From cineradiography to biorobots: an approach for designing robots to emulate and study animal locomotion

1. Introduction

Agile locomotion in animals results from a complex interplay of various components, involving: the central nervous system, the peripheral nervous system, the musculoskeletal system and interactions with the environment [1]. This makes decoding the mechanisms of locomotor control a difficult problem. Researchers have been trying to determine the role of each component with different approaches: (i) locomotion studies involving kinematic and dynamic recordings [2], (ii) electromyographic studies [3], (iii) neurophysiological studies in vitro and in vivo [4], (iv) electrical stimulation studies [5] and more. In addition to animal experiments, computational and robotic studies can be very useful in investigating interactions between the different components [6–8]. ‘Robots have multiple properties to complement animal studies: their actions are repeatable, they offer access to variables or quantities that would be difficult to measure on animals, they can perform movements that are unnatural or dangerous for animals, and their morphology can be systematically changed’ [8]. Used as the physical models of animals, robots are interesting as complements to neuromechanical simulations because they provide real physics. This is particularly important for locomotion that relies on complex interactions with the environment, such as swimming, crawling on mud, etc., because the motions involved are very difficult to simulate properly. Biorobots are therefore increasingly used as tools in locomotion studies to test hypotheses about biomechanics and neural control (see [8] for a review). There are several examples of studies [9–13] in which robots have been instrumental in understanding some properties of animal locomotion.

Two approaches can be distinguished among computational and physical models: template and anchor models [14]. ‘A template is the simplest model (least number of variables and parameters) that exhibits a targeted behaviour’. An anchor is ‘a more realistic model fixed firmly or grounded in the morphology and physiology of an animal’. Templates are useful for studying the general principles of locomotion. The same template model can represent several types of animals, such as the spring-loaded inverted pendulum (SLIP) model for legged running [15]. Physical models (i.e. robots) have been designed based on template models, for instance the biped ATRIAs robot [16], the hexapod RHex robot [17] and the salamander-like Salamandra robotica [10]. These robots were designed to use the lowest number of degrees of freedom (DOFs) to obtain and study a particular type of locomotion. Depending on the specific targeted behaviour, template models can be made as complex as necessary (but not more). Anchor models can then be used to validate the templates and to analyse multi-leg coordination, joint torques and neuromechanical aspects.

Salamanders have attracted the attention of researchers from various fields. In particular, they have garnered the interest of neuroscientists for investigating the neural mechanisms that produce their various aquatic and terrestrial locomotor modes as well as the cellular and molecular mechanisms underlying their impressive regenerative abilities [18–21]. Moreover, because salamanders resemble the early tetrapods in their skeletal morphology and locomotor modes more than any other extant species [22–32], they can be used as experimental models to obtain some insight into the neural mechanisms underlying aquatic-to-terrestrial transition in primitive tetrapods [10]. We are currently investigating the interplay between central pattern generation, sensory feedback and descending modulation for producing the large variety of motor behaviours involving whole-body movements as exhibited by salamanders. In previous work [10], we designed a simple template robot model of the salamander with a central pattern generator (CPG) model that could generate two motor behaviours of the salamander (swimming and walking trot) and that included two descending pathways (left–right stimulation). However, the salamander is capable of producing a larger variety of motor behaviours and is known to have more descending pathways. This motivated the design of an anchor model of the salamander. So far, we have mainly explored two descending pathways (left–right stimulation) but more pathways exist in the salamander. In the neural models, additional descending pathways can be added to stimulate subparts of the complete locomotor circuit (e.g. only the tail, only the hind left limb) similar to the action of strings in a marionette. The way in which specific behaviours are generated, when only the marionette is visible but not its strings, can be inferred from a model. The better the model captures the DOFs of the marionette, the closer one can estimate the number of strings needed for the model to reproduce the observed behaviours. In the same way, if the behaviour of the marionette depends on external interactions, then one has to be able to simulate those interactions with the model. Capturing those interactions accurately, especially when they cannot be properly simulated, is important and, for that reason, a physical model—in our case, a salamander-like robot—is necessary. It is important to try to include all the components that influence locomotion: the spinal cord circuits, the sensory feedback, the descending modulation, the internal body dynamics (i.e. muscle dynamics, the musculoskeletal dynamics) and the external body–environment dynamics. Locomotion will likely never be completely understood without investigating the interaction of all these components (i.e. while necessary, it is not sufficient to investigate these components in isolation). At the same time, we realize that any of these components will only be approximations, and future work will involve investigating the effect of these approximations, for instance by comparing the results of experiments carried out with components implemented at different levels of abstraction, e.g. coupled oscillator models versus spiking neural network models for the spinal circuits [33], and different types of muscle models.

