Multilevel dynamic adjustments of geckos (Hemidactylus frenatus) climbing vertically: head-up versus head-down

Abstract

Many climbing animals use direction-dependent adhesives to attach to vertical or inclined surfaces. These structures adhere when activated via a pull but detach when pushed. Therefore, a challenge arises when a change in climbing direction causes external forces such as gravity to change its acting orientation upon the lizard. To investigate how specialized climbers adjust, we studied kinematics and dynamics of six Hemidactylus frenatus geckos climbing head-up and head-down a vertical racetrack. We found that limbs functionally swap their adhesive role: feet above the centre of mass (COM) generated adhesive forces, feet below the COM compressive forces, both equal in magnitude across directions. To investigate how lizards perform this swap, despite the constraint of their direction-dependent adhesives, we analysed kinematic adjustments across multiple smaller levels of hierarchy: limbs, feet and toes. All levels contributed: the hindfoot angle was reoriented realigning the adhesive structure, the hindlimb centre range of motion was further protracted and the hindfoot toe spreading was reduced. Notably, all three variables were adjustments of hindlimbs, suggesting that they make a more flexible contribution in upward versus downward climbing, while forelimbs may be anatomically or functionally constrained. The relevance of multilevel dynamic adjustments might inform the development of performant gaits for legged climbing robots.

1. Introduction

The forces acting upon an animal differ between level and vertical locomotion. On the ground, animals support their bodyweight and generate propulsion perpendicular to the gravitational force [1–3]. However, on an inclined or vertical surface, acceleration must act against gravity when climbing head-up, and an additional adhesive force needs to be produced [1,2,4,5]. Yet the direction of locomotion, i.e. sideways or head-down, now changes the orientation of the gravitational force relative to the climbing direction, inducing additional challenges for generation of adhesion by putting different mechanical demands on the limbs [1].

Many climbing animals use direction-dependent adhesives or hook-like claws to attach to vertical or inclined surfaces [2,6–12]. These structures attach strongly when pulled toward the body and detach easily when pushed in the opposite direction. The rapid switch between attachment and detachment (15 ms) is essential for fast yet safe locomotion on vertical surfaces [2,10,12].

However, the generation of adhesion using these direction-dependent attachment structures can be challenging, because a change of the direction of climbing causes the orientation of in-plane forces to vary relative to the body axis of the lizard. Despite this difficulty, lizards, with body masses varying from 10 g to 10 kg, are capable of agile climbing head-up and head-down vertical surfaces, such as trees and rock faces [13,14].

A simple model based on work by Autumn et al. [2] illustrates the effect of the direction of climbing in terms of apparent forces and moments (figure 1b,c). A toppling moment arises because the lizard's centre of mass (COM) has some finite distance vertical to the surface. To balance this moment during head-up climbing, legs above the COM must produce adhesive forces, i.e. they pull on the wall; equilibrium of forces then requires that legs below the COM push on the wall (figure 1b) [2]. Thus, fore- and hindlimbs are expected to switch roles when the direction of climbing is inverted and the orientation of climbing to the gravitational force vector changes (figure 1c). This was indeed reported by Wang et al. [5] for geckos (Gekko Gecko) climbing head-up, sideways and head-down on a vertical surface. Yet, given the constraints of their direction-dependent adhesives, how do lizards swap the role of the limbs, and are both limbs equally capable of swapping?

Figure 1.

Shows the problem of direction-dependent structures when facing their least favourable orientation (i.e. during head-down climbing) (a) and the model of the role swap of the feet depending on their position to the COM (b). Feet above the COM generate adhesive force, while feet below the COM produce compressive force; both to balance the overturning moment (red arrow).

This question has previously been addressed in insects, such as cockroaches, which are also capable of both head-up and head-down climbing [12,15]. Cockroaches possess two different pads on their ‘heels’ and ‘toes’ with opposite direction dependence which are used differentially depending on the direction of climbing. While this suggests one possible solution among climbing animals, lizards do not appear to have obliquely orientated adhesive pads or claws [16], suggesting the need for a different strategy. They likely actively adjust the kinematics of the limbs depending on the direction of climbing.

Kinematic adjustment of the limbs could occur at multiple levels: at the whole limb, at the foot level or at the level of the toes. The hierarchy of the gecko adhesive system has been well studied [11,17–20], but the contribution of higher units of hierarchy, toes, feet, limbs and indeed the whole body, has received less attention.

1.1. Kinematic adjustments on the limb level and foot level

Substantial kinematic adjustments on the limb and foot level were reported for head-down versus head-up climbing [5,15,21–23]. Birn-Jeffery & Higham [21] examined kinematic changes for climbing at different slopes and found that Tokay geckos placed their hind feet more posteriorly and extend ankles 50% more on −45° slopes compared to level locomotion. Similar results were observed for Bibron's thick-toed geckos (Chondrodactylus bibronii), which rotated their hind limbs up to 70° more posteriorly on −45° slopes compared to level [22].

