A major feature of animal locomotion is that of its flexibility or adaptability, i.e. the capacity of the locomoting animal to maintain robust and consistent movement through a variable and constantly changing environment. This outstanding ability, perfected by a long evolutionary history, is manifested at all levels of control and execution of locomotion: from the central and local neuronal circuits controlling and generating locomotion-related motor patterns, through the complex interactions of the central nervous system with ongoing as well as transient sensory signals, via the interactions of the central and sensory system with the muscular system responsible for executing movement of the body parts (legs, tail, and trunk), and last but This is a provisional file, not the final typeset article 2 D. Owaki, P. Manoonpong, and A. AyaliBiological and Robotic Inter-limb Coordination not least, the dynamic interaction of these body parts with the physical environment (Fig. 1, Center). A number of contributions to this special issue have addressed the distinctive plasticity of animal locomotion, focusing on aspects of locomotion and inter-limb coordination related to the different levels noted above (Fig. 1,Left).Starting with the central circuits, David and Ayali (2021) present a detailed investigation of the locomotion central pattern generating (CPG) neuronal networks and their underlying connectivity scheme in the cockroach, an established model in the study of locomotion control. They discuss the role of rhythmic properties of the endogenous local (segmental) CPGs vs. inter-circuit coupling in the production of the functional, adaptable motor output during locomotion in the behaving animal. Yet another model insect, the cricket, is utilized by Naniwa and Aonuma (2021) in order to present the instrumental role of descending and ascending inputs into the thoracic motor control center (the CPGs controlling leg movements) in maintaining the walking pattern. They demonstrate that descending signals from the head ganglia play an inhibitory role in initiating leg movements; and that both the descending and ascending signals from the abdominal nervous system are important in initiating and coordinating the walking gait patterns.Inter-limb coordination is directly investigated by Niemeier et al. (2021) by way of controlled lesions of thoracic connectives in one of the leading models in the study of leg coordination -the stick insect.The importance of neural information transfer among the legs is nicely demonstrated. Furthermore, the findings show that spatial and temporal coordination of leg movements are obtained independently, with the former rather than the latter being affected by the experimental manipulations. Overall this offers yet another example of the importance of proprioceptive feedback in the generation of a coordinated gait.Insects search for and find the source of a desired odor as a basic locomotion behavior, such as when searching for food or a mate. This behavior offers an interesting research topic in regard to motor-cognitive function: how is such successful locomotion achieved under conditions of turbulent odor plumes, utilizing the insects' small number of neurons. Hernandez-Reyes et al. (2021) measured the behavior of moths using a virtual reality system that presents accurate and reproducible odor stimuli by using blue light and optogenetic moths. Their results demonstrate that behavioral variations have a higher probability of obtaining more information than "programmed behaviors" ( i.e., reactive, exploitative behaviors),suggesting that silk moths incorporate some stochasticity into their behavior in order to balance the exploration and exploitation of the acquired information.Moving from invertebrate to vertebrate models, Donatelli et al. (2021) utilize the unique model of the bluespot salamander to demonstrate the robustness of locomotion patterns. Animals adjust their gait to a changing environment. In addition to adjusting to heterogeneities in their environment, animals can adjust their locomotion to contend with damage to appendages (tail or legs). This is ubiquitous in salamanders, which have the potential to regenerate missing limbs, tails, and even parts of the spinal cord in some species.As the authors suggest, understanding the changes that take place in locomotion kinematics as a lost limb regrows, may provide important insights to assist roboticists working on terrestrial as well as amphibious locomotion.As noted above, one level of control, allowing consistency and also adaptability in inter-limb coordination; is the muscular system. Camardella et al. (2021) visit the cutting edge technique of myo-control: a type of brain-machine interface in which recorded electromyographic (EMG) signals are utilized in a computed control signal that drives robots or machines (e.g. limb prostheses control). For such applications, there is much interest in characterizing the minimum muscle set, termed an optimal set, that preserves performance and demonstrates a high consistency of motor activity. Such an optimal set is described as considering the best trade-off in terms of myo-control performance and muscle set size.
To date, robotics research has made substantial progress in reproducing (adaptive) inter-limb coordination inspired by animal locomotion. The contributions to this special issue present various methods of control (including central and local (neural) control with sensory feedback) that have been investigated and developed, as well as validated on different animal-like robots (Fig. 1, Right).Starting with a snake-like robot, Inazawa et al. (2021) proposed a unified model-based method for designing the motion of a robot to deal with complicated pipe structures. The central control with a model considering slippage between robot and pipe coordinates the connected pitch-axis and yaw-axis joints of the robot body. It enables the robot to perform various maneuvers to deal with multiple pipe structures and obstacles such as junctions, bends, changes in pipe diameter, shears, and blockages.Rather than employing system models for inter-limb coordination and locomotion generation, Owaki et al. ( 2021) proposed a model-free method for simulated bipedal robot locomotion. Their method is based on the Tegotae concept, which describes how well a perceived reaction based on sensory feedback matches the expectation (i.e., an intended motor command). The control method's implementation makes use of vertical and horizontal ground reaction forces (GRF), as well as decentralized local control circuits, to allow the robot to walk on both flat and uneven terrains while adapting to environmental changes.In addition to the snake and biped robots, several studies in this special issue employs quadruped robots as their experimental platforms in order to investigate and develop control mechanisms for adaptive inter- Using this control approach, they are able to generate versatile locomotion and short-term adaptation for a cat-like quadruped robot. The robot can, consequently, walk on natural terrain, walk with a leg malfunction, avoid a sudden obstacle, and climb a vertical ladder.
