Integrative Biomimetics of Autonomous Hexapedal Locomotion

Abstract

Despite substantial advances in many different fields of neurorobotics in general, and biomimetic robots in particular, a key challenge is the integration of concepts: to collate and combine research on disparate and conceptually disjunct research areas in the neurosciences and engineering sciences. We claim that the development of suitable robotic integration platforms is of particular relevance to make such integration of concepts work in practice. Here, we provide an example for a hexapod robotic integration platform for autonomous locomotion. In a sequence of six focus sections dealing with aspects of intelligent, embodied motor control in insects and multipedal robots-ranging from compliant actuation, distributed proprioception and control of multiple legs, the formation of internal representations to the use of an internal body model-we introduce the walking robot HECTOR as a research platform for integrative biomimetics of hexapedal locomotion. Owing to its 18 highly sensorized, compliant actuators, light-weight exoskeleton, distributed and expandable hardware architecture, and an appropriate dynamic simulation framework, HECTOR offers many opportunities to integrate research effort across biomimetics research on actuation, sensory-motor feedback, inter-leg coordination, and cognitive abilities such as motion planning and learning of its own body size.

Keywords: compliance; internal model; leg coordination; load sensing; motor control; motor learning; proprioception; walking.

Figure 1

HECTOR—from bio-inspiration to a physical robot. (A) The Indian stick insect Carausius morosus served as a template for the robot design. Especially, the relative distances of the leg onsets, the alignment of leg joint axes and the subdivision into three body segments were transferred during the design process. (B) Early abstraction of the three body segments prothorax, mesothorax and metathorax as compartments for the accommodation of “head-related” sensors, embedded computer system and battery, respectively. (C) First design sketch (Folkwang University of the Arts, Essen, Germany) of the hexapod robot considering the general shape demands from panels (A,B). (D) 3D-CAD-rendering of the light-weight, self-supporting body segments with an exoskeleton made of carbon fiber composites (manufactured at the Leibniz-Institute of Polymer Research in Dresden, Germany). Only few metal parts are included for directing the leg forces into the housings. (E) Photo of HECTOR. The body length of the assembled robot is 95 cm. The total mass is 13 kg. Approximately 7 kg of the mass comes from the 18 compliant joint drives in the legs.

Figure 2

Compliant joint drive with elastomer coupling. (A) The section view of an elastic joint drive of HECTOR. It contains a power- and control-electronics stack, a brushless DC motor, a light-weight harmonic drive gearbox, and a sensorised elastomer coupling with two position encoders. (B) Photographic depiction of the elastic joint drive with mounting points for adjacent segments. Stable force transmission is achieved by the positive locking of segment and seating (input flange and output flange). (C) Explosion view of the coupling shown in panel (D). The input flange is linked to the output of the gearbox. It connects to the input hub that carries three teeth, each of which extends into a corresponding notch of the elastomer. The remaining three notches in the elastomer are held by the three teeth of the output hub which, in turn, is fixed to the output flange. The elastic torsion of the elastomer and the resulting twist between input and output hubs is measured by a Hall-effect position sensor (after Paskarbeit et al., , with permission). (D) View of the elastomer coupling, as integrated into the drive. (E) Photo of input and output flange, together with elastomer star. (F) Image of the power- and control-electronics stack which is mounted in the back of the drive (after Paskarbeit et al., , with permission).

Figure 3

Distributed proprioception in the insect walking system. (A) Schematic of the reference frame for force detection by campaniform sensilla (CS) of an insect leg. For a given axis orientation (φ, ψ) and joint angle (α) of the thorax-coxa joint, all other leg joints move the leg within the leg plane (orange). The black arrows indicate the directional selectivity of four trochanteral CS groups (G1 to G4) and two tibial CS groups (G6a and G6b) in the stick insect. Owing to their location on the leg and to their physiology, four of these groups signal loading and unloading either within (G3, G4, G6a, G6b) or orthogonal (G1, G2) to the plane of leg movement. For example, G1 responds strongest to posteriorly directed forces. (B) Analogous sites for biomimetic strain measurements on the leg of HECTOR. (C) Scanning electron micrograph of the trochanter of a stick insect hind leg, with three enlarged sections showing the dorsal trochanteral hair plate (trHP, white circle), and trochanteral CS groups G2 (yellow), G3 (magenta) and G4 (purple). White double-arrows indicate the different preferred strain direction of each sensilla group. (D) Putative wiring diagram of known reflex loops involving trochanteral and tibial CS in a standing stick insect, indicating target and sign of the sensory-motor couplings mediated by individual CS groups. Thick lines represent verified sensory-motor couplings, thin lines are presumed on the basis of cursory observations. The schematic motor neuron pools are arranged according to their actions on joints either within the leg plane of movement (orange: levator/depressor system of the Coxa-Trochanter (CTr) joint and flexor/extensor system of the femur-tibia joint) or perpendicular to this plane (yellow: protractor/retractor system). Note that the excitatory connection from tibial CS group G6b to the depressor of the trochantero-femur establishes a muscle synergy through inter-joint coupling within the leg plane. The asterisk at the inhibitory connection of CS group G3 to the depressor indicates that a sign reversal is known to occur during walking.

