Multi-legged Locomotion Research Articles

In-Situ Calibration of Six-Axis Force/Torque Transducers on A Six-Legged Robot

Abstract Ground contact modeling for multi-legged locomotion is challenging due to the possibility of multiple slipping legs. To understand the interplay of contact forces among multiple legs, we integrated a robot with six high-precision 6-DoF force-torque sensors, and measured the wrenches (forces and torques) produced in practice. Here we present an in-situ calibration procedure for simultaneously measuring all foot contact wrenches of a hexapod using 6-DoF load cells installed at the hips. We characterized transducer offset, leg gravity offset and the wrench transformation error in our calibration model. Our calibration reduced the RSME by 63% for forces and 90% for torques in the residuals of the robot standing in different poses, compared with naive constant offset removal.

An Arch-Shaped Electrostatic Actuator for Multi-Legged Locomotion

An Arch-Shaped Electrostatic Actuator for Multi-Legged Locomotion

Theoretical investigation of an array of Josephson junction neuron circuits actuating a mechanical leg and the array in mimicking a multi-legged locomotion

Theoretical investigation of an array of Josephson junction neuron circuits actuating a mechanical leg and the array in mimicking a multi-legged locomotion

Bridging Locomotion and Manipulation Using Reconfigurable Robotic Limbs via Reinforcement Learning.

Locomotion and manipulation are two essential skills in robotics but are often divided or decoupled into two separate problems. It is widely accepted that the topological duality between multi-legged locomotion and multi-fingered manipulation shares an intrinsic model. However, a lack of research remains to identify the data-driven evidence for further research. This paper explores a unified formulation of the loco-manipulation problem using reinforcement learning (RL) by reconfiguring robotic limbs with an overconstrained design into multi-legged and multi-fingered robots. Such design reconfiguration allows for adopting a co-training architecture for reinforcement learning towards a unified loco-manipulation policy. As a result, we find data-driven evidence to support the transferability between locomotion and manipulation skills using a single RL policy with a multilayer perceptron or graph neural network. We also demonstrate the Sim2Real transfer of the learned loco-manipulation skills in a robotic prototype. This work expands the knowledge frontiers on loco-manipulation transferability with learning-based evidence applied in a novel platform with overconstrained robotic limbs.

Substrate-mediated leg interactions play a key role in insect stability on granular slopes.

Locomotion on granular inclines is a subject of high relevance in ecological physics as well as in biomimmetics and robotics. Enhancing stability on granular materials represents a huge challenge due to the fluidization transition when inclination approaches the avalanche angle. Our motivating example is the predator-prey system made of the antlion, its pit, and its prey. Recent studies have demonstrated that stability on granular inclines strongly depends on the pressure exerted on the substrate. In this work we show that for multilegged locomotion, along with pressure, the distance between the leg contacts on the substrate also plays a major role in the determination of the stability threshold. Through a set of model experiments using artificial sliders, we determine a critical distance below which stability is importantly affected by the interactions between the perturbed regions generated by each contact point. A simple model based on the Coulomb method of wedges allows us to estimate a stability criterion based on pressure, interleg distance, and substrate characteristics. Our work suggests that mass to leg-length allometric relationships, as the ones observed in ants, may be an important key in determining the locomotion success of multilegged locomotion on granular inclines.

Untethered Robotic Millipede Driven by Low-Pressure Microfluidic Actuators for Multi-Terrain Exploration

Mobile robots that can adapt to an extensive range of terrains play essential roles in many applications. Millipedes are one of the most terrain-adaptive creatures in nature due to their multi-legged locomotion and flexible body. Inspired by natural millipedes, we report an untethered robotic millipede with a 6-segments soft-rigid hybrid body that can actively bend and 24 legs driven by low-pressure microfluidic actuators. The 24 microfluidic actuators are driven by two independent low-pressure sources from miniature pumps, which allows the untethered locomotion of the robotic millipede in small size (length, 23 cm; width, 5 cm; height, 4 cm) and lightweight (150 g). Using a pre-defined gait for the multi-legs, the robotic millipede can locomote with a maximum speed of 30.96 cm/min (1.35 body length per minute) and a minimum turning radius of 15 cm (0.65 body length). Experiments also demonstrated that the robot was able to locomote effectively in various uneven terrains. Utilizing its passive or active mode of its flexible body, the robot could also achieve adaptive moves. The robotic millipede has the potential to perform a variety of environment exploration tasks by remotely controlling and transmitting real-time images wirelessly.