Our previous robots, Salamandra robotica I and II, were designed to investigate the transition between swimming and walking [10,34]. Those robots have 10 and 12 actuated DOFs, respectively, and use simple one DOF rotational limbs like the RHex robot [17] for ground locomotion. They can be seen as template models with just the minimal number of DOFs to investigate interlimb and body–limb coordination in steady-state swimming and walking gaits. However, the limited number of DOFs not only restricts our ability to study the organization of the limb CPG networks, but also prevents the study of richer motor skills (e.g. aquatic stepping gaits, turning, paddling, etc.) where multiple DOFs are used [35,36]. For example, we showed in previous work [34,37] that a single rotational DOF at each limb is a limiting factor for understanding turning in salamanders and discussed the importance of a knee joint. It is also easy to show that for aquatic stepping and paddling single-DOF limbs cannot capture the necessary interactions with the environment (e.g. regulating the distance between the feet and the girdles, so that traction with the ground is maintained, or orienting the limb in such way that the hydrodynamics are similar to the ones that the animal experiences).

Building an anchor robot involves multiple design challenges: (i) designing the proper kinematic structure, i.e. the topology and number of DOFs, capable of emulating the desired animal behaviours, (ii) matching similar dimensions and mass distributions, and (iii) replicating muscle-like properties and more generally viscoelastic properties of the body. However, even in anchor models, many trade-offs and simplifications need to be made. The constraints relate to technological limitations in actuation (size, weight, torque, power density and velocity limits) and sensing (size and accuracy), price and manufacturability which highly affect the accessibility of the platform to various researchers as well as studies of morphological variability. Variations of the optimized platform—possibly, but not necessarily, drawn from the variability found in salamanders and other sprawling animals—will give hints on the role of body morphology with respect to the organization of the locomotor network and the pathways that regulate it.

Here, we present an approach to design a biorobot as an anchor model and use it to create Pleurobot, an amphibious salamander-like robot that emulates Pleurodeles waltl (P. waltl). Key elements of Pleurobot's design are the number and placement of locomotion-relevant joints. Our approach is then composed of the following steps: (i) collecting three-dimensional kinematics of skeletal elements using biplanar high-speed cineradiography; (ii) optimization of the robot kinematic structure using a genetic algorithm (GA) to be able to replay the set of collected gaits; (iii) dynamic scaling, i.e. performing an analysis of the animal and robot dynamics to ensure that the animal and robot gaits are carried out within the same regimes of interaction forces with the environment; (iv) constructing the robot using three-dimensional printed parts, high-end servomotors and a tailored dry-suit; and (v) comparing the robot and animal gaits with motion capture and force plate measurements. The main features compared with previous design methods are the combination of cineradiography and optimization to identify important locomotion-relevant DOFs for making the robot structure that can easily change depending on the hypothesis being tested. Cineradiography, in our case biplanar, is increasingly used to characterize animal locomotion [38,39]. In biorobotics, it has been used to compare animal and robot locomotion, e.g. during sand swimming [11], or to extract design principles for template-like robots [40] or robot simulations [41], but to the best of our knowledge, it has not yet been used together with optimization algorithms to design a physical anchor-like robot model. An important feature that makes P. waltl an excellent animal to model is its low dynamic behaviours, especially during ground locomotion. Many of the skills that can enrich our understanding of the salamander's locomotor network are much less dynamic than other animals, like mammals for instance. Our methodology is based on this fact. Not only current technology reaching its limits in producing reliable dynamic platforms, but also muscle, tendon and bone properties become much more important during dynamic locomotion.