Figure 4

Distributed proprioception in a leg of HECTOR. (A) A single leg of HECTOR with elastic α-, β-, and γ-joint drives (equivalent to the thorax-coxa, CTr, and femur-tibia joints of insects). Yellow and purple/magenta ellipses on the femur segment indicate locations for application of strain gauge pairs on the carbon fiber rod under the femur cover. Each strain gauge pair is named according to the joint axis which is predominantly responsible for the bending of the respective pair (colors as in Figure 3). The γ-pair is situated on the tibia segment. (B) Small-scale strain gauge board for the processing of four strain gauge pairs. The board can be mounted on the femur segment and connects to all strain gauges used on the leg structure. It can also be connected to the BioFlex bus of the robot communication infrastructure (see Figure 5). (C) Femur segment of the leg without cover, revealing the strain gauge pairs glued to the carbon fiber rod. The diagonal pair is sensitive to torsion of the femur and has no obvious biological equivalent. (D) Time courses of the α-joint torsion and the corresponding reading of the α-strain gauge pair during a single step. During the experiment, the leg was mounted to a sliding tether that simulated body movement by allowing the leg to push its own base forward and upward during stance (x and z directions in A). The dark gray area highlights the time interval during which the leg base was actively lifted and during which the leg had to carry its own weight. The light gray area indicates loading and unloading. (E) Same as (D) but for β-joint torsion and β-strain gauge pairs.

Figure 5

Communication scheme and location of main electronic parts of HECTOR. The robot has three body segments (pro-, meso-, and metathorax), each one of which carries a pair of legs. The front segment looks like a head as it carries eyes (cameras) and antennae (tactile probes) (Hoinville et al., 2014). Each leg comprises three compliant joint drives that communicate with a bus master (BioFlex Bus) in the respective body segment. Each bus master has two channels (2 Mbit/s each) to connect to a maximum of 250 clients which are polled by the bus master to allow real-time operation. The box for the left front leg lists the 12 sensor readings provided by the integrated electronics board of each joint drive and shows the multi-taxel foot tip sensor of a front leg. The bus masters are connected to the host computer (PC/104) in the mesothorax via high-speed USB. A fourth bus master in the mesothorax is dedicated to the two spindle drive setups for the inter-segmental joints.

Figure 6

Horizontal ground reaction forces (GRF) during unrestrained locomotion. Average horizontal force vectors of an unrestrained forward walking stick insect on a planar surface (drawn as inverted ground reaction force vectors). The vectors are mapped onto the position trajectories of the respective tarsus in a body-centered coordinate system (origin: the center of mass, being located at the rear end of the metathorax). Data from one representative animal, with separate measurements per leg, normalized to the duration of the stance phase. Black lines show force vectors every 1% of stance duration. Colored arrows indicate magnitude and direction of the horizontal force components at specific times of stance (red: 10%, cyan: 30%, blue: 50%, green: 70%, purple: 90%). Walking direction is from left to right. For details on ground reaction force measurements, see Dallmann et al. (2016).

Figure 7

Multi-taxel foot tip sensor. (A) Tactile cell distribution across the foot tip surface. There are five concentric rings with 12 sensing cells per ring. (B) The section cut through the sensorized foot tip, revealing the layered construction of sensor. (C) Finished prototypes with electronics. Lower panel: directional sensitivity of the foot tip sensor. (D) Tactile images (top) and corresponding test situations (bottom) for six different end-effector poses. The more slanted the pose, the more marginal is the location of mean activity in the tactile image (adapted from Drimus et al., , with permission). (E) Sensorized end-effector mounted on HECTOR.