Multi-scopic neuro-cognitive adaptation for legged locomotion robots

Dynamic locomotion is realized through a simultaneous integration of adaptability and optimality. This article proposes a neuro-cognitive model for a multi-legged locomotion robot that can seamlessly integrate multi-modal sensing, ecological perception, and cognition through the coordination of interoceptive and exteroceptive sensory information. Importantly, cognitive models can be discussed as micro-, meso-, and macro-scopic; these concepts correspond to sensing, perception, and cognition; and short-, medium-, and long-term adaptation (in terms of ecological psychology). The proposed neuro-cognitive model integrates these intelligent functions from a multi-scopic point of view. Macroscopic-level presents an attention mechanism with short-term adaptive locomotion control conducted by a lower-level sensorimotor coordination-based model. Macrosopic-level serves environmental cognitive map featuring higher-level behavior planning. Mesoscopic level shows integration between the microscopic and macroscopic approaches, enabling the model to reconstruct a map and conduct localization using bottom-up facial environmental information and top-down map information, generating intention towards the ultimate goal at the macroscopic level. The experiments demonstrated that adaptability and optimality of multi-legged locomotion could be achieved using the proposed multi-scale neuro-cognitive model, from short to long-term adaptation, with efficient computational usage. Future research directions can be implemented not only in robotics contexts but also in the context of interdisciplinary studies incorporating cognitive science and ecological psychology.

Existence of a Long-Range Caudo-Rostral Sensory Influence in Terrestrial Locomotion.

In multisegmented locomotion, coordination of all appendages is crucial for the generation of a proper motor output. In running for example, leg coordination is mainly based on the central interaction of rhythm generating networks, called central pattern generators (CPGs). In slower forms of locomotion, however, sensory feedback, which originates from sensory organs that detect changes in position, velocity and load of the legs' segments, has been shown to play a more crucial role. How exactly sensory feedback influences the activity of the CPGs to establish functional neuronal connectivity is not yet fully understood. Using the female stick insect Carausius morosus, we show for the first time that a long-range caudo-rostral sensory connection exists and highlight that load as sensory signal is sufficient to entrain rhythmic motoneuron (MN) activity in the most rostral segment. So far, mainly rostro-caudal influencing pathways have been investigated where the strength of activation, expressed by the MN activity in the thoracic ganglia, decreases with the distance from the stepping leg to these ganglia. Here, we activated CPGs, producing rhythmic neuronal activity in the thoracic ganglia by using the muscarinic agonist pilocarpine and enforced the stepping of a single, remaining leg. This enabled us to study sensory influences on the CPGs' oscillatory activity. Using this approach, we show that, in contrast to the distance-dependent activation of the protractor-retractor CPGs in different thoracic ganglia, there is no such dependence for the entrainment of the rhythmic activity of active protractor-retractor CPG networks by individual stepping legs.SIGNIFICANCE STATEMENT We show for the first time that sensory information is transferred not only to the immediate adjacent segmental ganglia but also to those farther away, indicating the existence of a long-range caudo-rostral sensory influence. This influence is dependent on stepping direction but independent of whether the leg is actively or passively moved. We suggest that the sensory information comes from unspecific load signals sensed by cuticle mechanoreceptors (campaniform sensilla) of a leg. Our results provide a neuronal basis for the long-established behavioral rules of insect leg coordination. We thus provide a breakthrough in understanding the neuronal networks underlying multilegged locomotion and open new vistas into the neuronal functional connectivity of multisegmented locomotion systems across the animal kingdom.

Adaptive Centipede Walking via Synergetic Coupling Between Decentralized Control and Flexible Body Dynamics.

Multi-legged animals such as myriapods can locomote on unstructured rough terrain using their flexible bodies and legs. This highly adaptive locomotion emerges through the dynamic interactions between an animal’s nervous system, its flexible body, and the environment. Previous studies have primarily focused on either adaptive leg control or the passive compliance of the body parts and have shown how each enhanced adaptability to complex terrains in multi-legged locomotion. However, the essential mechanism considering both the adaptive locomotor circuits and bodily flexibility remains unclear. In this study, we focused on centipedes and aimed to understand the well-balanced coupling between the two abovementioned mechanisms for rough terrain walking by building a neuromechanical model based on behavioral findings. In the behavioral experiment, we observed a centipede walking when part of the terrain was temporarily removed and thereafter restored. We found that the ground contact sense of each leg was essential for generating rhythmic leg motions and also for establishing adaptive footfall patterns between adjacent legs. Based on this finding, we proposed decentralized control mechanisms using ground contact sense and implemented them into a physical centipede model with flexible bodies and legs. In the simulations, our model self-organized the typical gait on flat terrain and adaptive walking during gap crossing, which were similar to centipedes. Furthermore, we demonstrated that the locomotor performance deteriorated on rough terrain when adaptive leg control was removed or when the body was rigid, which indicates that both the adaptive leg control and the flexible body are essential for adaptive locomotion. Thus, our model is expected to capture the possible essential mechanisms underlying adaptive centipede walking and pave the way for designing multi-legged robots with high adaptability to irregular terrain.

