A Minimal Model Describing Hexapedal Interlimb Coordination: The Tegotae-Based Approach

Central pattern generators evolved for real-time adaptation to rhythmic stimuli

For a robot to be both autonomous and collaborative requires the ability to adapt its movement to a variety of external stimuli, whether these come from humans or other robots. Typically, legged robots have oscillation periods explicitly defined as a control parameter, limiting the adaptability of walking gaits. Here we demonstrate a virtual quadruped robot employing a bio-inspired central pattern generator (CPG) that can spontaneously synchronize its movement to a range of rhythmic stimuli. Multi-objective evolutionary algorithms were used to optimize the variation of movement speed and direction as a function of the brain stem drive and the centre of mass control respectively. This was followed by optimization of an additional layer of neurons that filters fluctuating inputs. As a result, a range of CPGs were able to adjust their gait pattern and/or frequency to match the input period. We show how this can be used to facilitate coordinated movement despite differences in morphology, as well as to learn new movement patterns.

Robust and reusable self-organized locomotion of legged robots under adaptive physical and neural communications

Introduction

Animals such as cattle can achieve versatile and elegant behaviors through automatic sensorimotor coordination. Their self-organized movements convey an impression of adaptability, robustness, and motor memory. However, the adaptive mechanisms underlying such natural abilities of these animals have not been completely realized in artificial legged systems.

Methods

Hence, we propose adaptive neural control that can mimic these abilities through adaptive physical and neural communications. The control algorithm consists of distributed local central pattern generator (CPG)-based neural circuits for generating basic leg movements, an adaptive sensory feedback mechanism for generating self-organized phase relationships among the local CPG circuits, and an adaptive neural coupling mechanism for transferring and storing the formed phase relationships (a gait pattern) into the neural structure. The adaptive neural control was evaluated in experiments using a quadruped robot.

Results

The adaptive neural control enabled the robot to 1) rapidly and automatically form its gait (i.e., self-organized locomotion) within a few seconds, 2) memorize the gait for later recovery, and 3) robustly walk, even when a sensory feedback malfunction occurs. It also enabled maneuverability, with the robot being able to change its walking speed and direction. Moreover, implementing adaptive physical and neural communications provided an opportunity for understanding the mechanism of motor memory formation.

Discussion

Overall, this study demonstrates that the integration of the two forms of communications through adaptive neural control is a powerful way to achieve robust and reusable self-organized locomotion in legged robots.

Locomotor resilience through load-dependent modulation of muscle co-contraction

Terrestrial locomotor behavior in variable environments requires resilience to sudden changes in substrate properties. For example, walking animals can adjust to substantial changes in slope and corresponding changes in load distribution among legs. In insects, slope-dependent adjustments have mainly been examined under steady-state conditions, whereas the transition dynamics have been largely neglected. In a previous study, we showed that steady-state adjustments of stick insects to ±45° slopes involve substantial changes in joint torques and muscle activity with only minor changes in leg kinematics. Here, we take a close look at the time course of these adjustments as stick insects compensate for various kinds of disturbances to load distribution. In particular, we test whether the transition from one steady state to another involves distinct transition steps or follows a graded process. To resolve this, we combined simultaneous recordings of whole-body kinematics and hind leg muscle activity to elucidate how freely walking Carausius morosus negotiated a step-change in substrate slope. Step-by-step adjustments reveal that muscle activity changed in a graded manner as a function of body pitch relative to gravity. We further show analogous transient adjustment of muscle activity in response to destabilizing lift-off events of neighboring legs and the disappearance of antagonist co-activation during crawling episodes. Given these three examples of load-dependent regulation of antagonist muscle co-contraction, we conclude that stick insects respond to both transient and sustained changes in load distribution by regulating joint stiffness rather than through distinct transition steps.

Motion Hacking – Understanding by Controlling Animals –

Insects exhibit resilient and flexible capabilities allowing them to adapt their walk in response to changes of the environment or body properties, for example the loss of a leg. While the motor control paradigm governing inter-leg coordination has been extensively studied in the past for such adaptive walking, the neural mechanism remains unknown. To overcome this situation, the project “Motion Hacking” develops a method for hacking leg movements by electrostimulating leg muscles while retaining the natural sensorimotor functions of the insect. This research aims to elucidate the flexible inter-leg coordination mechanism underlying insect walking by observing the adapting process of inter-leg coordination with the insect nervous system when leg movements are externally controlled via motion hacking.

