the form of movement, for obtaining information. Here, we propose that the combination of reliance on adaptive sensors, the linkage between movement and sensing, and task-level control inevitably gives rise to the emergence of active sensing movements. In this way, active sensing is not driven by sensory goals, such as minimizing uncertainty about the state, but rather is necessary for task-level control. This hypothesis, that active sensing subserves control, is supported by both empirical data from organisms and mathematical theory. Interestingly, active sensing behaviors often occur in discrete epochs, interspersed with goal-oriented behavior. This suggests that animals switch between two behavioral modes with distinct control policies, an `explore' mode in which animals produce dynamic movements to shape sensory feedback, and an `exploit' mode in which animals produce slower compensatory movements that are directly related to achieving task goals. This strategy for feedback control that relies on adaptive sensors, active sensing, and mode switching is not commonly used in engineered systems despite being ubiquitous in biology. Engineered systems comprising state-of-the-art sensors, actuators, and mechanical designs can outperform animals with respect to ``cost functions'' such as maximum force generation, precision, and speed. Nevertheless, animals routinely achieve robust, graceful behaviors that are currently unmatched by engineered systems, suggesting that current control systems are insufficient. These insights, expressed in the language of control theory, may be critical for improving robotic sensing and control.

q-bio.NC↗

Bio-Inspired Event-Based Visual Servoing for Ground Robots

Biological sensory systems are inherently adaptive, filtering out constant stimuli and prioritizing relative changes, likely enhancing computational and metabolic efficiency. Inspired by active sensing behaviors across a wide range of animals, this paper introduces a principled 1D event-based visual servoing framework for ground robots operating in structured environments. Utilizing a Dynamic Vision Sensor (DVS), we demonstrate that by applying a fixed spatial kernel to the asynchronous event stream generated from structured logarithmic intensity-change patterns, the resulting net event flux analytically isolates specific combinations of kinematic states. We establish a generalized theoretical bound for this event rate estimator and show that linear and quadratic spatial profiles isolate the robot's velocity and position-velocity product, respectively. Leveraging these properties, we employ a multi-pattern stimulus to directly synthesize a nonlinear state feedback term entirely without traditional state estimation. To overcome the inescapable loss of linear observability at equilibrium inherent in event sensing, we propose a bio-inspired active sensing limit-cycle controller. Experimental validation on a 1/10-scale autonomous ground vehicle confirms the efficacy, extreme low-latency, and computational efficiency of the proposed direct-sensing approach.

cs.RO↗

Modeling Adaptive Tracking of Predictable Stimuli in Electric Fish

The weakly electric fish \emph{Eigenmannia virescens} naturally swims back and forth to stay within a moving refuge, tracking its motion using visual and electrosensory feedback. Previous experiments show that when the refuge oscillates as a low-frequency sinusoid (below about 0.5 Hz), the tracking is nearly perfect, but phase lag increases and gain decreases at higher frequencies. Here, we model this nonlinear behavior as an adaptive internal model principle (IMP) system. Specifically, an adaptive state estimator identifies the \emph{a priori} unknown frequency, and feeds this parameter estimate into a closed-loop IMP-based system built around a lightly damped harmonic oscillator. We prove that the closed-loop tracking error of the IMP-based system, where the online adaptive frequency estimate is used as a surrogate for the unknown frequency, converges exponentially to that of an ideal control system with perfect information about the stimulus. Simulations further show that our model reproduces the fish refuge tracking Bode plot across a wide frequency range. These results establish the theoretical validity of combining the IMP with an adaptive identification process and provide a basic framework in adaptive sensorimotor control.

eess.SY↗

The Geometry of Optimal Gait Families for Steering Kinematic Locomoting Systems

Motion planning for locomotion systems typically requires translating high-level rigid-body tasks into low-level joint trajectories-a process that is straightforward for car-like robots with fixed, unbounded actuation inputs but more challenging for systems like snake robots, where the mapping depends on the current configuration and is constrained by joint limits. In this paper, we focus on generating continuous families of optimal gaits-collections of gaits parameterized by step size or steering rate-to enhance controllability and maneuverability. We uncover the underlying geometric structure of these optimal gait families and propose methods for constructing them using both global and local search strategies, where the local method and the global method compensate each other. The global search approach is robust to nonsmooth behavior, albeit yielding reduced-order solutions, while the local search provides higher accuracy but can be unstable near nonsmooth regions. To demonstrate our framework, we generate optimal gait families for viscous and perfect-fluid three-link swimmers. This work lays a foundation for integrating low-level joint controllers with higher-level motion planners in complex locomotion systems.