1.2. Kinematic adjustments on the toe level

Kinematic alterations can not only occur on a limb level, but geckos also possess individually manipulatable toes. Toe spreading and toe alignment relative to the gravitational force vector vary with climbing direction [16,24,25]. Song et al. [16] also reported differences in structure within a single toe, yet in contrast to cockroaches, both structures have the same direction dependence. The proximal base of each toe bears non-adhesive scales, but the distal tips are covered in adhesive setae. Both display anisotropic friction, generating higher forces pulled with than against the adhesive direction [16].

Increasing toe spreading angles might help to enhance stability by increasing the probability that at least some toes are in a favourable orientation for attachment [24], or by enabling each individual toe to be pulled toward the centre of the foot, engaging direction-dependent adhesive structures, independent of the body COM gravitational force vector, as in gripping [26]. Alternatively, a decrease in toe spreading might allow a better alignment of the adhesive structure with the gravitational force vector for multiple toes, therefore enhancing the attachment [25].

Given the multilevel versatility for kinematic adjustments, it is unclear which strategies are most important for geckos as the direction of climbing is changed. By comparing multiple levels of kinematic adjustment simultaneously we will be able not only to explore how the different levels integrate during locomotion, but to directly compare their magnitudes of adjustment and the dominant changes at different levels.

In this paper we investigate multiple levels of climbing kinematics and dynamics in the gecko species Hemidactylus frenatus during head-up versus head-down climbing. We want to understand if there is an anatomical level (whole-body, limb, foot, toe) that contributes most to the adjustments needed for inverting direction and if there is a difference between the fore versus hind limbs. We further aim to address how lizards perform the role swap for producing adhesive forces, when they are constrained by their direction-dependent adhesives, and if other locomotor tasks of limbs might suffer in turn, like propulsion or braking.

2. Methods

2.1. Data collection on climbing dynamics

We recorded kinematics and ground reaction forces (GRF) during vertical climbing in six individual geckos (Hemidactylus frenatus; 3.2 ± 0.9 g mass, 54 ± 3 mm snout–vent length (SVL), mean ± s.d., N = 6). Geckos were filmed running up and down a vertical racetrack (8 cm × 38 cm), made from Corflute^TM, with barriers on either side. A retreat was attached to the top and the bottom of the track to motivate the lizards to climb. Two i-Speed 211 high-speed cameras equipped with Nikon 28 mm, 1:2:8 D lenses (500 fps, 1/550 s shutter speed, 1280 × 600 px) were used to film the trials from a dorsal and lateral view (figure 2a). Geckos were introduced to either the bottom or the top of the racetrack and encouraged to climb with gentle tapping of the tail tip. Animals were allowed at least one minute of rest between successive runs.

Figure 2.

Display of the experimental set-up, the labels used for automated tracking and the calculation of the different kinematic variables on the different levels of the gecko (whole-body, limb, foot and toe level). (a) A racetrack built of Corflute with an in-built force plate and two retreats at top and bottom; animals were introduced and filmed with high-speed cameras (500 fps, 1/550 s shutter, 1280 × 600 px) from a top and a lateral view while climbing head-up and head-down. (b) Cut-out gecko from a video with the actual tracked results and a silhouette with the different labels used for the markerless pose-estimator DeepLabCut. Multiple points were tracked along the spine and tail (blue), three points per leg (green) and additionally the individual toe tips of each foot (orange). These labels were then used to calculate kinematic variables (c,d). (Details for each of these calculations can be found in electronic supplementary material, table S2.)

A force plate based on a Nano17 load cell (ATI Industrial Automation, Apex, NC, USA, F/T Sensor: Nano17 IP65/IP68, resolution: 1/320 N) was incorporated into the racetrack. To this end, a plate (20 mm × 20 mm) covered with the racetrack material was mounted on top of the sensor such that it was level with the surface of the racetrack. GRF of individual feet were collected with a sample frequency of 10 kHz, and forces were synchronized with video frames using a trigger which stopped high-speed and force recordings simultaneously.

Following climbing trials, the geckos were weighed using electronic scales to ±0.1 g. Measurements of SVL and tail length were made in ImageJ from extracted video frames, using the known force plate dimensions for top view calibrations, and calibration videos included a ruler in frame, aligned with the image plane, for lateral view calibrations (figure 2a). All morphometrics and px-to-mm conversion factors are provided in electronic supplementary material, table S1.

In the following we use the term kinematics to include all kinematic variables without the underlaying forces, looking plainly at angles etc., while we use dynamics if we include the force data.

