DOI: 10.5061/dryad.wpzgmsbsw
title: Data from: A hierarchical model for external electrical control of an insect, accounting for inter-individual variation of muscle force properties

description: Cyborg control of insect movement is promising for developing miniature,
 high-mobility, and efficient biohybrid robots. However, considering the
 inter-individual variation of the insect neuromuscular apparatus and its
 neural control is challenging. We propose a hierarchical model including
 inter-individual variation of muscle properties of three leg muscles 14
 involved in propulsion (retractor coxae), joint stiffness (pro- and
 retractor coxae), and stance-swing transition (protractor coxae and
 levator trochanteris) in the stick insect Carausius morosus. To estimate
 mechanical effects induced by external muscle stimulation, the model is
 based on the systematic evaluation of joint torques as functions of
 electrical stimulation parameters. A nearly linear relationship between
 the stimulus burst duration and generated torque was observed. This
 stimulus-torque characteristic holds for burst durations of up to 500ms,
 corresponding to the stance and swing phase durations of medium to fast
 walking stick insects. Hierarchical Bayesian modeling revealed that
 linearity of the stimulus-torque characteristic was invariant, with
 individually varying slopes. Individual prediction of joint torques
 provides significant benefits for precise cyborg control.
description: Experimental setup<br>The insect was fixed dorsal side up
 on a balsa wood platform, using insect pins. The coxa of the right middle
 leg was located at the platform edge (Fig. 1 A right in the manuscript).
 We selected three leg muscles (protractor, retractor, and levator) in the
 right middle leg for electrical stimulation (Fig. 1 B in the manuscript).
 When stick insects walk, they use the protractor to swing the leg forward
 during the swing phase, the retractor to move the leg backward during the
 stance phase, and levator to initiate the stance-to-swing transition
 (Rosenbaum et al., 2010; Dallmann et al., 2019; Günzel et al., 2022;
 Bässler and Wegner, 1983). Moreover, co-contraction of the protractor and
 retractor are known to vary based on the overall load distribution, thus
 being important for postural control by regulating joint stiffness
 (Dallmann et al., 2019; Günzel et al., 2022). Electrical stimulation of
 the protractor and retractor muscles generate forward and backward leg
 movements at the thorax–coxa (ThC) joint, whereas stimulation of the
 levator muscle generates an upward leg movement at the coxa–trochanter
 (CTr) joint (Dallmann et al., 2016). To estimate the joint torque
 generated during the stimulation, we used a custom-made force transducer
 with strain gauges. Prior to the experiments, the measured force [mN] was
 calibrated from the force-sensor value [V] with weights of known mass
 (0.2–5 g). Two small insect pins attached to the tip of the force
 transducer held the middle part of the femur of the middle leg (Fig. 1 A
 right in the manuscript). The length between the ThC or CTr joints and the
 attachment point at the femur was measured and used as the moment arm for
 the calculation of torque. [See the manuscript for more
 details.]
description: Software used for each data are: [Figure 2] Python
 (3.9.7); [Figures 3 to 7]: R Studio, R version (4.1.3) and Stan
 (2.21.0) #We have not checked version dependencies for
 all code