Adaptive Interlimb Coordination Mechanism for Hexapod Locomotion Based on Active Load Sensing

Insects can flexibly coordinate their limbs to adapt to various locomotor conditions, e.g., complex environments, changes in locomotion speed, and leg amputation. An interesting aspect of insect locomotion is that the gait patterns are not necessarily stereotypical but are often highly variable, e.g., searching behavior to obtain stable footholds in complex environments. Several previous studies have focused on the mechanism for the emergence of variable limb coordination patterns. However, the proposed mechanisms are complicated and the essential mechanism underlying insect locomotion remains elusive. To address this issue, we proposed a simple mathematical model for the mechanism of variable interlimb coordination in insect locomotion. The key idea of the proposed model is “decentralized active load sensing,” wherein each limb actively moves and detects the reaction force from the ground to judge whether it plays a pivotal role in maintaining the steady support polygon. Based on active load sensing, each limb stays in the stance phase when the limb is necessary for body support. To evaluate the proposed model, we conducted simulation experiments using a hexapod robot. The results showed that the proposed simple mechanism allows the hexapod robot to exhibit typical gait patterns in response to the locomotion speed. Furthermore, the proposed mechanism improves the adaptability of the hexapod robot for leg amputations and lack of footholds by changing each limb's walking and searching behavior in a decentralized manner based on the physical interaction between the body and the environment.

Insect-Inspired Robots: Bridging Biological and Artificial Systems

This review article aims to address common research questions in hexapod robotics. How can we build intelligent autonomous hexapod robots that can exploit their biomechanics, morphology, and computational systems, to achieve autonomy, adaptability, and energy efficiency comparable to small living creatures, such as insects? Are insects good models for building such intelligent hexapod robots because they are the only animals with six legs? This review article is divided into three main sections to address these questions, as well as to assist roboticists in identifying relevant and future directions in the field of hexapod robotics over the next decade. After an introduction in section (1), the sections will respectively cover the following three key areas: (2) biomechanics focused on the design of smart legs; (3) locomotion control; and (4) high-level cognition control. These interconnected and interdependent areas are all crucial to improving the level of performance of hexapod robotics in terms of energy efficiency, terrain adaptability, autonomy, and operational range. We will also discuss how the next generation of bioroboticists will be able to transfer knowledge from biology to robotics and vice versa.

Adaptive and Energy-Efficient Optimal Control in CPGs Through Tegotae-Based Feedback

To obtain biologically inspired robotic control, the architecture of central pattern generators (CPGs) has been extensively adopted to generate periodic patterns for locomotor control. This is attributed to the interesting properties of nonlinear oscillators. Although sensory feedback in CPGs is not necessary for the generation of patterns, it plays a central role in guaranteeing adaptivity to environmental conditions. Nonetheless, its inclusion significantly modifies the dynamics of the CPG architecture, which often leads to bifurcations. For instance, the force feedback can be exploited to derive information regarding the state of the system. In particular, the Tegotae approach can be adopted by coupling proprioceptive information with the state of the oscillation itself in the CPG model. This paper discusses this policy with respect to other types of feedback; it provides higher adaptivity and an optimal energy efficiency for reflex-like actuation. We believe this is the first attempt to analyse the optimal energy efficiency along with the adaptivity of the Tegotae approach.

Tegotae-Based Control Produces Adaptive Inter- and Intra-limb Coordination in Bipedal Walking

Despite the appealing concept of central pattern generator (CPG)-based control for bipedal walking robots, there is currently no systematic methodology for designing a CPG-based controller. To remedy this oversight, we attempted to apply the Tegotae approach, a Japanese concept describing how well a perceived reaction, i.e., sensory information, matches an expectation, i.e., an intended motor command, in designing localised controllers in the CPG-based bipedal walking model. To this end, we developed a Tegotae function that quantifies the Tegotae concept. This function allowed incorporating decentralised controllers into the proposed bipedal walking model systematically. We designed a two-dimensional bipedal walking model using Tegotae functions and subsequently implemented it in simulations to validate the proposed design scheme. We found that our model can walk on both flat and uneven terrains and confirmed that the application of the Tegotae functions in all joint controllers results in excellent adaptability to environmental changes.