2.2. Data analysis

2.2.1. Motion tracking

DeepLabCut (DLC) v. 2.2rc2 was used to perform markerless pose-estimation of 34 key points per frame [27]. To this end, a resnet-50 network was trained for 700 000 iterations, using 90 hand-labelled frames: 10 frames each from 9 videos as a training dataset. The network reached a test error of 3.48 px; individual specific errors can be found in electronic supplementary material, table S1. An example of the tracking results including the tracked labels is provided in figure 2b as well as in electronic supplementary material, video S1. Frames, steps or step phases (depending on calculation) with a DLC label likelihood less than 90% were excluded from all further calculations.

2.2.2. Calculation of kinematic parameters

The kinematic analysis was conducted using a custom Python script (DOKA; electronic supplementary material, data S1), which extracts desired kinematic parameters automatically from DLC output files. Stance and stride phases were automatically detected from the velocity of the feet relative to that of the body, after smoothing each with a Butterworth low pass filter and a Savitzky–Golay smoothing filter (for a detailed description, see [28,29]). On a whole-body level, we extracted direction of climbing (up or down), body deflection from vertical (for filtering data), defined as the average deviation of the body axis (shoulder, hip) from the vertical axis of the race track, speed, duty factor, stride frequency and stride length. Next, we calculated a variety of kinematic parameters, at different anatomical levels (figure 2c): on the limb level, we calculated limb range of motion angles (limb ROM), pro- and retraction angles of the limbs (centre range of motion (CROM) angle), and the width between the feet during midstance (foot width); on the foot level, we extracted the foot angles at the wrist/ankle in relation to the gecko's body axis; and on the toe level, we extracted the toe spreading angles and individual toe alignment angles relative to the lizard's body axis (figure 2d; see electronic supplementary material, table S2, for further details). All lengths were normalized with SVL. In total, we extracted 1750 strides, 1011 of which were climbing head-up, 639 climbing head-down. Only data where the animals climbed in a direction deviating 10° or less from vertical (body deflection) were included.

2.2.3. Ground reaction force analysis

We recorded GRF for 88 steps: 40 for geckos running down (fore left (FL): 7, fore right (FR): 9, hind left (HL): 9, hind right (HR): 15) and 48 for geckos running up (FL: 12, FR: 14, HL: 10, HR: 12). Force traces for each step were extracted using a custom Matlab script (Force Data Matlab Script; electronic supplementary material, data S2). In brief, force readings were baselined, smoothed using a moving average filter (spaps.m) and synchronized with the video recordings, using frame rate of forces and video and the video length to calculate the start of the video within the force data (video and force recordings were stopped simultaneously). For each footfall, we extracted the mean, maximum and minimum values for the normal, fore–aft and lateral forces, respectively. The smoothing parameters used within the spaps function for each force axis of each run can be found in electronic supplementary material, table S3.

Kinematic and force data were subsequently combined to analyse step dynamics (electronic supplementary material, data S3). Strides were excluded if the climbing direction deviated by more than 10° from vertical, leaving us with a total of 68 combined force and kinematic footfalls (up: 38, down: 30). All forces were normalized by body weight in newtons. Further, the resultant in-plane force was calculated from the lateral (F_lat) and the fore–aft (F_fore–aft) force:

$$F_{xy}=\sqrt{F_{\mathrm{fore}-\mathrm{aft}}^2+{(F_{\mathrm{lat}})}^2}.$$ 2.1

The orientation of the in-plane (F_xy) force vector (α_xy) relative to the gravitational force vector was defined such that a clockwise orientation is positive:

$${\alpha }_{xy}=\arctan {\displaystyle \frac{(F_{\mathrm{lat}}/F_{\mathrm{fore}-\mathrm{aft}})\times 180}{\pi }.}$$

Forces normal to the climbing surface are referred to as adhesion forces if they are directed towards the animal, and as compressive forces if they point away from it. Fore–aft forces are aligned with the direction of climbing and can be directed upwards or downwards. We used the term braking force for the situation where the fore–aft force was aligned with direction of climbing and the feet were in a compressive configuration. Lateral forces are perpendicular to the direction of climbing and hence can point left or right of the animal.

2.3. Spatio-temporal kinematics

In order to test if any alterations in dynamics arise as a consequence of the direction of climbing, or indirectly reflect differences in speed, we tested whether relative speed, defined as SVL per second, differed between head-up and head-down climbing using a generalized linear model in R (nlme package v3.1.142, R v.: 3.6.2).

2.4. Statistics

All statistical analyses were performed in R (3.6.2). Differences between climbing direction for individual kinematic parameters were tested using linear mixed effects models, implemented in nlme (3.1.142) [30] with individual as a random factor. For kinematic parameters on the whole-body level, we tested influence of direction of climbing. For all other parameters on the limb, foot and toe level we also tested the difference between fore versus hind limbs. To test for differences between up and down for individual toe alignment we used an ANOVA. We further tested the opposing alignment of the in-plane force vector (F_xy) with the foot angle and the individual toe angles by calculating the angle between these respectively and testing for a significant difference from 180° using a t-test, with 180° representing perfect opposing alignment.