2. Pleurobot's design methodology and development

Our robot is based on P. waltl, a salamander that exhibits both terrestrial and aquatic locomotion. This salamander represents a good candidate for our design approach, having been subject to neurophysiological [19,42], electromyographic [43] and biomechanical [10,36] studies in the past. Its morphology is composed of an elongated body (trunk and tail) and four limbs located at the pectoral and pelvic girdles (figure 1). The average body length and weight of P. waltl specimens (n = 2, 8.45 ± 0.078 cm snout–vent length, SVL) considered for this study were approximately 17.6 cm and 23.8 g. Biplanar high-speed cineradiographic (Neurostar^® Siemens AG) recordings at 500 fps and image resolution of 1536 × 1024 were performed at the University of Jena, Germany. The data presented here have been partially published elsewhere [36] and in detail in a doctoral thesis [44]. More specifically, walking gaits have been described in [36], whereas the data for aquatic stepping and swimming are original. A comparison between animal and robot sizes is provided in table 1.

As discussed in Introduction, several constraints guide the design of an anchor robot. Some are related to technology, and some are driven by the designer's goals. For Pleurobot, we consider one of the most important constraints to be the ability to easily produce copies and variations of the robot at a reasonable price and time, while still being able to test hypotheses on rich motor skills. Most of the rich behaviours of the salamander depend on its segmented limbs (turning, paddling and more), so particular focus was given in replicating the DOFs of the limbs. An important technological constraint is actuation. Currently, the most accessible, efficient and cost-effective actuator is the DC motor. However, DC motors still remain inefficient in very small scales, and we had to choose larger DC motors than we would have liked. Therefore, the motors' size guides the robot's final size, which is larger than the animal (table 1). Given these constraints, the key element of Pleurobot's design is to determine two important engineering considerations: (i) the number of locomotion-relevant joints and (ii) the placement of each joint along the robot's body.

Therefore, we developed a dataset of sequential whole-body postures for walking, swimming and aquatic stepping using the cineradiographic recordings and the three-dimensional reconstruction of kinematics obtained from experiments with P. waltl. In order to derive the three-dimensional reconstruction from the cineradiographic recordings, the salamander skeleton was manually tracked in all the videos where the animals showed straight and steady-state locomotion. For this purpose, a custom software based on OpenCV (open graphics C/C++ library) was developed and used. The top and side views were digitized at a frame rate of 40 Hz for swimming and 80 Hz for walking. The dataset of body postures was then used to guide an optimization problem with two goals: (i) optimal segmentation of the robot, i.e. minimum number of joints and (ii) their optimal placement, so that the segmented body can reproduce recorded animal postures in our dataset. The spine, forelimbs and hindlimbs were optimized as three separate kinematic chains.

2.4. Transformation to joint angles for Pleurobot

Finally, given the introduced design methodology, it is possible to impose kinematics recorded from the animal on Pleurobot. We will show in §5 how this together with a careful scaling analysis (§4) can be used to validate our design. To transfer the cineradiographic movement recordings to Pleurobot, we solve two optimization problems related to the spinal and limb joints, respectively. Note that in this optimization problem as opposed to that for the robot design, the segment lengths are given, and we solve for the joint angles. Motion sequences from the three-dimensional reconstruction of the cineradiographic recordings contained between 12 and 190 timesteps.

