Kendrick M. Shaw

Continuous wave peristaltic motion in a robot

We have developed several innovative designs for a new kind of robot that uses a continuous wave of peristalsis for locomotion, the same method that earthworms use, and report on the first completed prototypes. This form of locomotion is particularly effective in constrained spaces, and although the motion has been understood for some time, it has rarely been effectively or accurately implemented in a robotic platform. As an alternative to robots with long segments, we present a technique using a braided mesh exterior to produce smooth waves of motion along the body of a worm-like robot. We also present a new analytical model of this motion and compare predicted robot velocity to a 2D simulation and a working prototype. Because constant-velocity peristaltic waves form due to accelerating and decelerating segments, it has been often assumed that this motion requires strong anisotropic ground friction. However, our analysis shows that with smooth, constant velocity waves, the forces that cause accelerations within the body sum to zero. Instead, transition timing between aerial and ground phases plays a critical role in the amount of slippage, and the final robot speed. The concept is highly scalable, and we present methods of construction at two different scales.

Efficient worm-like locomotion: slip and control of soft-bodied peristaltic robots

In this work, we present a dynamic simulation of an earthworm-like robot moving in a pipe with radially symmetric Coulomb friction contact. Under these conditions, peristaltic locomotion is efficient if slip is minimized. We characterize ways to reduce slip-related losses in a constant-radius pipe. Using these principles, we can design controllers that can navigate pipes even with a narrowing in radius. We propose a stable heteroclinic channel controller that takes advantage of contact force feedback on each segment. In an example narrowing pipe, this controller loses 40% less energy to slip compared to the best-fit sine wave controller. The peristaltic locomotion with feedback also has greater speed and more consistent forward progress

Selective extracellular stimulation of individual neurons in ganglia

Selective control of individual neurons could clarify neural functions and aid disease treatments. To target specific neurons, it may be useful to focus on ganglionic neuron clusters, which are found in the peripheral nervous system in vertebrates. Because neuron cell bodies are found primarily near the surface of invertebrate ganglia, and often found near the surface of vertebrate ganglia, we developed a technique for controlling individual neurons extracellularly using the buccal ganglia of the marine mollusc Aplysia californica as a model system. We experimentally demonstrated that anodic currents can selectively activate an individual neuron and cathodic currents can selectively inhibit an individual neuron using this technique. To define spatial specificity, we studied the minimum currents required for stimulation, and to define temporal specificity, we controlled firing frequencies up to 45 Hz. To understand the mechanisms of spatial and temporal specificity, we created models using the NEURON software package. To broadly predict the spatial specificity of arbitrary neurons in any ganglion sharing similar geometry, we created a steady-state analytical model. A NEURON model based on cat spinal motor neurons showed responses to extracellular stimulation qualitatively similar to those of the Aplysia NEURON model, suggesting that this technique could be widely applicable to vertebrate and human peripheral ganglia having similar geometry.

Phase Resetting in an Asymptotically Phaseless System: On the Phase Response of Limit Cycles Verging on a Heteroclinic Orbit ∗

Rhythmic behaviors in neural systems often combine features of limit-cycle dynamics (stability and periodicity) with features of near heteroclinic or near homoclinic cycle dynamics (extended dwell times in localized regions of phase space). Proximity of a limit cycle to one or more saddle equilibria can have a profound effect on the timing of trajectory components and response to both fast and slow perturbations, providing a possible mechanism for adaptive control of rhythmic motions. Reyn [“Generation of limit cycles from separatrix polygons in the phase plane” in Geometrical Approaches to Differential Equations, Lecture Notes in Math. 810, Springer, New York, 1980, pp. 264–289] showed that for a planar dynamical system with a stable heteroclinic cycle (or separatrix polygon), small perturbations satisfying a net inflow condition will generically give rise to a stable limit cycle (see also [J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, 3rd ed...

A controller for continuous wave peristaltic locomotion

While soft-bodied animals have an extraordinarily diverse set of robust behaviors, soft-bodied robots have not yet achieved this flexiblity. In this paper, we explore controlling a truly continuously deformable structure with a CPG-like network. Our recently completed soft wormlike robot with a continuously deformable outer mesh, along with a continuum analysis of peristalsis, has suggested the neural control investigated here. We use a Wilson-Cowan neuronal model in a continuum arrangement that mirrors the arrangement of muscles in an earthworm. We show that such a system is well suited to incorporate sensory input and can create both rhythmic and nonrhythmic activity. The system can be controlled using straightforward descending signals whose effects are largely decoupled and can modulate the properties from CPG-like behaviors to static waves. This approach will be useful for designing robotic systems that express multiple adaptive behavioral modes.