In order to identify kinematic variables, which contribute most, we performed a principal component analysis (PCA) in R using the prcomp function (stats package). All variables were scaled (using the standard deviation: each column—after centring—is divided by the square root of sum-of-squares over n − 1, where n is the number of non-missing values) to account for different minimum to maximum value ranges of kinematic parameters and mean-centred (excluding missing data) as part of the internal function.

The influence of body mass on the adjustment of kinematic variables with change of direction was tested using lme in R, including the interaction of body mass and direction, with individual as a random variable.

3. Results

3.1. Geckos swap functional role of feet during head-up versus head-down climbing

During head-up climbing (HU), we expected geckos to generate adhesive force with their feet above the COM (fore feet) and compressive forces with the feet below it (hind feet). During head-down climbing (HD), in turn, we predicted this functional division of labour to swap.

3.1.1. Normal force

The average relative normal force for the fore feet was 0.21 ± 0.24 body weight (BW) for HU; fore feet showed adhesive forces. The force magnitude during HD was similar, but the force changed orientation; front feet now pushed into the surface (−0.24 ± 0.35 BW), generating a compressive force instead. In direct analogy, hind feet exerted compressive forces when HU (−0.12 ± 0.20 BW) but pulled on the surface when HD (0.34 ± 0.60 BM; figure 3d). During HD the force magnitude for feet above the COM and for feet below the COM was higher than the force magnitude for feet above and below the COM during HU, by 0.13 BW and 0.12 BW, respectively. In the following, we refer to feet above the COM being in the adhesive configuration, producing adhesive forces.

Figure 3.

Results of the GRF for head-up (purple) and head-down (green) climbing, split by fore and hind feet (b,d) and additionally subsectioned by left and right, because lateral forces are involved (a,c). Boxplots display results for (a) lateral forces, (b) fore–aft forces, (c) in-plane forces (lateral + fore–aft; equation (2.1)), and (d) normal forces. All forces were divided by the respective body weight of the animal, hence are displayed as a dimensionless number.

3.1.2. Fore–aft force

All fore–aft forces pointed downwards. Hence the force was directed against climbing direction for HU and aligned with climbing direction for HD. Average fore–aft forces for HU did not differ significantly between fore and hind feet (fore mean: 0.67 ± 0.71 BW, hind mean: 0.88 ± 0.68 BW, t₃₆ = −0.40, p = 0.689). Both feet thus contributed equally to propulsion up the wall. However, hind feet produced a significantly higher fore–aft force during HD (fore mean: 0.22 ± 0.15 BW, hind mean: 1.25 ± 1.18 BW, t₂₇ = −3.55, p = 0.001), while the fore–aft force of the fore feet for HD showed only a small but measurable force (t₁₂ = 3.027, p = 0.011; figure 3b).

3.1.3. Lateral force

Average lateral forces displayed a clear distinction between feet above versus below the COM. Only the feet above the COM, which were in the adhesive configuration, produced significant lateral forces (FL_up mean: 0.48 BW, t₁₃ = 4.25, p < 0.001; FR_up mean: −0.38 BW, t₇ = −2.441, p = 0.045; HL_down mean: 0.55, t₆ = 2.636, p = 0.039; HR_down mean: −0.98, t₈ = −3.027, p = 0.016). The lateral forces for the feet below the COM were not significantly different from zero (figure 3a; electronic supplementary material, table S5).

3.1.4. In-plane force

The in-plane force gives a good representation of the importance of propulsive versus lateral forces, as it is their vector sum (equation (2.1)). The magnitude of the in-plane force for the fore feet was 0.85 ± 0.78 BW for HU, much higher than for HD (0.25 ± 0.18 BW). This difference was smaller for the hind feet; the in-plane force was 0.97 ± 0.69 BW for HU and increased to 1.48 ± 1.36 BW for HD (figure 3c). For feet above the COM, in adhesive configuration, the lateral component of the in-plane force was relatively bigger, resulting in a force vector pointing to the body-middle of 36° for the fore feet and 26° for the hind feet, relative to the gravitational force vector. In comparison, the in-plane force for feet below the COM was at 17° for the fore feet and 6.5° for the hind feet.

3.2. Kinematic adjustments on different levels

We have split the large number of kinematic variables into different levels of anatomy: the whole-body level, represented by general spatio-temporal variables; the limb level, represented by limb ROM, limb CROM and foot width; the foot level, including foot angle; and the toe level, represented by toe spreading and toe alignment with direction of climbing (figure 2c).