To compute the corresponding spinal joint angles for Pleurobot, the trunk and tail postures of P. waltl were first approximated using piecewise linear segments, where the length of each segment was given from the spinal segmentation on Pleurobot. Subsequently, at each time instance, within a particular movement cycle (with 40 fps for swimming and 80 fps for walking), we solved an optimization problem as follows

2.1

In this planar problem, y_t(x) describes the target posture in Cartesian coordinates. x_i and y_i denote coordinate points corresponding to the ith joint on Pleurobot. As shown in equation (2.1), the optimization problems are solved sequentially, starting from the first (head) until the last joint (tail). The problem was solved using the unconstrained nonlinear optimization function fminsearch from Matlab, with default parameters. The solutions provide us with a piecewise linear approximation of the posture y_t(x). Finally, the joint angles can be extracted by computing the relative angles between segments.

Related to the limb joint angles, the postures on P. waltl were identified by means of five tracking points located at the hip, the femur–crus joint, the crus–tarsus joint, the metatarsus–phalanges joint and the mid-phalanx tip (and corresponding points in the forelegs). The postures (again at each time instance) had to be approximated by the segmented robot limbs, where the first segment represents femur/humerus and the second segment the connection from elbow/knee to the metatarsus. In order to compute the corresponding yaw, pitch, roll and elbow/knee angle, we set up an inverse kinematics optimization problem for each posture:

2.2

where describes the joint angles, p_d1 and p_d2 indicate the three-dimensional positions of shoulder/hip and elbow/knee joints on P. waltl and the corresponding forward kinematics on Pleurobot are described by and .

3. Dynamical scaling

Ideally, our robot should have a similar size to its biological counterpart. However, owing to the unavailability of powerful miniature actuators at this stage in technology and our particular choice of servomotors, we are dealing with a robot that is geometrically scaled up by a factor of 8.6 with respect to P. waltl. Similar to other studies [9,45,46], it was therefore important to perform a dynamical scaling study, so that the robot could faithfully be used to investigate locomotion of the salamander, in aquatic and terrestrial environments. This is necessary to ensure that the physical interactions with the environment are dynamically equivalent, for instance in terms of hydrodynamics regimes.

In this context, an important question was how the robot should apply movements at speeds and while exerting forces that are comparable to the salamander. Based on the proposed design methodology, relative lengths of different body elements (geometric scaling) as well as the range of joint angles remained the same as for P. waltl (except for a 1.67 times increased robot head size, owing to the placement of the control board). As a consequence, it was also ensured that the robot operates in the same range of movement. To incorporate the speeds and forces, we also used the criterion for dynamic similarity as defined by Alexander [47]

3.1

where m denotes the total body mass, v is the forward moving speed and l is the characteristic length of the robot. F describes the main forces that act on the system while moving. Dynamic similarity has been used to compare different types of gaits across animals as well as to analyse, for instance, the relation of mass and locomotion speed in animals of different sizes [48–50]. Let g, ρ, μ, f be the gravitational acceleration, fluid density, dynamic viscosity and the frequency, respectively, then the Froude , Reynolds () and Strouhal () numbers are non-dimensional quantities that can be obtained from the dynamic similarity criterion (equation (3.1)). The Froude number is typically used to compare walking gaits, where gravitational forces are dominant [6].

By definition the Reynolds number determines the type of interaction forces with mainly viscous forces at low Re numbers and inertial forces at high Re numbers. The Re number was measured between 1.45 × 10⁴ and 7.81 × 10⁴ in the experiments with P. waltl and between 1.97 × 10⁵ and 4.48 × 10⁵ in our swimming experiments for Pleurobot. These high numbers indicate that both animal and robot are in a regime where inertial forces have a greater influence compared with viscous forces. Furthermore, it is important to note that in the particular case of P. waltl (as well as Pleurobot) we are analysing swimming at the water surface. Surface swimming is defined as swimming at a depth that is smaller than one body length [51,52]. It is considered a special case as ‘drag is increased substantially owing to the formation of waves’ [53] and the wave resistance force is a function of the Fr number [54]. Therefore, we can expect to have dynamically similar behaviour at similar Fr numbers, which is also supported by common practice in naval architecture [55], where the Fr number is used to create dynamically similar models of ships. Finally, related to periodic movements, the St number can be used to analyse movements at different frequencies. Intuitively, this measure covers observations in which smaller animals generally tend to move at much higher frequencies than bigger animals [56].