Generation of Direct-, Retrograde-, and Source-Wave Gaits in Multi-Legged Locomotion in a Decentralized Manner via Embodied Sensorimotor Interaction.

Multi-legged animals show several types of ipsilateral interlimb coordination. Millipedes use a direct-wave gait, in which the swing leg movements propagate from posterior to anterior. In contrast, centipedes use a retrograde-wave gait, in which the swing leg movements propagate from anterior to posterior. Interestingly, when millipedes walk in a specific way, both direct and retrograde waves of the swing leg movements appear with the waves' source, which we call the source-wave gait. However, the gait generation mechanism is still unclear because of the complex nature of the interaction between neural control and dynamic body systems. The present study used a simple model to understand the mechanism better, primarily how local sensory feedback affects multi-legged locomotion. The model comprises a multi-legged body and its locomotion control system using biologically inspired oscillators with local sensory feedback, phase resetting. Each oscillator controls each leg independently. Our simulation produced the above three types of animal gaits. These gaits are not predesigned but emerge through the interaction between the neural control and dynamic body systems through sensory feedback (embodied sensorimotor interaction) in a decentralized manner. The analytical description of these gaits' solution and stability clarifies the embodied sensorimotor interaction's functional roles in the interlimb coordination.

Effect of Thoracic Connective Lesion on Inter-Leg Coordination in Freely Walking Stick Insects

Multi-legged locomotion requires appropriate coordination of all legs with coincident ground contact. Whereas behaviourally derived coordination rules can adequately describe many aspects of inter-leg coordination, the neural mechanisms underlying these rules are still not entirely clear. The fact that inter-leg coordination is strongly affected by cut thoracic connectives in tethered walking insects, shows that neural information exchange among legs is important. As yet, recent studies have shown that load transfer among legs can contribute to inter-leg coordination through mechanical coupling alone, i.e., without neural information exchange among legs. Since naturalistic load transfer among legs works only in freely walking animals but not in tethered animals, we tested the hypothesis that connective lesions have less strong effects if mechanical coupling through load transfer among legs is possible. To do so, we recorded protraction/retraction angles of all legs in unrestrained walking stick insects that either had one thoracic connective cut or had undergone a corresponding sham operation. In lesioned animals, either a pro-to-mesothorax or a meso-to-metathorax connective was cut. Overall, our results on temporal coordination were similar to published reports on tethered walking animals, in that the phase relationship of the legs immediately adjacent to the lesion was much less precise, although the effect on mean phase was relatively weak or absent. Lesioned animals could walk at the same speed as the control group, though with a significant sideward bias toward the intact side. Detailed comparison of lesion effects in free-walking and supported animals reveal that the strongest differences concern the spatial coordination among legs. In free walking, lesioned animals, touch-down and lift-off positions shifted significantly in almost all legs, including legs of the intact body side. We conclude that insects with disrupted neural information transfer through one connective adjust to this disruption differently if they experience naturalistic load distribution. While mechanical load transfer cannot compensate for lesion-induced effects on temporal inter-leg coordination, several compensatory changes in spatial coordination occur only if animals carry their own weight.

Fast and flexible multilegged locomotion using learned centroidal dynamics

We present a flexible and efficient approach for generating multilegged locomotion. Our model-predictive control (MPC) system efficiently generates terrain-adaptive motions, as computed using a three-level planning approach. This leverages two commonly-used simplified dynamics models, an inverted pendulum on a cart model (IPC) and a centroidal dynamics model (CDM). Taken together, these ensure efficient computation and physical fidelity of the resulting motion. The final full-body motion is generated using a novel momentum-mapped inverse kinematics solver and is responsive to external pushes by using CDM forward dynamics. For additional efficiency and robustness, we then learn a predictive model that then replaces two of the intermediate steps. We demonstrate the rich capabilities of the method by applying it to monopeds, bipeds, and quadrupeds, and showing that it can generate a very broad range of motions at interactive rates, including banked variable-terrain walking and running, hurdles, jumps, leaps, stepping stones, monkey bars, implicit quadruped gait transitions, moon gravity, push-responses, and more.