Figure 8

Load-based inter-leg coordination in an insect. (A) Experimental setup for the simultaneous measurement of kinematics, GRF and muscle activity. Side view of an animal carrying a light-weight EMG backpack and motion capture markers (white circles) while standing on a force plate with its right middle (RM) leg just as the right hind leg is about to touch down. (B) Graphical summary of the putative mechanism underlying the transition from swing to stance in the RM leg after touch-down of the ipsilateral hind leg. CS groups G3 and G4 on the dorsal trochanter are highly sensitive to cuticular strains in the trochantero-femur of that leg. G3 is activated when dorsad bending torques increase, as by loading of the leg during stance. G4 activity signals a decrease of dorsad bending, as during unloading. Schematic of the G3/G4 reflex pathways onto coxal muscles in active animals. Broken lines indicate functional motor effects. G3 afferent activity excites (+) the depressor, i.e., a stance muscle, and inhibits (−) the levator, i.e., a swing muscle (Zill et al., 2012). G4 afferent activity is assumed to have the opposite effect. Unloading induced by a neighboring leg may reverse afferent activity from G3 to G4, thereby promoting the leg’s stance-to-swing transition. (C) Unloading of the middle leg coincides with a cessation of depressor activity. CTr torque of the RM leg and simultaneously recorded activity of the levator muscle (blue) and depressor muscle (red) of an example step. Dots above EMG traces indicate muscle spikes detected based on amplitude. TD: touch-down; LO: lift-off; t_UL: time of unloading. (D) Raster plot of detected muscle spikes aligned to t_UL of the RM leg (n = 73 steps from N = 8 animals). Walking speed corresponds to the mean speed of the center of mass during stance. The black box marks the step shown in (C). Note that the depressor activity stops at the time of unloading while levator activation shows a considerable time delay and cannot account for the onset of unloading of the middle leg. This holds true for the entire range of walking speeds tested (adapted from Dallmann et al., , with permission).

Figure 9

Spatial coordination in insects. (A) Active movements of antennae and walking legs of a stick insect delimit a volume around the body within which the limbs may touch an object. Since this volume comprises that part of the ambient space within which motor activity, proprioceptive and tactile sensory input may coincide, it may be called the peripersonal space of an insect. (B) Transfer of spatial contact information can work only in those parts of peripersonal space where at least two limbs may reach the same position in space. Since for all such positions, a contact experience of one limb indicates a potential contact position on another limb, an affordance is generated: a limb may reach a contact location on another limb. This was proposed as affordance space by Dürr and Schilling (2018). (C) Top: schematic postures of head and thorax as a stick insect climbs a sequence of two stairs. Middle: the inclination of the metathorax changes strongly (red; plotted as a function of metathorax position) and the head and all thorax segments move relative to each other. The head is pitched relative to the prothorax (black), the prothorax relative to the mesothorax (blue) and the mesothorax against the metathorax (green). Gray lines indicate the instants corresponding to the schematic postures above. Bottom: head pitch angle as a function of head position[adapted from Dürr and Schilling, (A,B; CC BY 4.0) and Theunissen et al., (C), with permission].

Figure 10

Spatial coordination in HECTOR. To direct the robot into a desired direction, two “pull points” may be used. (A) The two pull points, p₀ and p₁ are defined on the virtual body midline (blue circles). Foot positions are shown as red dots. (B) Concept for the computation of the rotation angle ω and the displacement vector d. Based on these two values, a transformation matrix can be constructed. The inverse of this matrix is applied to the leg tips in order to calculate the leg trajectories for the next time step which is shown in (C). Panel (D) indicates the movement of the pull points and the robot midline for a sequence of transformations. (E) During the resulting stance movement of a single foot on the ground, the leg must not leave its physically limited working area. In HECTOR this limit is formulated in terms of an unrestrictedness measure. For an ongoing stance movement, the current trajectory is extrapolated beyond the current position, yielding a test point that is checked for its unrestrictedness value. If this value lies below zero, a swing movement is elicited. (F) The target of the swing movement is set to a point on the unrestrictedness boundary. It is the intersection point with the backward extension of the current robot movement (red dotted line, attached to the home position of the leg). Instead of explicit transformation matrices, the internal body model may be used as well to estimate the respective movements of the feet.

Figure 11

The unrestrictedness measure in HECTOR. Volumetric representation of unrestricedness values for the left middle leg of HECTOR. The horizontal slices are set at distances of 0.1 m in z-direction. Panel (A) shows the joint angle unrestrictedness. Black and red contour lines are given for α-angles of 0 and ± 1 rad. (B,C) The singularity unrestrictedness (B) and the torque unrestrictedness (C) for a vertically directed gravity vector. (D) Combination (product) of the three unrestrictednes measures of (A–C). Any unrestrictedness value larger than 0 indicates a position which can be reached safely. Panels (E,F) show a non-collision and a collision situation between two neighboring legs, respectively. The distance between the enveloping geometric primitives can also be used for a further unrestrictedness measure.