3.3. Allometry of different body parts might influence dynamic alterations

Cameron et al. [31] confirmed an allometry between limb and head size in male geckos, which could lead to some variation in measured kinematic alterations. We did not collect detailed morphological measurements, but we tested for an influence of body mass. There was no significant difference for all kinematic variables, apart from hind foot angle and mean toe spreading in the fore foot (electronic supplementary material, figure S2 and table S9). Further relative speed did not differ significantly (F_1,1123 = 0.1146, p = 0.7351), indicating that any differences in dynamics likely are triggered by differences in direction of climbing alone (for further details, see electronic supplementary material, figure S1 and table S8).

3.3.1. Whole-body level

Relative speed did not significantly vary between HU and HD (HU: 9.84 ± 4.02 SVL s⁻¹, HD: 10.10 ± 5.99 SVL s⁻¹, F_1,761: 0.33, p = 0.564). Although stride frequency increased significantly from 12.33 ± 2.77 Hz (HU, median: 11.63 Hz) to 14.65 Hz (HD, median: 14.2, F_{1, 608}: 150.29, p < 0.001), the relative stride length decreased significantly from 0.96 ± 0.18 SVL (HU, median: 1.01 SVL) to 0.89 ± 0.24 SVL, resulting in approximately equal speed (HD, median: 0.87 SVL, F_{1, 88}: 6.51, p = 0.013). The duty factor decreased from 0.57 ± 0.07 for HU to 0.53 ± 0.12 for HD (F_{1, 744}: 8.12, p = 0.005). The density plots for the whole-body kinematics can be found in electronic supplementary material, figure S1, and the statistics in electronic supplementary material, table S8.

3.3.2. Limb level

The relative width between both fore and hind feet during mid-stance was smaller during HD (fore: F_{1, 477}: 394.67, p < 0.001; hind: F_{1, 477}: 73.57, p < 0.001). The relative width for HU was 0.42 ± 0.04 SVL (fore) and 0.43 ± 0.04 SVL (hind) and for HD was 0.38 ± 0.04 SVL (fore) and 0.41 ± 0.05 SVL (hind) (figure 4a). For both fore and hind feet, the limb ROM decreased from 65 ± 18° and 84 ± 22° (fore, hind respectively, HU) to 56 ± 21° (fore, F_{1, 195}: 13.66, p < 0.001) and 73 ± 20° (hind, F_{1, 449}: 30.46, p < 0.001, HD; figure 4b). Finally, the limb CROM for the fore feet was retracted and did not change significantly with direction of climbing (HU: −29 ± 12°, median: −26°, HD: −29 ± 11°, median: −28). The CROM of the hindfoot, in contrast, increased by about a factor of two, from 12 ± 12° to 21 ± 11° (F_{1, 450}: 86.05, p < 0.001; figure 4c).

Figure 4.

Adjustments on the limb level. (a) The relative width (width divided by the SVL of the animal) between the feet was decreased for both fore foot (left) and hind foot (right) when changing from head-up (purple) to head-down (green) climbing. (b) Limb ROM (in degrees) was decreased for both feet when turning to head-down climbing. (c) The CROM (in degrees) for the hind feet was protracted further for head-down climbing. The asterix (*) indicates a significant change between directions.

3.3.3. Foot level

The foot angles varied significantly with the direction of climbing. The forefoot angle increased from 36 ± 21° for HU to 47 ± 27° for HD (F_{1, 383}: 51.17, p < 0.001). The hindfoot angle increased from 85 ± 22° for HU to 125 ± 28° for HD (F_{1, 492}: 585.80, p < 0.001; figure 5a).

Figure 5.

Adjustments on the foot level. (a) Both fore and hind foot angle (in degrees) increase when changing from head-up (purple) to head-down (green) climbing. (b) The foot angle of the feet in the current adhesive configuration (up: purple arrow fore foot; down: green arrow hind foot), aligns well with the in-plane force vector (red arrow), while when in the non-adhesive configuration (below the COM) that angle is much smaller, about perpendicular for head-up climbing (angle between purple and red arrow hind foot), and even smaller for head-down climbing (angle between green and red arrow fore foot). These angles are illustrated with the black arrows.

We further tested the opposing alignment of the in-plane force vector (F_xy) with the foot angle and the individual toe angles (next section). The in-plane force vector (F_xy) orientation opposed the forefoot angle almost perfectly for HU (mean 184°, t₁₃ = 0.43, p = 0.667). However, this was not the case for the forefoot for HD or the hindfoot for either direction. Instead, the force vector was closer to a 90° angle to the foot angle of the hindfoot for HU and HD climbing (figure 5b).

3.3.4. Toe level

We found significant differences in mean toe spreading angles across climbing directions. Mean forefoot toe angles increased from 53 ± 6° for HU to 59 ± 9° for HD (F_{1, 378}: 69.51, p < 0.001). The hind feet mean toe spreading angle showed an opposite trend. The angle decreased from 47 ± 8° for HU to 40 ± 6° for HD (F_{1, 491}: 125.72, p < 0.001; figure 6a).