Based on the Fr and St numbers, which should be the same for the robot and the animal, we use the subsequent scaling law to determine the corresponding speeds and locomotion frequencies on the robot in order to conserve dynamic similarity with P. waltl

3.2

and

3.3

Accordingly, given that the ratio is 8.6, we should be able to obtain dynamically similar behaviour by scaling the salamander speeds by 2.94 and frequencies by 0.34 for walking and swimming.

4. Experimental validation of Pleurobot

To verify the design of our robot and to quantify the locomotor abilities with respect to P. waltl, we carried out a series of experiments and compared kinematics as well as dynamics. For this, we replicated walking, swimming and aquatic stepping gaits by replaying the precise body posture sequences that were obtained from cineradiographic recordings. Of course, by design, Pleurobot is made to incorporate all the necessary DOFs in order to replay fairly closely the joint kinematics for the three recorded gaits. But rather than focusing on the joint kinematics themselves, we ask the question of how the robot locomotes using those (i.e. how it progresses from one place to another and, more generally, how its orientation changes in three-dimensional space).

The aims of the following experiments are (i) to demonstrate that we can reproduce the two basic behaviours of the salamander, so well that it has the potential to reproduce more complex locomotor behaviours if these are recorded from the animal and (ii) to validate whether replaying kinematics recorded from the animal, provided the scaling factors, can yield behaviours (i.e. Cartesian kinematics and ground reaction forces, GRF) comparable to the salamander's. Especially the second point will help us validate future experiments in which Pleurobot is driven by a neuronal model instead of pre-recorded animal kinematics.

4.2. Characterization of locomotion

To compare the movements between Pleurobot and P. waltl, we investigated their lateral displacements and forward velocities. These quantities were measured with reference to the line of locomotion that was computed with the following linear regression

4.1

where k denotes the kth cycle and m_k, q_k are the resulting slope and offset of the regression. P_k describes the set of all tracked spinal points with coordinates (x_i, y_i) in the kth cycle. The robot lateral displacement for walking was computed based on the MOCAP recordings and from video data for the swimming gaits. In the case of swimming, characteristic midline points were computed in two steps. First, a curve was fitted (spline interpolation) through 21 manually selected points along the hypothetical midline of the body. The starting point of the midline was defined as the tip of the head and the endpoint was defined as the end of the tail. The midline was then resampled to 13 equidistant points. For P. waltl, the corresponding measure was computed based on the cineradiographic tracking data.

Forward velocity of the robot was computed in steady state, which was reached starting from the second locomotion cycle for walking and starting from the third locomotion cycle for swimming. The corresponding forward displacement over time was then averaged over two cycles for walking and three cycles for swimming. The rigid body marker and the LED marker were used as reference markers, respectively.

Besides the above-mentioned kinematic measures, we furthermore recorded GRFs on the robot for part of the validation. In this context, forces in three dimensions were recorded using force plates (type 9260AA3, Kistler, 2011) at a sampling frequency of 1 kHz. The GRFs were measured for both front and hindlimbs. To select appropriate experimental runs for the analysis, video recordings were obtained during the measurements. Only experiments in which the robot was walking straight and only a single foot was touching a force plate were taken into account. Finally, seven experimental runs for the front limbs and eight experimental runs for the hindlimbs were selected for the analysis. The data were processed using Matlab (Matlab 2014). The stance phases within a cycle were extracted, using the normal force profile for the front limbs (force indicating stance, no force indicating swing). For the hindlimbs, as a matter of fact, in many experiments, the foot was slightly touching the ground when protracting. Therefore, the stance phase for the hindlimbs was identified, using the anteroposterior as well as the normal force profile. As such, the beginning of stance was identified as soon as propulsive force (retraction) was registered, whereas the end of stance (lift off) was defined when the normal force dropped to zero. This is consistent with the force measurements in [58], where propulsive stance was also analysed. Furthermore, forces were smoothed using a moving average filter (n = 100, over/under smoothing was checked visually). For the analysis, the stance duration was normalized from 0% to 100% in order to compare the different experiments. All the forces were expressed with respect to the percentage of body weight, which facilitates the comparison with the salamander.