Figure 12

Hierarchical internal body model. (A) The body model comprises a body level network (blue) and six subordinate leg level networks (green). Left: the body level network controls the six leg vectors, l₀ to l₅, and the three main body segment vectors, s₀ to s₂. Right: each one of the six leg level networks controls a leg with three joints and segments. The two levels are inter-connected via the shared representation of the leg vector (white arrow) (adapted from Schilling and Cruse, , CC BY 4.0). (B) Higher level of the internal body model. Arrows show all constituting vectors that are used to construct the local equations and relationships used to set up an Mean of Multiple Computations (MMC) network for the control of HECTOR. (C,D) One specific walking situation of a tripod gait, with the left front and hind leg on the ground together with the RM leg (with and without the underlying robot schematic). During the control of stance only those leg vectors are considered that are interacting with the ground, thus potentially contributing to propulsion, balance and steering. Legs that are currently in swing are suppressed within the body model (adapted from Schilling et al., ; © 2012 IEEE).

Figure 13

Curve walking in stick insects and HECTOR with and without a body model. (A) Sequence of a free walking, blindfolded stick insect on a horizontal plane. Black line segments and red dots show body axis and head every 200 ms (duration: 106 s; median speed was 35 mm/s at the beginning and 25 mm/s at the end). Bold blue line labels the part shown in the podogram. (B) Podogram with black lines showing stance episodes of all six legs (L1 to L3: left front to hind legs; R1 to R3: right front to hind legs) and corresponding yaw rotation of the body axis. Blue lines show median rotational velocity per 60 ms window (thin dark blue) and per 1 s window (thick light blue). (C) Snapshots of the simulated HECTOR turning to the right using the internal body model of Figure 12. The internal body model was constantly pulled to the front and the right. Snapshots show one body posture per second and four leg postures per second (Figure 8B from Schilling et al., , CC BY 4.0). (D) Podogram of the complete run shown corresponds to a turn of about 180°. The lower bar corresponds to 5 s of real time, or 500 iterations of the simulation time (adapted from Figure 7 from Schilling et al., ; CC BY 4.0). (E,F) Trajectories (E) and corresponding podogram (F) of the HECTOR simulation using the restrictedness measure as described in Figure 10, but not the body model. Red, green and blue lines in (E) show trajectories of the hind, middle and front segment, respectively. Gray arrow shows the pull vector.

Figure 14

Navigation control structure inspired by the Drosophila Central Complex. (A) Block scheme of the control structure. The visual system transfers information to the protocerebral bridge (PB) that is involved in body-size learning. The fan-shaped body (FB) participates in visual learning and orientation control whereas the ellipsoid body (EB) is in charge of spatial memory formation. (B) Scheme of the network devoted to learning whether an object is reachable within a certain number of steps and whether it is traversable depending on the acquired visual inputs. The green boxes represent simple mathematical transformations, whereas the blue circles represent spiking neurons. The learning process is performed at the level of the output neurons (red boxes). (C) Scheme of the angular positions acquired by the visual system as the robot moves forward from point (A) to point (B). The object of interest is a gate where different points of interest are detected. Different angles are acquired from the visual system to be processed by the network in (B) (adapted by permission from Patané et al., © 2018).

Figure 15

Demonstration of body-size learning. (A) The simulation environment consists of four rooms, each one containing three potential passages of different width and height. Each room is 10 × 10 m², the gates facing outside are too small to be passed (width: 0.6–0.8 m, height: 0.3–0.4 m) whereas the other gates are large enough (width: 1.5–2.4 m, height: 0.7–1.0 m). (B) Trajectory walked by the simulated robot while exploring the environment during the learning phase. During the learning phase, the robot acquires the knowledge needed for the formation of the internal body-size model. (C) Trajectory walked by the robot during the test phase. The body-size model is now used to select and pass the suitable gates while avoiding the others. (D) Distribution of the possible behavioral choices made on the basis of the distance output neuron. When the traveled distance is next to the maximum reachable value (i.e. 12 steps) the robot, as in the biological counterpart, can either try to attempt unsuccessfully or to give up incorrectly. (E) Comparison between the unsuccessful attempts in three simulations, where the HECTOR model was changed by reducing the tibia segment by 10% (red) and 30% (blue).