cs.RO↗

An exact active sensing strategy for a class of bio-inspired systems

We consider a general class of translation-invariant systems with a specific category of output nonlinearities motivated by biological sensing. We show that no dynamic output feedback can stabilize this class of systems to an isolated equilibrium point. To overcome this fundamental limitation, we propose a simple control scheme that includes a low-amplitude periodic forcing function akin to so-called "active sensing" in biology, together with nonlinear output feedback. Our analysis shows that this approach leads to the emergence of an exponentially stable limit cycle. These findings offer a provably stable active sensing strategy and may thus help to rationalize the active sensing movements made by animals as they perform certain motor behaviors.

eess.SY↗

Adaptive Gait Modeling and Optimization for Principally Kinematic Systems

Robotic adaptation to unanticipated operating conditions is crucial to achieving persistence and robustness in complex real world settings. For a wide range of cutting-edge robotic systems, such as micro- and nano-scale robots, soft robots, medical robots, and bio-hybrid robots, it is infeasible to anticipate the operating environment a priori due to complexities that arise from numerous factors including imprecision in manufacturing, chemo-mechanical forces, and poorly understood contact mechanics. Drawing inspiration from data-driven modeling, geometric mechanics (or gauge theory), and adaptive control, we employ an adaptive system identification framework and demonstrate its efficacy in enhancing the performance of principally kinematic locomotors (those governed by Rayleigh dissipation or zero momentum conservation). We showcase the capability of the adaptive model to efficiently accommodate varying terrains and iteratively modified behaviors within a behavior optimization framework. This provides both the ability to improve fundamental behaviors and perform motion tracking to precision. Notably, we are capable of optimizing the gaits of the Purcell swimmer using approximately 10 cycles per link, which for the nine-link Purcell swimmer provides a factor of ten improvement in optimization speed over the state of the art. Beyond simply a computational speed up, this ten-fold improvement may enable this method to be successfully deployed for in-situ behavior refinement, injury recovery, and terrain adaptation, particularly in domains where simulations provide poor guides for the real world.

cs.RO↗

A Data-Driven Approach to Geometric Modeling of Systems with Low-Bandwidth Actuator Dynamics

It is challenging to perform system identification on soft robots due to their underactuated, high-dimensional dynamics. In this work, we present a data-driven modeling framework, based on geometric mechanics (also known as gauge theory) that can be applied to systems with low-bandwidth control of the system's internal configuration. This method constructs a series of connected models comprising actuator and locomotor dynamics based on data points from stochastically perturbed, repeated behaviors. By deriving these connected models from general formulations of dissipative Lagrangian systems with symmetry, we offer a method that can be applied broadly to robots with first-order, low-pass actuator dynamics, including swelling-driven actuators used in hydrogel crawlers. These models accurately capture the dynamics of the system shape and body movements of a simplified swimming robot model. We further apply our approach to a stimulus-responsive hydrogel simulator that captures the complexity of chemo-mechanical interactions that drive shape changes in biomedically relevant micromachines. Finally, we propose an approach of numerically optimizing control signals by iteratively refining models, which is applied to optimize the input waveform for the hydrogel crawler. This transfer to realistic environments provides promise for applications in locomotor design and biomedical engineering.

cs.RO↗

Prospective Learning: Principled Extrapolation to the Future

Learning is a process which can update decision rules, based on past experience, such that future performance improves. Traditionally, machine learning is often evaluated under the assumption that the future will be identical to the past in distribution or change adversarially. But these assumptions can be either too optimistic or pessimistic for many problems in the real world. Real world scenarios evolve over multiple spatiotemporal scales with partially predictable dynamics. Here we reformulate the learning problem to one that centers around this idea of dynamic futures that are partially learnable. We conjecture that certain sequences of tasks are not retrospectively learnable (in which the data distribution is fixed), but are prospectively learnable (in which distributions may be dynamic), suggesting that prospective learning is more difficult in kind than retrospective learning. We argue that prospective learning more accurately characterizes many real world problems that (1) currently stymie existing artificial intelligence solutions and/or (2) lack adequate explanations for how natural intelligences solve them. Thus, studying prospective learning will lead to deeper insights and solutions to currently vexing challenges in both natural and artificial intelligences.