Robust robot state estimation and sensory event mistiming detection are important issues for adaptive inter-limb coordination. Accordingly, Calandra et al. (2021) proposed a data-driven method using reservoir computing for translating local proprioceptive feedback, acquired at the leg joints of a simulated quadruped robot, into global exteroceptive information, which include both GRFs at the level of the different legs and information about the type of terrain traversed by the robot. This mechanism enables the robot to effectively estimate its walking state (i.e., estimating the GRFs from joint torques) and classify terrains for walking on level ground, the salamander coordinates not only its legs but also other body parts such as the trunk, head, and tail, i.e., body-limb coordination, to generate the standing and traveling waves of lateral bending depending on the walking speed and stride length. Suzuki et al. (2021) showed that a CPG-based controller with four feedback rules, limb-to-limb, limb-to-body, body-to-limb, and body-to-body, without assuming any inter-leg coupling is able to reproduce various walking patterns, suggesting that sensory feedback plays a crucial role in flexible body-limb coordination during sprawling quadruped locomotion.Quadruped robots possess the minimum number of legs required for postural stability; hence, it is also a useful platform to discuss the effects of a lower level of control and of biomechanics, e.g., spinal reflexes or body softness, due to the high postural stability and relative simplicity of leg coordination control. Tanikawa et al. (2021) focused on spinal reflex, which is essential for quadruped walking, and experimentally verified the reflex mechanism using a robotic platform that mimics legs with high back-drivability and Hill-type muscle properties. Their findings suggest that the basic structure of the reflex circuit is that of the reciprocal coupling between extensor muscles via excitatory neural pathways, followed by the prolongation of the stance phase caused by the reciprocal excitatory reflex contributing greatly to the generation of a steady gait. Masuda et al. (2021) showed the feasibility of generating various quadruped gaits using only actuators and body dynamics. Although the developed robot has no sensors or microprocessors, its motors were able to autonomously adjust the phase according to the leg dynamics and its locomotion eventually converges to a stable gait pattern. Furthermore, by increasing the input voltage to the motors, the robot is able to reproduce pacing, bounding, rotary galloping, and half-bound-like lateral galloping. Tanaka et al. (2021) developed a quadruped robot driven by McKibben pneumatic artificial muscles and verified its turning motion. In particular, the experiments demonstrate that the softness of legs leads to adaptive changes in inter-leg coordination and enables the robot to turn dynamically, merely by changing the phase difference between the left and right hind legs. Their results suggest that a soft body can simplify the design of the controller for leg coordination in locomotion even for complex tasks.Hopping motion offers an effective test-bed for theoretical approaches and systematic verification of energy optimization. The simple mechanical structure and constrained one-dimensional vertical motion allows simulation and robotic platform to uncover the contributing mechanisms and control schemes. Their results suggested that the Tegotae-based approach combined with a reflex-like actuation generate optimal energy-efficient motion as well as environmental adaptability and gait transitions. Discrete impact with the ground is a major factor of instability during legged locomotion due to their unknown timing and impact magnitude. Ashtiani et al. (2021) examined the effect of the combination of passive and active compliance on leg control during the landing event. Simulation and experiment with a single leg robot, followed by simulation with a quadruped robot were conducted. Their results showed that hybrid passive/active control was robust against feedback delays, comparable to the sensory-motor delays of neuromuscular systems in animals.
In this research topic, we have brought together studies that provide an overview of recent developments in biological and robotic inter-limb coordination. Since inter-limb coordination constitutes the fundamental basis of motion control, the studies covered range from high-level cognitive functions to CPGs and spinal reflexes, as well as biomechanics and interaction with the environment. In terms of animal species, the studies in biological inter-leg coordination incorporate insects, salamanders, and human muscle control.The robotic inter-leg coordination studies, center on quadrupedal robots that display posture stability and controllability, and include monopod, biped, salamander, hexapod, and even snake locomotion. A birds-eye-view of the overall research topic reveals that "modeling," including abstract mathematical description and physical implementation, is a key approach for discussing and understanding inter-leg coordination mechanisms in a unified manner encompassing biology and engineering. In addition, recent pioneering technologies, such as animal cyborgs that externally control the behavioral output of animals, and Virtual Reality (VR) or Augmented Reality (AR) systems that externally manipulate the sensory input to animals, are expected to lead to further understanding of the leg coordination mechanisms in animals. We hope that this research topic devoted to biological and robotic inter-limb coordination will help researchers to enter novel research areas related to leg coordination and that novel research results will ensue, based on the further integration of biology and robotics.
