Adaptive load feedback robustly signals force dynamics in robotic model of Carausius morosus stepping

Abstract

Animals utilize a number of neuronal systems to produce locomotion. One type of sensory organ that contributes in insects is the campaniform sensillum (CS) that measures the load on their legs. Groups of the receptors are found on high stress regions of the leg exoskeleton and they have significant effects in adapting walking behavior. Recording from these sensors in freely moving animals is limited by technical constraints. To better understand the load feedback signaled by CS to the nervous system, we have constructed a dynamically scaled robotic model of the Carausius morosus stick insect middle leg. The leg steps on a treadmill and supports weight during stance to simulate body weight. Strain gauges were mounted in the same positions and orientations as four key CS groups (Groups 3, 4, 6B, and 6A). Continuous data from the strain gauges were processed through a previously published dynamic computational model of CS discharge. Our experiments suggest that under different stepping conditions (e.g., changing "body" weight, phasic load stimuli, slipping foot), the CS sensory discharge robustly signals increases in force, such as at the beginning of stance, and decreases in force, such as at the end of stance or when the foot slips. Such signals would be crucial for an insect or robot to maintain intra- and inter-leg coordination while walking over extreme terrain.

Keywords: campaniform sensilla; dynamic scaling; insects; legged locomotion; robotics; strain gauges.

FIGURE 1

(A) C. morosus robotic model of the middle leg connected to a linear guide. The linear guide is constrained to movement in the vertical direction or z axis. The free movement in the vertical directions forces the leg to support its own weight as it steps on the treadmill. (B) Middle leg of a C. morosus for biological size and degrees of freedom comparison.

FIGURE 2

(A) C. morosus robotic middle leg with three degrees of freedom. The leg segments, joint axes, and joint angles are indicated. The strain gauge rosettes are labeled on the tibia and trochanterofemur. (B) Strain gauge rosette inset, which displays orientation, is relative to the long axis of the leg segment. (C) CS groups which are labeled on an illustration of a C. morosus leg.

FIGURE 3

(A) Stance angles of robotic leg plotted against the x-coordinate of the foot in space as in Cruse and Bartling (1995). The x-coordinate is the anterior-posterior position of the foot. θ₁ is the ThC joint, θ₂ is the CTr joint, and θ₃ is the FTi joint. (B) The projected footpath of the scaled C. morosus footpath in the x-y plane. The y-coordinate is the lateral position of the foot. (C) Swing joint angles of robotic leg plotted against the x-coordinate of the foot in space. (D) The projected footpath on the x-z plane. The z-coordinate is the dorso-ventral position of the foot.

FIGURE 4

(A) Biological experiment with ramp and hold stimulus with resulting CS output. Adapted from Figure 6C of Zill et al. (2012). (B) The model CS discharge (group 3 and 4) in response to a single ramp-and-hold-and-release stimulus with distal end of the trochanterofemur fixed. (C) Axial and transverse strain of the trochanterofemur with distal end fixed. (D) Ramp-and-hold-and-release motion commanded to the Dynamixel servomotors. When the distal end of the trochanterofemur is fixed, the servo’s torque generates the bending moment that strains the segment. (E) The model CS discharge (group 3 and 4) in response to a single ramp-and-hold-and-release stimulus with distal end of the trochanterofemur free to move. (F) Axial and transverse strain of the trochanterofemur with distal end free. (G) Ramp-and-hold-and-release motion commanded to the Dynamixel servomotors. (H) The model CS discharge (group 3 and 4) in response to a single ramp-and-hold-and-release stimulus with distal end of the trochanterofemur fixed. (I) Axial and transverse strain of the trochanterofemur with distal end fixed. (J) Ramp-and-hold-and-release motion commanded to the Dynamixel servomotors.

FIGURE 5

(A) Diagram of robotic leg configuration. Green arrows show type and direction of movement for the servomotors. Distal end of leg is fixed in place and the leg is commanded to draw a 12-point asterisk shown with green arrows. (B) Trochanterofemur strain output when distal end of leg is fixed, and the robotic leg is commanded to draw an asterisk pattern. The leg would return to the center of the asterisk before moving to the next position. (C) Polar plot of the trochanterofemur strain data with anterior, posterior, dorsal and ventral sides of robotic leg labeled.

FIGURE 6

(A) Diagram of robotic leg configuration. Green arrows show type and direction of movement for the servomotors, linear guide, and treadmill. A weight indicated by the red arrow can be added to the linear guide to simulate additional body weight. (B) The raw trochanterofemur strain data of four subsequent steps in baseline configuration (no added weight). The axial strain is indicated in shades of blue and transverse indicated in shades of red. Positive changes in values indicate compression in that direction; negative changes in values indicate tension in that direction. The black bars indicate stance phase. (C) The trochanterofemur (group 3 and 4) CS model discharge from four subsequent steps in baseline configuration. (D) The tibial strain data from the same four subsequent steps (E): The tibia CS model discharge (group 6B and 6A) from four subsequent steps in baseline configuration. (F) The raw trochanterofemur strain from individual steps in each of the three load configurations. The configurations are baseline (no added weight), 500 g configuration (added weight to linear guide), and 1,000 g configuration (added weight to linear guide). (G) The CS model discharge of the trochanterofemur groups in the three configurations. (H) The raw tibia strain of individual steps in the three configurations. (I) The CS model outputs of the tibia groups in the three configurations. (J) Rate of change of the trochanterofemur strain. (K) Rate of change of the tibia strain.

FIGURE 7

(A) Diagram of robotic leg configuration. Green arrows show type and direction of movement for the leg servomotors, perturbation servomotor, linear guide, and treadmill. The perturbation servomotor can apply a controlled load to the linear guide. (B) The applied angle positions of the perturbation servomotor. Black bar indicates stance phase (C) resulting transient mass to linear carriage from perturbation servomotor. (D) The raw trochanterofemur strain of individual steps in the baseline and perturbation configuration. Positive changes in values indicate compression in that direction; negative changes in values indicate tension in that direction. Black bar indicates stance phase. (E) The raw tibia strain of individual steps in the baseline and perturbation configuration. (F) The model CS outputs (group 3 and 4) of the trochanterofemur baseline and perturbation steps. (G) The model tibia CS (group 6B and 6A) outputs of the baseline and perturbation steps.

FIGURE 8

(A) Diagram of robotic leg configuration. Green arrows show type and direction of movement for the servomotors, linear guide, and treadmill. A green arrow shows the direction the tibia is forced to slip in. (B) Stance joint angles of servomotors in baseline configuration (no slip condition) (C) Stance joint angles of servomotors with added slip condition as seen in middle of stance. Shaded bars indicate duration and location of slip condition. (D) The raw trochanterofemur strain of individual steps in baseline and slip configurations. Positive changes in values indicate compression in that direction; negative changes in values indicate tension in that direction. The axial is indicated in shades of blue and transverse indicated in shades of red. The black bars indicate stance phase. (E) The raw tibia strain of individual steps in baseline and slip configurations. (F) The model CS output of the trochanterofemur in baseline configuration. (G) The model CS output of the tibia in the baseline configuration. (H) The model CS outputs of the trochanterofemur in slip configuration. (I) The model CS outputs of the tibia in the slip configuration.