Figure 6.

Adjustments on the toe level. (a) The mean toe spreading angle (in degrees) increased for fore feet but decreased for hind feet across head-up (purple) and head-down (green) climbing. (b) Polar plot of the individual toe alignment angles comparing head-up (purple) and head-down (green) climbing for fore feet (left) and hind feet (right). The yellow arrows show the overall foot angle measured and the red arrows represent the orientation of the in-plane (F_xy) force vector. 0° represents the direction of climbing, 90° the outwards facing side of the animal. Green and purple transparent areas show the total span of the toe spreading.

Changes in individual toe alignment were also apparent. Apart from ti1 (the second most inward-facing toe) of the fore feet, all individual toes changed their alignment with respect to the vertical significantly from HU to HD climbing (electronic supplementary material, table S6). The change in orientation in individual hind toes was much larger, between 35° and 57°, while the change in individual fore toes only measured between 1° and 10°.

As reported above, the direction of the in-plane force vector (F_xy) only opposed the foot angle of the forefoot for HU. This suggests that there might be alignment with an individual toe instead of the whole foot for the other cases. The alignment of to1 (the second outermost toe) of the hind feet in their adhesive role (head-down) was almost perfect with the F_xy vector, yet with 184° significantly different from the directly opposing 180° (t₂₀₅ = 5.63, CI: 182.98; 186.20, p < 0.001; figure 6b). No other significant alignments could be determined (electronic supplementary material, table S7).

3.3.5. Principal component analysis reveals a clear clustering between up and down

Several individual kinematic variables displayed significant changes when inverting the direction of climbing. To determine which of these variables might have a stronger influence in differentiating HU versus HD, we performed a PCA. We reshaped the dataset so that individual strides were in the rows with each kinematic variable split by fore and hind as columns. The steps were then grouped by direction of climbing. PC1 explained 31.7% of the variance; PC2 explained 20% of the variance. Three hindfoot kinematic variables had a strong weight in the first component: mean toe spreading of the hind feet, CROM of the hind feet and the foot angle of the hind feet (−0.41, 0.42 and 0.48, respectively; figure 7a).

Figure 7.

(a) Plot of the PCA on all kinematic variables split by fore and hind feet and further grouped by direction of climbing, showing principal component 1, which explains 31.7% of the variance plotted over principal component 2, which explains 20% of the variance. The groups ‘up’ (purple) and ‘down’ (green) were clearly separated along PC1, displayed with the ellipses. Three variables were apparent with a weight of more than 0.40 within PC1: foot angle hind and CROM hind, as well as mean toe spreading hind. (b) Overview of the kinematic adjustments of the feet in the adhesive role comparing configurations of head-up versus head-down climbing.

4. Discussion

Locomotion on non-level surfaces is a challenging task, even more so for animals like lizards, which possess direction-dependent adhesive structures. On inclines, more mechanical work as well as the establishment of adhesion to the surface is required to produce propulsive forces against gravity, while another challenge is the overturning moment acting upon the bottom limbs of the lizard. On declines, many species decrease velocity and display a lower duty factor compared to level, hence a shorter phase of surface contact, which could indicate a reduction in locomotor stability [1] resulting from the need to work against the passive acceleration through gravity.

Although several studies have investigated climbing locomotion of different lizard species on different inclines and different climbing directions (up, down, sideways and upside down), the number of studies which investigated vertical head-down climbing is small, and a comprehensive analysis of a wide range of kinematic variables as well as dynamics across anatomical levels of the animal is lacking. Previous studies have suggested a split in limb functionality for locomotion on inclines or declines [1–3]. Further, expanding upon mechanical models presented by Autumn et al. [2] and Wang et al. [5], we expected that the function of the feet is determined by their position relative to the COM, with the feet above the COM pulling into the wall, while the feet below the COM push off the wall to equalize the apparent overturning moment. Supported by GRF data by Wang et al. [5] and our force results (figure 3d), the magnitudes for these pulling and compressing forces are equal between the respective foot pairs (above/below COM) between the two directions of climbing. This result indicates that despite different mechanical challenges for head-up and head-down climbing, lizards can adjust their kinematics to maintain the same force profile for normal forces. However, given the direction dependence of the adhesive system, and the difference in fore and hind limb morphology (segment lengths, joint constraints, muscle attachments etc.), there are likely limb functions that suffer in order to achieve this swap of functionality (i.e. braking).

Our results suggest indeed that hind limbs seem to be more flexible in providing consistent contribution across upward and downward climbing, while the contribution of the fore limbs appears diminished for head-down climbing, a finding we discuss in detail below.