Descending and Ascending Signals That Maintain Rhythmic Walking Pattern in Crickets

The cricket is one of the model animals used to investigate the neuronal mechanisms underlying adaptive locomotion. An intact cricket walks mostly with a tripod gait, similar to other insects. The motor control center of the leg movements is located in the thoracic ganglia. In this study, we investigated the walking gait patterns of the crickets whose ventral nerve cords were surgically cut to gain an understanding of how the descending signals from the head ganglia and ascending signals from the abdominal nervous system into the thoracic ganglia mediate the initiation and coordination of the walking gait pattern. Crickets whose paired connectives between the brain and subesophageal ganglion (SEG) (circumesophageal connectives) were cut exhibited a tripod gait pattern. However, when one side of the circumesophageal connectives was cut, the crickets continued to turn in the opposite direction to the connective cut. Crickets whose paired connectives between the SEG and prothoracic ganglion were cut did not walk, whereas the crickets exhibited an ordinal tripod gait pattern when one side of the connectives was intact. Crickets whose paired connectives between the metathoracic ganglion and abdominal ganglia were cut initiated walking, although the gait was not a coordinated tripod pattern, whereas the crickets exhibited a tripod gait when one side of the connectives was intact. These results suggest that the brain plays an inhibitory role in initiating leg movements and that both the descending signals from the head ganglia and the ascending signals from the abdominal nervous system are important in initiating and coordinating insect walking gait patterns.

A Comparative Study of Adaptive Interlimb Coordination Mechanisms for Self-Organized Robot Locomotion

Walking animals demonstrate impressive self-organized locomotion and adaptation to body property changes by skillfully manipulating their complicated and redundant musculoskeletal systems. Adaptive interlimb coordination plays a crucial role in this achievement. It has been identified that interlimb coordination is generated through dynamical interactions between the neural system, musculoskeletal system, and environment. Based on this principle, two classical interlimb coordination mechanisms (continuous phase modulation and phase resetting) have been proposed independently. These mechanisms use decoupled central pattern generators (CPGs) with sensory feedback, such as ground reaction forces (GRFs), to generate robot locomotion autonomously without predefining it (i.e., self-organized locomotion). A comparative study was conducted on the two mechanisms under decoupled CPG-based control implemented on a quadruped robot in simulation. Their characteristics were compared by observing their CPG phase convergence processes at different control parameter values. Additionally, the mechanisms were investigated when the robot faced various unexpected situations, such as noisy feedback, leg motor damage, and carrying a load. The comparative study reveals that the phase modulation and resetting mechanisms demonstrate satisfactory performance when they are subjected to symmetric and asymmetric GRF distributions, respectively. This work also suggests a strategy for the appropriate selection of adaptive interlimb coordination mechanisms under different conditions and for the optimal setting of their control parameter values to enhance their control performance.

Leg amputation modifies coordinated activation of the middle leg muscles in the cricket Gryllus bimaculatus

Insects alter their walking pattern in order to respond to demands of an ever-changing environment, such as varying ground surface textures. They also exhibit resilient and flexible ability to retain the capacity to walk even after substantial changes in their body properties, e.g. leg amputation. While the motor control paradigm governing the inter-leg coordination in such adaptive walking has been extensively described in past studies, the mechanism remains unknown. Here, we examined this question by using the cricket (Gryllus bimaculatus), which shows a tetrapod/tripod gait on a flat surfaces, like many other insects. We performed leg amputation experiments to investigate modifications of leg movements and coordination of muscle activities. We simultaneously recorded (1) the leg movements, locomotion velocity, and body rotation and (2) the leg movements and leg muscles activities before and after leg amputation. Crickets displayed adaptive coordination of leg movement patterns in response to amputations. The activation timings of levator muscles in both middle legs tended to synchronize in phase when both legs were amputated at the coxatrochanteral joint. This supports the hypothesis that an intrinsic contralateral connection within the mesothoracic ganglion exists, and that mechanosensory feedback from the legs override this connection, resulting in the anti-phase movement of a normal gait.

Decoding Decentralized Control Mechanism Underlying Adaptive and Versatile Locomotion of Snakes

Snakes have no limbs and can move in various environments using a simple elongated limbless body structure obtained through a long-term evolutionary process. Specifically, snakes have various locomotion patterns, which they change in response to conditions encountered. For example, on an unstructured terrain, snakes actively utilize the terrain's irregularities and move effectively by actively pushing their bodies against the "scaffolds" that they encounter. In a narrow aisle, snakes exhibit concertina locomotion, in which the tail part of the body is pulled forward with the head part anchored, and this is followed by the extension of the head part with the tail part anchored. Furthermore, snakes often exhibit three-dimensional (3-D) locomotion patterns wherein the points of ground contact change in a spatiotemporal manner, such as sidewinding and sinus-lifting locomotion. This ability is achieved possibly by a decentralized control mechanism, which is still mostly unknown. In this study, we address this aspect by employing a synthetic approach to understand locomotion mechanisms by developing mathematical models and robots. We propose a Tegotae-based decentralized control mechanism and use a 2-D snake-like robot to demonstrate that it can exhibit scaffold-based and concertina locomotion. Moreover, we extend the proposed mechanism to 3D and use a 3-D snake-like robot to demonstrate that it can exhibit sidewinding and sinus-lifting locomotion. We believe that our findings will form a basis for developing snake-like robots applicable to search-and-rescue operations as well as understanding the essential decentralized control mechanism underlying animal locomotion.