Benchmarking Agility For Multilegged Terrestrial Robots

In this paper, we present a novel and practical approach for benchmarking agility. We focus on terrestrial, multilegged locomotion in the field of bio-inspired robotics. We define agility as the ability to perform a set of different but specific tasks executed in a fast and efficient manner. This definition is inspired by the analysis of natural role models, such as dogs and horses as well as robotic systems. An evaluation of existing benchmarks in robotics is done and taken into account in our proposed benchmark. After the general definition, the actual normalized benchmarking values are defined, and measuring methods, as well as an online database for agility score collection and distribution, are presented. To provide a baseline for agile locomotion, various videos of dog-agility competitions were analyzed and agility scores calculated wherever applicable. Finally, validation and implementation of the benchmark are done with different robots directly available to the authors. In conclusion, our benchmark will enable researchers not only to compare existing robots and find out strengths and weaknesses in different design approaches, but also give a tool to define new fitness functions for optimization, learning processes, and future robots developments, intensifying the links between biology and technology even further.

Coulomb Friction Crawling Model Yields Linear Force–Velocity Profile

Abstract Conventional wisdom would have it that moving mechanical systems that dissipate energy by Coulomb friction have no relationship between force and average speed. One could argue that the work done by friction is constant per unit of distance travelled, and if propulsion forces exceed friction, the net work is positive, and the system accumulates kinetic energy without bound. We present a minimalistic model for legged propulsion with slipping under Coulomb friction, scaled to parameters representative of single kilogram robots and animals. Our model, amenable to exact solutions, exhibits nearly linear (R2 > 0.96) relationships between actuator force and average speed over its entire range of parameters, and in both motion regimes, it supports. This suggests that the interactions inherent in multilegged locomotion may lead to governing equations more reminiscent of viscous friction than would be immediately obvious.

Simultaneous Contact, Gait and Motion Planning for Robust Multi-Legged Locomotion via Mixed-Integer Convex Optimization

Traditional motion planning approaches for multi-legged locomotion divide the problem into several stages, such as contact search and trajectory generation. However, reasoning about contacts and motions simultaneously is crucial for the generation of complex whole-body behaviors. Currently, coupling theses problems has required either the assumption of a fixed gait sequence and flat terrain condition, or non-convex optimization with intractable computation time. In this paper, we propose a mixed-integer convex formulation to plan simultaneously contact locations, gait transitions and motion, in a computationally efficient fashion. In contrast to previous works, our approach is not limited to flat terrain nor to a pre-specified gait sequence. Instead, we incorporate the friction cone stability margin, approximate the robot's torque limits, and plan the gait using mixed-integer convex constraints. We experimentally validated our approach on the HyQ robot by traversing different challenging terrains, where non-convexity and flat terrain assumptions might lead to sub-optimal or unstable plans. Our method increases the motion generality while keeping a low computation time.

Advantage of straight walk instability in turning maneuver of multilegged locomotion: a robotics approach.

Multilegged locomotion improves the mobility of terrestrial animals and artifacts. Using many legs has advantages, such as the ability to avoid falling and to tolerate leg malfunction. However, many intrinsic degrees of freedom make the motion planning and control difficult, and many contact legs can impede the maneuverability during locomotion. The underlying mechanism for generating agile locomotion using many legs remains unclear from biological and engineering viewpoints. The present study used a centipede-like multilegged robot composed of six body segments and twelve legs. The body segments are passively connected through yaw joints with torsional springs. The dynamic stability of the robot walking in a straight line changes through a supercritical Hopf bifurcation due to the body axis flexibility. We focused on a quick turning task of the robot and quantitatively investigated the relationship between stability and maneuverability in multilegged locomotion by using a simple control strategy. Our experimental results show that the straight walk instability does help the turning maneuver. We discuss the importance and relevance of our findings for biological systems and propose a design principle for a simple control scheme to create maneuverable locomotion of multilegged robots.

位相リセットが多足歩行に及ぼす影響のシンプルモデルを用いた解析

Multi-legged animals show several types of ipsilateral interlimb coordination. Millipedes show the direct wave gait in which the swing leg movements propagate from posterior to anterior. On the other hand, some centipedes show the retrograde wave gait in which the swing leg movements propagate from anterior to posterior. Interestingly, when some millipede walks in a specific way, it is reported that both direct and retrograde waves of the leg movements can coexist with a source part of the waves (we call it as source wave gaits). However, the mechanism behind the gait generation is still unclear because of the complex nature of the interaction between neural control and body dynamic systems. In this paper, we propose a simple model to gain a better understanding of the mechanism, especially how a local sensory feedback affects multi-legged locomotion. We design a planar multi-legged model and its locomotion control system based on biologically-inspired oscillators with a local sensory feedback, phase resetting. Each oscillator controls each leg, and there are no direct interactions among oscillators. Our simulation results reveal three types of gaits, which have different ipsilateral phase relationships (Direct, retrograde and source wave gaits like animals). These gaits are neither predesigned or predetermined, but emerge through the interaction between the neural control and body dynamic systems through phase resetting. These results suggest that the local sensory feedback is important to form proper interlimb coordination and thereby effectively generates multi-legged gaits. In addition, our mathematical analysis with the simple model successfully extracts the essential feature of these gaits, and suggests that these types of locomotion can exist regardless of the number of legs in our system.

