Modeling the Dynamic Sensory Discharges of Insect CS
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Sense organs that detect forces are critical for animals to generate adaptive walking
[7], and similar sensors may also help robots walk. One prominent role that such organs
serve for insects is to indicate when a leg is in contact with the substrate by registering
forces due to supporting and propelling the body (i.e. during the “stance phase”). This
is particularly true for CS on the proximal leg segments [8, 9]. For this reason, we have
assembled legged robots in the past that include strain sensors on proximal leg segments
that return analog feedback regarding the forces acting on the leg [10, 11]. The robots’
neural controllers incorporate this information to assist the transition between the stance
phase and swing phase of stepping [12]. Related robots have similar sensor suites [13].
However, the performance of such a controller is sensitive to the precise tuning and
calibration of the strain sensors, making them impractical for real-world robotic use.
We believe that one reason insects are such adept walkers is that their CS are highly
dynamic and adaptive, effectively comparing measurements to their “history” in order
to accentuate their sensitivity to changing forces and cancel constant offsets. By more
thoroughly understanding CS responses with a dynamic model, we anticipate that we
can make our robot sensing more detailed and robust, which may lead to more effective
walking control in the future.
The goal of this manuscript is to construct a dynamic model that captures the response
of a group of CS when strained in its preferred direction [5, 6]. Previous experimental
and modeling work has shown that the CS response is dominated by nonlinear effects,
including a transient response that exhibits power law decay instead of exponential decay
[14] and frequency-independent phase locking with periodic inputs [15]. These features
preclude a linear systems description of CS responses, motivating the nonlinear systems
description presented in this manuscript.
Our model’s goal is to capture the following features of CS responses: Encode the
amplitude of the applied force; reflect the rate of the applied force; adapt to constant
applied forces; and exhibit hysteresis to cyclic applied forces. We hypothesize that such
features will emerge from a simple dynamic model wherein the sensory response is the
sum of three terms: One proportional to the instantaneous input; one that adapts to the
current force level via a nonlinear low-pass filter; and a constant offset.
In this manuscript, we describe the collection of CS responses from animal experiments (i.e. “animal data”) and the formulation and tuning of our dynamic model of CS
responses. We use animal data to select values for our model parameters. We show that
the model successfully describes animal data not used in the tuning process, supporting
that our model is capturing the fundamental properties of the system. We show that the
model can capture several gross features of CS responses, including responses that reflect
both the level of force and the rate of force, as well as hysteresis in the response to cyclic
loading. Finally, we discuss possible sources for these dynamics, possible implications
for how the nervous system must process load, and what advantages these dynamics
may offer robots in the future.
343
Sense organs that detect forces are critical for animals to generate adaptive walking
[7], and similar sensors may also help robots walk. One prominent role that such organs
serve for insects is to indicate when a leg is in contact with the substrate by registering
forces due to supporting and propelling the body (i.e. during the “stance phase”). This
is particularly true for CS on the proximal leg segments [8, 9]. For this reason, we have
assembled legged robots in the past that include strain sensors on proximal leg segments
that return analog feedback regarding the forces acting on the leg [10, 11]. The robots’
neural controllers incorporate this information to assist the transition between the stance
phase and swing phase of stepping [12]. Related robots have similar sensor suites [13].
However, the performance of such a controller is sensitive to the precise tuning and
calibration of the strain sensors, making them impractical for real-world robotic use.
We believe that one reason insects are such adept walkers is that their CS are highly
dynamic and adaptive, effectively comparing measurements to their “history” in order
to accentuate their sensitivity to changing forces and cancel constant offsets. By more
thoroughly understanding CS responses with a dynamic model, we anticipate that we
can make our robot sensing more detailed and robust, which may lead to more effective
walking control in the future.
The goal of this manuscript is to construct a dynamic model that captures the response
of a group of CS when strained in its preferred direction [5, 6]. Previous experimental
and modeling work has shown that the CS response is dominated by nonlinear effects,
including a transient response that exhibits power law decay instead of exponential decay
[14] and frequency-independent phase locking with periodic inputs [15]. These features
preclude a linear systems description of CS responses, motivating the nonlinear systems
description presented in this manuscript.
Our model’s goal is to capture the following features of CS responses: Encode the
amplitude of the applied force; reflect the rate of the applied force; adapt to constant
applied forces; and exhibit hysteresis to cyclic applied forces. We hypothesize that such
features will emerge from a simple dynamic model wherein the sensory response is the
sum of three terms: One proportional to the instantaneous input; one that adapts to the
current force level via a nonlinear low-pass filter; and a constant offset.
In this manuscript, we describe the collection of CS responses from animal experiments (i.e. “animal data”) and the formulation and tuning of our dynamic model of CS
responses. We use animal data to select values for our model parameters. We show that
the model successfully describes animal data not used in the tuning process, supporting
that our model is capturing the fundamental properties of the system. We show that the
model can capture several gross features of CS responses, including responses that reflect
both the level of force and the rate of force, as well as hysteresis in the response to cyclic
loading. Finally, we discuss possible sources for these dynamics, possible implications
for how the nervous system must process load, and what advantages these dynamics
may offer robots in the future.