General Distributed Neural Control and Sensory Adaptation for Self-Organized Locomotion and Fast Adaptation to Damage of Walking Robots

Walking animals such as invertebrates can effectively perform self-organized and robust locomotion. They can also quickly adapt their gait to deal with injury or damage. Such a complex achievement is mainly performed via coordination between the legs, commonly known as interlimb coordination. Several components underlying the interlimb coordination process (like distributed neural control circuits, local sensory feedback, and body-environment interactions during movement) have been recently identified and applied to the control systems of walking robots. However, while the sensory pathways of biological systems are plastic and can be continuously readjusted (referred to as sensory adaptation), those implemented on robots are typically static. They first need to be manually adjusted or optimized offline to obtain stable locomotion. In this study, we introduce a fast learning mechanism for online sensory adaptation. It can continuously adjust the strength of sensory pathways, thereby introducing flexible plasticity into the connections between sensory feedback and neural control circuits. We combine the sensory adaptation mechanism with distributed neural control circuits to acquire the adaptive and robust interlimb coordination of walking robots. This novel approach is also general and flexible. It can automatically adapt to different walking robots and allow them to perform stable self-organized locomotion as well as quickly deal with damage within a few walking steps. The adaptation of plasticity after damage or injury is considered here as lesion-induced plasticity. We validated our adaptive interlimb coordination approach with continuous online sensory adaptation on simulated 4-, 6-, 8-, and 20-legged robots. This study not only proposes an adaptive neural control system for artificial walking systems but also offers a possibility of invertebrate nervous systems with flexible plasticity for locomotion and adaptation to injury.

Flexible Spiking CPGs for Online Manipulation During Hexapod Walking

Neural signals for locomotion are influenced both by the neural network architecture and sensory inputs coordinating and adapting the gait to the environment. Adaptation relies on the ability to change amplitude, frequency, and phase of the signals within the sensorimotor loop in response to external stimuli. However, in order to experiment with closed-loop control, we first need a better understanding of the dynamics of the system and how adaptation works. Based on insights from biology, we developed a spiking neural network capable of continuously changing amplitude, frequency, and phase online. The resulting network is deployed on a hexapod robot in order to observe the walking behavior. The morphology and parameters of the network results in a tripod gait, demonstrating that a design without afferent feedback is sufficient to maintain a stable gait. This is comparable to results from biology showing that deafferented samples exhibit a tripod-like gait and adds to the evidence for a meaningful role of network topology in locomotion. Further, this work enables research into the role of sensory feedback and high-level control signals in the adaptation of gait types. A better understanding of the neural control of locomotion relates back to biology where it can provide evidence for theories that are currently not testable on live insects.

Sea star inspired crawling and bouncing

The oral surface of sea stars is lined with arrays of tube feet that enable them to achieve highly controlled locomotion on various terrains. The activity of the tube feet is orchestrated by a nervous system that is distributed throughout the body without a central brain. How such a distributed nervous system produces a coordinated locomotion is yet to be understood. We develop mathematical models of the biomechanics of the tube feet and the sea star body. In the model, the feet are coupled mechanically through their structural connection to a rigid body. We formulate hierarchical control laws that capture salient features of the sea star nervous system. Namely, at the tube foot level, the power and recovery strokes follow a state-dependent feedback controller. At the system level, a directionality command is communicated through the nervous system to all tube feet. We study the locomotion gaits afforded by this hierarchical control model. We find that these minimally coupled tube feet coordinate to generate robust forward locomotion, reminiscent of the crawling motion of sea stars, on various terrains and for heterogeneous tube feet parameters and initial conditions. Our model also predicts a transition from crawling to bouncing consistently with recent experiments. We conclude by commenting on the implications of these findings for understanding the neuromechanics of sea stars and their potential application to autonomous robotic systems.

Integrative Biomimetics of Autonomous Hexapedal Locomotion

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.