Adaptive and Energy Efficient Walking in a Hexapod Robot Under Neuromechanical Control and Sensorimotor Learning.

The control of multilegged animal walking is a neuromechanical process, and to achieve this in an adaptive and energy efficient way is a difficult and challenging problem. This is due to the fact that this process needs in real time: 1) to coordinate very many degrees of freedom of jointed legs; 2) to generate the proper leg stiffness (i.e., compliance); and 3) to determine joint angles that give rise to particular positions at the endpoints of the legs. To tackle this problem for a robotic application, here we present a neuromechanical controller coupled with sensorimotor learning. The controller consists of a modular neural network for coordinating 18 joints and several virtual agonist-antagonist muscle mechanisms (VAAMs) for variable compliant joint motions. In addition, sensorimotor learning, including forward models and dual-rate learning processes, is introduced for predicting foot force feedback and for online tuning the VAAMs' stiffness parameters. The control and learning mechanisms enable the hexapod robot advanced mobility sensor driven-walking device (AMOS) to achieve variable compliant walking that accommodates different gaits and surfaces. As a consequence, AMOS can perform more energy efficient walking, compared to other small legged robots. In addition, this paper also shows that the tight combination of neural control with tunable muscle-like functions, guided by sensory feedback and coupled with sensorimotor learning, is a way forward to better understand and solve adaptive coordination problems in multilegged locomotion.

A network model comprising 4 segmental, interconnected ganglia, and its application to simulate multi-legged locomotion in crustaceans.

Inter-segmental coordination is crucial for the locomotion of animals. Arthropods show high variability of leg numbers, from 6 in insects up to 750 legs in millipedes. Despite this fact, the anatomical and functional organization of their nervous systems show basic similarities. The main similarities are the segmental organization, and the way the function of the segmental units is coordinated. We set out to construct a model that could describe locomotion (walking) in animals with more than 6 legs, as well as in 6-legged animals (insects). To this end, we extended a network model by Daun-Gruhn and Tóth (Journal of Computational Neuroscience, doi: 10.1007/s10827-010-0300-1 , 2011). This model describes inter-segmental coordination of the ipsilateral legs in the stick insect during walking. Including an additional segment (local network) into the original model, we could simulate coordination patterns that occur in animals walking on eight legs (e.g., crayfish). We could improve the model by modifying its original cyclic connection topology. In all model variants, the phase relations between the afferent segmental excitatory sensory signals and the oscillatory activity of the segmental networks played a crucial role. Our results stress the importance of this sensory input on the generation of different stable coordination patterns. The simulations confirmed that using the modified connection topology, the flexibility of the model behaviour increased, meaning that changing a single phase parameter, i.e., gating properties of just one afferent sensory signal was sufficient to reproduce all coordination patterns seen in the experiments.

Synchronization of a class of cyclic discrete-event systems describing legged locomotion

It has been shown that max-plus linear systems are well suited for applications in synchronization and scheduling, such as the generation of train timetables, manufacturing, or traffic. In this paper we show that the same is true for multi-legged locomotion. In this framework, the max-plus eigenvalue of the system matrix represents the total cycle time, whereas the max-plus eigenvector dictates the steady-state behavior. Uniqueness of the eigenstructure also indicates uniqueness of the resulting behavior. For the particular case of legged locomotion, the movement of each leg is abstracted to two-state circuits: swing and stance (leg in flight and on the ground, respectively). The generation of a gait (a manner of walking) for a multiple legged robot is then achieved by synchronizing the multiple discrete-event cycles via the max-plus framework. By construction, different gaits and gait parameters can be safely interleaved by using different system matrices. In this paper we address both the transient and steady-state behavior for a class of gaits by presenting closed-form expressions for the max-plus eigenvalue and max-plus eigenvector of the system matrix and the coupling time. The significance of this result is in showing guaranteed robustness to perturbations and gait switching, and also a systematic methodology for synthesizing controllers that allow for legged robots to change rhythms fast.