cs.LG↗

Optimal Estimation with Sensor Delay

Given a plant subject to delayed sensor measurement, there are several approaches to compensate for the delay. An obvious approach is to address this problem in state space, where the $n$-dimensional plant state is augmented by an $N$-dimensional (Padé) approximation to the delay, affording (optimal) state estimate feedback vis-à-vis the separation principle. Using this framework, we show: (1) Feedback of the estimated plant states partially inverts the delay; (2) The optimal (Kalman) estimator decomposes into $N$ (Padé) uncontrollable states, and the remaining $n$ eigenvalues are the solution to a reduced-order Kalman filter problem. Further, we show that the tradeoff of estimation error (of the full state estimator) between plant disturbance and measurement noise, only depends on the reduced-order Kalman filter (that can be constructed independently of the delay); (3) A subtly modified version of this state-estimation-based control scheme bears close resemblance to a Smith predictor. This modified state-space approach shares several limitations with its Smith predictor analog (including the inability to stabilize most unstable plants), limitations that are alleviated when using the unmodified state estimation framework.

math.OC↗

An observability result related to active sensing

For a general class of translationally invariant systems with a specific category of nonlinearity in the output, this paper presents necessary and sufficient conditions for global observability. Critically, this class of systems cannot be stabilized to an isolated equilibrium point by dynamic output feedback. These analyses may help explain the active sensing movements made by animals when they perform certain motor behaviors, despite the fact that these active sensing movements appear to run counter to the primary motor goals. The findings presented here establish that active sensing underlies the maintenance of observability for such biological systems, which are inherently nonlinear due to the presence of the high-pass sensor dynamics.

math.DS↗

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.

math.DS↗

Identification of a Hybrid Spring Mass Damper via Harmonic Transfer Functions as a Step Towards Data-Driven Models for Legged Locomotion

There are limitations on the extent to which manually constructed mathematical models can capture relevant aspects of legged locomotion. Even simple models for basic behaviors such as running involve non-integrable dynamics, requiring the use of possibly inaccurate approximations in the design of model-based controllers. In this study, we show how data-driven frequency domain system identification methods can be used to obtain input--output characteristics for a class of dynamical systems around their limit cycles, with hybrid structural properties similar to those observed in legged locomotion systems. Under certain assumptions, we can approximate hybrid dynamics of such systems around their limit cycle as a piecewise smooth linear time periodic system (LTP), further approximated as a time-periodic, piecewise LTI system to reduce parametric degrees of freedom in the identification process. In this paper, we use a simple one-dimensional hybrid model in which a limit-cycle is induced through the actions of a linear actuator to illustrate the details of our method. We first derive theoretical harmonic transfer functions of our example model. We then excite the model with small chirp signals to introduce perturbations around its limit-cycle and present systematic identification results to estimate the harmonic transfer functions for this model. Comparison between the data-driven HTF model and its theoretical prediction illustrates the potential effectiveness of such empirical identification methods in legged locomotion.

cs.RO↗

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.

q-bio.QM↗

Optimal Control with Noisy Time

This paper examines stochastic optimal control problems in which the state is perfectly known, but the controller's measure of time is a stochastic process derived from a strictly increasing Lévy process. We provide dynamic programming results for continuous-time finite-horizon control and specialize these results to solve a noisy-time variant of the linear quadratic regulator problem and a portfolio optimization problem with random trade activity rates. For the linear quadratic case, the optimal controller is linear and can be computed from a generalization of the classical Riccati differential equation.

math.OC↗

Nodal dynamics, not degree distributions, determine the structural controllability of complex networks

Structural controllability has been proposed as an analytical framework for making predictions regarding the control of complex networks across myriad disciplines in the physical and life sciences (Liu et al., Nature:473(7346):167-173, 2011). Although the integration of control theory and network analysis is important, we argue that the application of the structural controllability framework to most if not all real-world networks leads to the conclusion that a single control input, applied to the power dominating set (PDS), is all that is needed for structural controllability. This result is consistent with the well-known fact that controllability and its dual observability are generic properties of systems. We argue that more important than issues of structural controllability are the questions of whether a system is almost uncontrollable, whether it is almost unobservable, and whether it possesses almost pole-zero cancellations.

physics.soc-ph↗