Designing higher fourier harmonics of Tegotae function using genetic algorithm-a case study with an earthworm locomotion

'Tegotae' is a Japanese concept describing how well a perceived reaction matches a generated action. We previously proposed a novel decentralised control scheme for animals' adaptive locomotion based on a Tegotae function, a function which quantifies Tegotae and is generally given by the product of action and reaction terms. Although this scheme is helpful for extracting common control principles underlying various types of animal locomotion, there remains further room for improvement of its design. Specifically, while the previous works assumed that the action term is given by a sinusoidal function, it is expected that introducing higher Fourier harmonics in the action term improves locomotion performance. In this study, taking earthworm locomotion as an example, we design a Tegotae function whose action term includes higher Fourier harmonics by using a genetic algorithm. We demonstrate via simulations that the performance improves by implementing the higher Fourier harmonics.

Body-limb coordination mechanism underlying speed-dependent gait transitions in sea roaches

The sea roach is an isopod with 14 legs; owing to its many degrees of freedom and coordination thereof, it can walk rapidly on rough terrain. Although there likely exists a remarkable decentralized control mechanism that facilitates fast and adaptive locomotion of sea roaches, it still remains elusive. To address this issue, we performed behavioural experiments and revealed that sea roaches often change their gait patterns depending on the locomotion speed. We suggest that the bending of the body trunk in the pitch direction is essential for the gait transitions, and we propose a decentralized control mechanism for body-limb coordination. We demonstrate this with a sea-roach-like robot whose gait transition is achieved by the proposed mechanism. This mechanism has some points in common with control mechanisms proposed for other legged animals. Thus, our findings will help unveil the common principle of legged locomotion and aid the design of multi-legged robots that move like animals.

Simple analytical model reveals the functional role of embodied sensorimotor interaction in hexapod gaits

Insects have various gaits with specific characteristics and can change their gaits smoothly in accordance with their speed. These gaits emerge from the embodied sensorimotor interactions that occur between the insect’s neural control and body dynamic systems through sensory feedback. Sensory feedback plays a critical role in coordinated movements such as locomotion, particularly in stick insects. While many previously developed insect models can generate different insect gaits, the functional role of embodied sensorimotor interactions in the interlimb coordination of insects remains unclear because of their complexity. In this study, we propose a simple physical model that is amenable to mathematical analysis to explain the functional role of these interactions clearly. We focus on a foot contact sensory feedback called phase resetting, which regulates leg retraction timing based on touchdown information. First, we used a hexapod robot to determine whether the distributed decoupled oscillators used for legs with the sensory feedback generate insect-like gaits through embodied sensorimotor interactions. The robot generated two different gaits and one had similar characteristics to insect gaits. Next, we proposed the simple model as a minimal model that allowed us to analyze and explain the gait mechanism through the embodied sensorimotor interactions. The simple model consists of a rigid body with massless springs acting as legs, where the legs are controlled using oscillator phases with phase resetting, and the governed equations are reduced such that they can be explained using only the oscillator phases with some approximations. This simplicity leads to analytical solutions for the hexapod gaits via perturbation analysis, despite the complexity of the embodied sensorimotor interactions. This is the first study to provide an analytical model for insect gaits under these interaction conditions. Our results clarified how this specific foot contact sensory feedback contributes to generation of insect-like ipsilateral interlimb coordination during hexapod locomotion.

The function of the ophiuroid nerve ring: how a decentralized nervous system controls coordinated locomotion

Echinoderms lack a centralized nervous control system yet each extant echinoderm class has evolved unique and effective strategies for locomotion. Brittle stars (Ophiuroidea) stride swiftly over the seafloor by coordinating motions of their five muscular arms. Their arms consist of many repeating segments, requiring them to use a complex control system to coordinate motions among segments and between arms. We conducted in vivo experiments with brittle stars to analyze the functional role of the nerve ring, which connects the nerves in each arm. These experiments were designed to determine how the ophiuroid nervous system performs complex decision-making and locomotory actions under decentralized control. Our results show that brittle star arms must be connected by the nerve ring for coordinated locomotion, but information can travel bidirectionally around the nerve ring so that it circumvents the severance. Evidence presented indicates that ophiuroids rely on adjacent nerve ring connections for sustained periodic movements. The number of arms connected via the nerve ring is correlated positively with the likelihood that the animal will show coordinated locomotion, indicating that integrated nerve ring tissue is critical for control. The results of the experiments should provide a basis for the advancement of complex artificial decentralized systems.