The significance of dynamical architecture for adaptive responses to mechanical loads during rhythmic behavior

Many behaviors require reliably generating sequences of motor activity while adapting the activity to incoming sensory information. This process has often been conceptually explained as either fully dependent on sensory input (a chain reflex) or fully independent of sensory input (an idealized central pattern generator, or CPG), although the consensus of the field is that most neural pattern generators lie somewhere between these two extremes. Many mathematical models of neural pattern generators use limit cycles to generate the sequence of behaviors, but other models, such as a heteroclinic channel (an attracting chain of saddle points), have been suggested. To explore the range of intermediate behaviors between CPGs and chain reflexes, in this paper we describe a nominal model of swallowing in Aplysia californica. Depending upon the value of a single parameter, the model can transition from a generic limit cycle regime to a heteroclinic regime (where the trajectory slows as it passes near saddle points). We then study the behavior of the system in these two regimes and compare the behavior of the models with behavior recorded in the animal in vivo and in vitro. We show that while both pattern generators can generate similar behavior, the stable heteroclinic channel can better respond to changes in sensory input induced by load, and that the response matches the changes seen when a load is added in vivo. We then show that the underlying stable heteroclinic channel architecture exhibits dramatic slowing of activity when sensory and endogenous input is reduced, and show that similar slowing with removal of proprioception is seen in vitro. Finally, we show that the distributions of burst lengths seen in vivo are better matched by the distribution expected from a system operating in the heteroclinic regime than that expected from a generic limit cycle. These observations suggest that generic limit cycle models may fail to capture key aspects of Aplysia feeding behavior, and that alternative architectures such as heteroclinic channels may provide better descriptions.

Motor neuronal activity varies least among individuals when it matters most for behavior

How does motor neuronal variability affect behavior? To explore this question, we quantified activity of multiple individual identified motor neurons mediating biting and swallowing in intact, behaving Aplysia californica by recording from the protractor muscle and the three nerves containing the majority of motor neurons controlling the feeding musculature. We measured multiple motor components: duration of the activity of identified motor neurons as well as their relative timing. At the same time, we measured behavioral efficacy: amplitude of grasping movement during biting and amplitude of net inward food movement during swallowing. We observed that the total duration of the behaviors varied: Within animals, biting duration shortened from the first to the second and third bites; between animals, biting and swallowing durations varied. To study other sources of variation, motor components were divided by behavior duration (i.e., normalized). Even after normalization, distributions of motor component durations could distinguish animals as unique individuals. However, the degree to which a motor component varied among individuals depended on the role of that motor component in a behavior. Motor neuronal activity that was essential for the expression of biting or swallowing was similar among animals, whereas motor neuronal activity that was not essential for that behavior varied more from individual to individual. These results suggest that motor neuronal activity that matters most for the expression of a particular behavior may vary least from individual to individual. Shaping individual variability to ensure behavioral efficacy may be a general principle for the operation of motor systems.

Worms, waves and robots

The Biologically Inspired Robotics group at Case Western Reserve University has developed several innovative designs for a new kind of robot that uses peristalsis, the method of locomotion used by earthworms. Unlike previous wormlike robots, our concept uses a continuously deformable outer mesh that interpolates the body position between discrete actuators. Here, we summarize our progress with this soft hyper-redundant robot.

A segmental mobile robot with active tensegrity bending and noise-driven oscillators

Tensegripede, the first prototype in a new series of modular, biologically inspired robots is presented. The robot platform is used to test innovative mechanical and controller designs. The robot is comprised of rigid body segments joined via tensegrity joint structures. These joints provide compliance to the structure and can be actuated via drive cables to change relative segment orientation. The tensegrity connections allow the robot to actively steer and rear body segments to navigate over and around obstacles. Tensegripede is capable of climbing objects up to 0.75 times the wheel diameter without rearing and can rear to heights of 1.13 times the wheel diameter. Tensegripede employs a new biologically inspired motor controller using stable heteroclinic channels to control motor speed with a simple PWM-like scheme.

Sensory Feedback Reduces Individuality by Increasing Variability within Subjects

Behavioral variability is ubiquitous [1-6], yet variability is more than just noise. Indeed, humans exploit their individual motor variability to improve tracing and reaching tasks [7]. What controls motor variability? Increasing the variability of sensory input, or applying force perturbations during a task, increases task variability [8, 9]. Sensory feedback may also increase task-irrelevant variability [9, 10]. In contrast, sensory feedback during locust flight or to multiple cortical areas just prior to task performance decreases variability during task-relevant motor behavior [11, 12]. Thus, how sensory feedback affects both task-relevant and task-irrelevant motor outputs must be understood. Furthermore, since motor control is studied in populations, the effects of sensory feedback on variability must also be understood within and across subjects. For example, during locomotion, each step may vary within and across individuals, even when behavior is normalized by step cycle duration [13]. Our previous work demonstrated that motor components that matter for effective behavior show less individuality [14]. Is sensory feedback the mechanism for reducing individuality? We analyzed durations and relative timings of motor pools within swallowing motor patterns in the presence and absence of sensory feedback and related these motor program components to behavior. Here, at the level of identified motor neurons, we show that sensory feedback to motor program components highly correlated with behavioral efficacy reduces variability across subjects but-surprisingly-increases variability within subjects. By controlling intrinsic, individual differences in motor neuronal activity, sensory feedback provides each subject access to a common solution space.