5. Discussion

We presented a possible way of designing biorobots in a systematic way and outlined the design procedure, which is based on high-speed cineradiographic recordings and numerical optimization, along with kinematic and dynamic validation respecting physics scaling laws. We used the approach to construct Pleurobot, a salamander-like robot with 27 DOFs that can emulate the walking and swimming gaits of the salamander P. waltl.

It could be seen as trivial that Pleurobot's locomotion matches that of the real salamander, because the robot replays the sequence of animal postures. Moving a robot with predefined joint angle trajectories is indeed trivial in the sense that it will, given a good controller and strong actuators, produce the expected robot postures. However, unlike automatons in amusement parks that are solidly fixed to the ground, Pleurobot's displacements in three-dimensional space are the results of (complex) physical interactions between the internal movements of the robot and the environment. The robot must be properly designed such that the interaction forces match those of the animal [60]. For instance, during ground locomotion, inaccurate mass distribution could lead to incorrect body orientations and incorrect contact with the ground (e.g. a limb not touching the ground when it should) and hence different locomotor patterns and locomotion speeds. Similarly, the swimming of the robot could be very different from that of the animal if geometrical and dynamical properties of the robot had not been properly adjusted with the dynamic scaling. The indirect (stride lengths and lateral displacements) and direct (GRFs) comparisons between robot and animal presented here indicate that the interaction dynamics closely correspond.

Our approach results in a physical tool that provides an interface between computational models and the environment on which rich motor skills can be tested in the future. The success of our approach is of course tested with behaviours with slow dynamics like those typically seen in salamanders and in particular P. waltl. In principle, it could be applied to the design of other types of robots that match different animals and modes of locomotion provided that the model is able to capture the dynamic conditions. Cineradiography allows one to observe bone movements, from which detailed and accurate kinematic information can be extracted. This allows one to identify locomotion-relevant joints (active or passive). Compared with motion capture based on markers and cameras, it prevents possible problems of movements of surface markers owing to motion of soft tissues [61], and of occlusions. It has however the disadvantages that more work is required to extract the three-dimensional data frame by frame from the biplanar images (either manually, like in our case, or through machine vision algorithms), and that the recording volume is limited.

In our case with P. waltl, optimization based on kinematic data was then sufficient to find a good robot design. We were able to replay gaits on the robot without modulating gaits based on feedback. For other animals and other modes of locomotion, similar steps could be taken but additional mechanical design and control steps could be necessary. For instance, it might be needed to use remote actuation with cables in order to obtain the right mass distribution as for the cat-like robot Cheetah-Cub [62]. Different gaits on other robots might also need explicit feedback control (e.g. for balance), whereas we are benefiting from the intrinsically stable sprawling posture of the salamander. The choice of servomotors was convenient in our design of a salamander-like robot. It substantially decreases the time and cost to build and transform. However, more generally, other actuators (e.g. with low gear ratio, passive elements, etc.) could be used depending on the type of locomotion and the questions that have to be addressed.

We furthermore applied the scaling laws that have to be respected in order to obtain dynamic similarity between the robot and the animal. For the salamander, it was shown that the Froude number had to be used for walking and surface swimming. In other cases, such as e.g. deeper three-dimensional swimming (depth larger than a body length), the Reynolds number should be used.