A PCA performed on all kinematic variables grouped by limbs as well as direction of climbing identified three variables which show the greatest adjustment between directions: CROM, foot angles, and toe spreading (figure 7a). Notably, all these variables were hind feet adjustments; thus hind feet either (1) are more crucial, compensating for limited versatility of the fore feet or (2) they require greater adjustments to resemble the adhesive function of the fore feet. Further, each variable falls on a different hierarchical level of the locomotor anatomy, illustrating that all three levels are important and possibly strongly interconnected. In the following, we focus on these three variables further, discuss how they interact, and assess the capabilities of fore versus hind feet when above or below the COM to overcome the constraints imposed by the direction-dependent structures.

The hind feet CROM represents a kinematic adjustment on the limb level. Hind limbs were twice as protracted when climbing head-down compared to head-up (figure 4c), supporting previous studies, which showed similar adjustments on −45° slopes [22]. Yet even though the limbs are protracted forwards, the foot angle is adjusted caudally, such that hind feet point backwards (or upwards). This change seemingly aligns the foot to oppose the gravitational force vector, but a significant in-plane force component in the lateral direction remained.

Several studies have reported that lizards and other climbing animals such as cockroaches adhere to the surface with foot angles diverging from the direction of climbing. The associated lateral forces can reach up to 50% of the vertical (fore–aft) forces, suggesting this may be a common modification in adhesion strategy [15,23,28,32–34]. Using a modular gecko-inspired robot, Schultz et al. [35] and Beck et al. [32] investigated a wide range of combinations of fore- and hindfoot angles to determine why foot angles diverge from the seemingly ideal direction where they oppose the gravitational force vector directly. Mirroring the results reported here for the forefoot of the geckos during head-up climbing (i.e. the limb in the adhesive configuration), the robot showed a performance optimum for forefoot angles of 20° evidenced by the highest climbing speeds and most stable climbs (100% success). In sharp contrast, when robotic foot angles directly opposed gravity, climbs were slow and often unsuccessful [35]. This optimum foot angle suggests an important role in lateral forces on the adhesive limb to stabilize the gait, and probably represents an important addition to a climbing template [15]. As joints associated with locomotion increase mechanical work typically through an increase in extensor moments, while animal postures during climbing are more sprawled compared to level when climbing on an uphill [1], lateral forces may serve to reduce joint torques by aligning the joint movements better with the apparent GRF.

We might expect that the changes in the foot orientation allow better alignment with the resultant in-plane force vector rather than with the direction of climbing. This was certainly true while in the adhesive configuration, highlighting the importance of the re-orientation of the pads to produce adhesion. Yet when the feet are below the COM, and therefore not in the adhesive configuration, we measured negligible lateral forces with the foot angle orientated outwards, perpendicular to the in-plane force vector (figure 3a). This result did not strictly align with previous measured GRF by Autumn et al. [2] and Wang et al. [5], both which reported lateral forces pulling toward the body midline for feet below the COM. Yet Wang et al. [5] found a 50% decrease in lateral forces for this case. All studies share the observation that feet in the non-adhesive configuration did not oppose the in-plane force vector, and instead are oriented laterally. The reason for the lateral orientation of the non-adhesive feet, independent of the in-plane force vector, remains unclear. A possible mechanism was illustrated by Clark et al. [33]. Using a bioinspired robotic prototype built upon the climbing template proposed by Autumn et al. [2], head-up climbing was achieved using only two adhesive fore feet; the hind feet were just a simplified rod extending to either side to prevent long-axis roll [33]. This might explain variation in the kinematics observed for our gecko movement patterns: the lateral orientation of the feet in the non-adhesive condition, perhaps combined with the increased width between the feet, increases the moment arm available to resist this lateral roll.

The large change in foot angles is likely linked with changes at the toe level, via modification in alignment or spreading. An increase in toe spreading might allow for toes to function independently. Song et al. [24] showed that individual toes produce different force magnitudes and hypothesized that toe spreading might be important to have at least one toe aligned with the in-plane force vector.

Yet Song et al. [24] and our results (figure 6b) suggest that the middle toes were best aligned with the in-plane force vector for adhesive feet, while outer toes rarely showed a good alignment. This could indicate a more important function for these toes, or an increased ability to support force. An increased muscle count or more tendon attachment sites for these toes could support this [36,37]. Yet we show that feet in the adhesive configuration display a decrease in toe spreading, perhaps to align as many toes as possible with the in-plane force vector, similar to results presented by Imburgia et al. [25]. Thus, changes in foot orientation might be more important for the feet in the adhesive configuration, but changes in toe spreading dominate in feet in the non-adhesive configuration.

When not in the adhesive configuration, the toes must perform a different role and be able to push into the surface and produce frictional forces. For example, the fore feet during head-down climbing were orientated against their adhesive direction (figure 6b), yet they did not detach and even produced smaller significant braking forces (figure 3b). Autumn et al. [2] described that the directional structure of the geckos is capable of producing friction against the adhesive direction, albeit at a much lower magnitude, reporting a 10-fold difference for an extracted setal array. We similarly found an 8.3-fold difference in the fore–aft forces between fore and hind feet for head-down climbing (figure 3b).

