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.

Experimental setup
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.]

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