The analysis of footfall patterns and the aquatic stepping experiments (electronic supplementary material) revealed the limitations in the current design of Pleurobot with respect to its biological counterpart P. waltl, indicating that the role of the phalanges is important for stepping locomotion (in terrestrial and aquatic environments). The abstraction of the feet to single contact points is an important simplification that makes Pleurobot less of an anchor than the original aim. However, future versions will focus on integrating as many aspects of the foot as possible given their complexity. Furthermore, actuator limitations in size and power currently restrict the reproduction of some dynamically similar swimming motion, especially at higher frequencies and stride lengths. However, our approach shows promising results for the reproduction of walking patterns of the salamander P. waltl that conserve respective characteristics such as stride length, footfall patterns as well as similar GRFs.

One aspect that we did not address is internal dynamics [63], i.e. how internal forces and torques generate body deformations (i.e. postures). In the animal, body deformations are due to sets of muscles acting on the joints, whereas in the robot, they are due to torques produced by the PD controllers of the servomotors. There are some similarities between the two types of actuation, because with the proportional P and derivative D gains elasticity and damping can be adjusted to some extent. Nonetheless, there are also important differences: (i) antagonist muscles allow the change of stiffness and (ii) multiarticular muscles act on more than one joint. Muscle properties can be simulated if the gearboxes are back-drivable (or torque sensors with very fast control loops are available) and when the motors are used to control direct torque output. Given motors with these properties, this will allow us in the future to investigate the role of muscle properties in locomotion and to address questions related to locomotion efficiency (for instance how to obtain a given speed with minimal muscle activation, i.e. minimal metabolic cost). There is also the possibility to add elastic elements in series [62,64,65] to provide mechanical elasticity and energy restoration.

In the future, we envision Pleurobot as a useful tool for neuroscience. Locomotion is the result of interaction of many components, and a physical model such as Pleurobot can provide the interface between, on the one hand, computational models of the nervous system and of muscles, and, on the other hand, physical interactions with terrestrial and aquatic environments. As a realistic physical model of the salamander capable of emulating basic and complex behaviours, it can serve to test hypotheses about the interactions between the different components underlying locomotion, in particular the interactions between descending modulation, central pattern generation, sensory inputs and interaction forces from the environment. Compared with our previous robots and previous studies, the robot will for instance allow us to investigate (i) the organization of the limb CPGs with multiple neuronal oscillators (similarly to what has been found in the salamander [66]), (ii) the effect of adding more descending pathways to our spinal cord models, and (iii) the generation of a larger variety of motor behaviours such as turning, walking backwards, scratching, paddling, etc.

Obviously, it is by performing these future studies that we will really validate the design methodology presented in this article and its usefulness for neuroscience. It is possible that additional design iterations might be needed (for instance with the addition of more DOFs, the replacement of motors with stronger ones, the use of cables for remote actuation, the addition of sensors, etc.), but the current robot already opens the door to many investigations.

Furthermore, other fields, including functional morphology, palaeontology and field robotics, might benefit from the robot or its design methodology. In terms of robotics, an amphibious salamander-like robot capable of locomotion in different environments could find useful applications for inspection or search-and-rescue operations.

Supplementary Material

Authors' contributions

K.K. developed the design methodology, evaluated cineradiographic data, designed and built the robot, programmed the robot, and designed robot experiments; R.T. evaluated cineradiographic data, designed and evaluated robot experiments, and contributed to the final manuscript; K.M. designed and evaluated robot experiments, introduced the scaling methodology, and contributed to the final manuscript; T.H. helped with robot experiments and programmed the robot; N.K.M. evaluated cineradiographic data; S.T. contributed to the scaling methodology; J.M.C. contributed to collect cineradiographic data and helped with the final manuscript, A.J.I. directed the project and contributed to the design methodology and to the final manuscript.

Competing interests

We declare we have no competing interests.

Funding

We acknowledge financial support from the Swiss National Center of Competence in Research in Robotics, and from the Swiss National Science Foundation (project CR23I2_140714).