From our GRF data, we estimated the friction coefficient for the fore feet during head-down climbing, assuming Coloumb friction:

$$\mu ={\displaystyle \frac{F_{\mathrm{fore}-\mathrm{aft}}}{F_{\mathrm{normal}}}.}$$

The resulting friction coefficient µ for the forefeet for head-down climbing was 0.68, close to the friction coefficient reported by Song et al. [16] for sliding the toe base reverse to scale direction (0.62). The much higher braking fore–aft forces for the hind feet (8.3-fold) for head-down climbing indicate their importance to compensate for the reduced fore–aft force produced by the fore feet. During head-up climbing, the magnitudes in propulsive forces were equal between feet above and below the COM, presumably enabled by the favourable orientations of toes relative to the gravitational force vector. Non-apparent or small braking forces in the fore feet for head-down climbing could also suggest that they only absorb the mechanical work rather than also producing braking forces. This difference in contribution of front and hind feet might originate from functional constraints arising from differences in musculoskeletal arrangement. Russell [36] and Zaaf et al. [37] examined osteology and myology of the fore and hind feet of a gecko (Gekko gecko) in detail, and found distinct differences between fore and hind feet in joint morphologies, muscle counts and muscle attachment sites.

Further studies might explore other species which are less optimized for climbing. Russell [36] found that geckos possess a higher distal muscle mass than cursorial lizards, which is likely related to their need for fine control of their toes for climbing. Other lizards might therefore have to rely more on different levels of kinematic adjustments to address the change in force regimes with inversion of direction of climbing. This dependence on different levels might not only be influenced by the musculoskeletal morphology but also by the type of surface the lizard is climbing on. Most gecko studies along with ours use smooth surfaces in laboratory environments, yet geckos manoeuvre many different surface roughnesses in their natural environment [38]. A surface which is more challenging for adhesion might force the lizard to focus on kinematic alteration on broader levels, i.e. whole-body, limb and maybe foot level, the role differentiation becoming less conspicuous. Yet, we would expect that the role differentiation between fore and hind limb, which was found in all variables across the different levels, remains apparent. Future studies comparing different species on different surface types, especially some ‘more natural’, might bring some clarity to this.

5. Conclusion

Our results provide novel insights into climbing locomotion, showing how the hierarchical adhesive pads of geckos integrate into kinematics on multiple levels of the animal during head-up versus head-down climbing. Feet perform different roles depending on their position relative to the COM. Feet above the COM produce pulling normal (adhesive) forces, while feet below the COM create compressing forces of equal magnitude, to counterbalance the toppling moment. The capability to swap the adhesive role of the limbs, despite the constraint of the direction dependence of the adhesives, suggests the need for complex kinematic adjustments. We found one kinematic variable being adjusted largely on each level: limb, foot, and toe. Notably, kinematic adjustments dominated for hind feet, suggesting a higher flexibility in these to make a more consistent contribution across climbing directions. This suggestion is further supported by the fore–aft forces which are equal between feet for HU but for HD the fore–aft force for the fore feet diminishes while the hind feet fore–aft forces increase largely.

These highlight key results which might be of importance for the designs of industrial robotic gaits. Most robotic gaits do not include a variation of limb movement depending on their location relative to the COM. Legged locomotion for robots still remains a challenge, typically requiring hard-coded adjustments depending on the environment; e.g. hard ground versus granular medium [39]. However, if legged locomotion can be better understood, it may open more versatile applications than possible with wheeled robots, especially in environments which are uneven or covered with various obstacles [40,41].

Ethics

All lizards were wild caught and transported in cotton bags to the Animal Ecology Laboratory at the University of the Sunshine Coast under animal ethics permit ANA16104.

Data accessibility

Data and code used for all statistical analyses within this paper are available at https://figshare.com/projects/Multilevel_dynamic_adjustments_of_geckos_Hemidactylus_frenatus_climbing_vertically_head-up_versus_head-down/153924. Code for automation of lizard biomechanics is available via github: https://github.com/JojoReikun/ClimbingLizardDLCAnalysis. All further code and data files are stated in the electronic supplementary material and also available on figshare.

The data are provided in electronic supplementary material [42].

Authors' contributions

J.T.S.: conceptualization, data curation, formal analysis, investigation, methodology, software, validation, visualization, writing—original draft, writing—review and editing; D.L.: supervision, writing—review and editing; C.J.C.: conceptualization, data curation, formal analysis, funding acquisition, methodology, project administration, supervision, validation, writing—review and editing.

All authors gave final approval for publication and agreed to be held accountable for the work performed therein.

Conflict of interest declaration

We declare we have no competing interests.

Funding

This study was funded by an Australian Research Council Discovery Grant (grant no. DP180100220) awarded to C.J.C.