A gecko-inspired robot with CPG-based neural control for locomotion and body height adaptation

The limb structure of the gecko-inspired robot was developed based on an analysis of the skeletal system and kinematics of real geckos. From the top view of the gecko's bone structure (figure 2(a)), we can see that the limb structure is symmetric on the sagittal plane, and the fore limb and hind limb have a large degree of similarity in structure. Therefore, only the kinematics data of the right front limb were chosen for the analysis and used for all robot limbs (figure 2(a)).

Zoom In Zoom Out Reset image size

The gecko limb can be divided into three main parts: the thigh, crus, and footpad. Each part of the limb rotates around different joints. The thigh can be seen as a rotation around the shoulder. The crus can rotate around the elbow joint in a plane built by the thigh and crus. The footpad is linked to the crus by the wrist joint (similar to the shoulder joint), which has three DOFs, but has a shorter linking bar that poses more restrictions on the working space.

The kinematic model for analyzing the joint angle change of the right front limb is shown in figure 2(b). The Y₀ axis of the world frame (frame 0) points to the moving forward direction, and the Z₀ axis of the world frame points to the perpendicular direction of the gecko moving surface. For better analyzing and decomposing the movement of each joint, the reference frames 1 and 2 were built at the centre of the shoulder joint and elbow joint, respectively. The X₁ axis was built along the straight line starting from the left shoulder and pointing to the right shoulder. The Y₁ axis was vertical to the plane which was made up of the built X₁ axis and the Z₀ axis in the world frame. Thus, a Cartesian coordinate (reference frame 1) following the right-hand rule was built in the right shoulder. The shoulder degree 1 (angle between the projected thigh in the X₁ OY₁ plane and X₁ axis) and shoulder degree 2 (angle between the thigh and X₁ OY₁ plane) were defined under the reference frame 1. The X₂ axis was built along the straight line starting from the shoulder and pointing to the elbow. The Z₂ axis was created by projecting the Z₁ axis onto a plane perpendicular to the X₂ axis. The shoulder degree 3 was the rotation angle around its central axis, which was defined as the angle between the projected crus (projected in to the X₂ OY₂) and the negative Z₂. The movement of the elbow joint (green marker) was defined as the angle between the upper and lower arms, indicated by a light yellow shadow in the middle part of figure 2(b). The movement of the wrist was indicated by the angle between the lower arm and the substrate, which is called the crus angle, as shown in the lower part of figure 2(b).

To estimate the moving range of real gecko's limbs, a climbing experiment was conducted with real geckos on a slope of 45°. The results are presented in figure 2(c). The grey shadow or white region indicates that the gecko was in the stance or swing phase of the gait cycle. From the kinematic results, the shoulder degree 1 ranged from approximately 20° to 60°, the shoulder degree 2 ranged from approximately 0° to 25°, and shoulder degree 3 ranged from approximately −80° to 30°, the elbow angle ranged from approximately 65° to 125°, and the variation range of the crus angle in the stance phase was approximately 10° to 130°. Furthermore, the decomposed moving angles above indicate that all these DOFs contribute to the locomotion of the real gecko (figure 2(c)). Based on concepts extracted from the kinematic analysis of real geckos, an abstract structure with four active DOFs for the limb and three passive DOFs for the foot was designed for the gecko-inspired robot.

The design of the leg of the gecko-inspired robot was first formulated according to the analysis of the skeletal system and the developed kinematic model. Figure 2(d) illustrates the joint configuration of the robot, where the shoulder joint of the robot comprises three blue cylinders (three active DOFs), the elbow joint comprises one green cylinder (one active DOF), and the wrist joint is indicated by the orange point (three passive DOFs). Under this concept, the physical right front limb of the robot was constructed (figure 2(e)). Four servomotors provide four active DOFs, and an alloy ball with a ball bearing provides the three passive DOFs. The servomotors 'XM430-W350-R Dynamixel' with a rotational angle of 360° were chosen as the actuators. The selection and arrangement of the driving motors mainly consider that the motion space of the robot is as close as possible to the motion space of the gecko, and define the torque and size requirements of the robot. The shoulder degree 1 (joint 1) ranges from −90° to 90°, the shoulder degree 2 (joint 2) ranges from −90° to 55°, and the shoulder degree 3 (joint 3) ranges from −78° to 78°. The range of elbow joint angle (joint 4) ranges from 41° to 176°, and the motion of the wrist joint (joint 5) ranges from 55° to 125° (figure 2(e)). A summary of the joint angles of the gecko and robot is presented in table 1.

After the development of the limb structure, a gecko-inspired robot with a symmetrical body structure was built. The total weight of the robot was 2400 g, and the size of the robot was 35.5 cm × 6 cm × 7.8 cm. A comparison of the standing posture of the gecko and the robot is shown in figures 3(a) and (b), respectively. The blue, green, and orange circles represent the shoulder, elbow, and wrist joints, respectively. A summary table of the sizes of the gecko and robot is shown in table 2.

Zoom In Zoom Out Reset image size

A good adhesive mechanism on the feet can guarantee that the climbing robot has sufficient adhesive force to move freely and stably on slopes or even walls, as inspired by geckos. The top and bottom views of the foot of the gecko are shown in figure 3(c), and the right part of the figure shows the toes of the gecko, which are the basic adhesion units that generate the adhesive force and interact with the real environment. Based on the anatomy analysis [15] (figure 3(d)) of a single toe, a three-layer structure with different functions was found, as indicated by the arrows. The attachment and detachment movements of the toes are performed by a rigid part referred to as the phalanx. Adaptability and cushioning are provided by the soft adjustable part in the middle, which comprises the flexor tendon, reticular network, and sinus [15]. The adhesive force is generated from the bottom adhesive lamella, which contains an array of setae [16] (figure 3(e)), and the tip bifurcated structure of a single seta shows the origin of the adaptability of the adhesive foot (figure 3(e)).

The three-layer structure of the gecko's foot was extracted as a hybrid soft-rigid adhesive mechanism, which was applied to our gecko-inspired robot. Figures 3(f) and (h) demonstrate the comparable structure of the foot mechanism, comprising three different parts, and the wrist with a ball joint, which share similar functions with those of the gecko foot and wrist. The upper layer of the foot was a rigid layer made of an aluminium alloy. The middle layer is a custom soft layer made of an adjustable PDMS-based soft material [17]. The bottom layer contains a bio-inspired adhesive material. The non-directional adhesive material was chosen as the bottom layer material because of its reliable and promising adhesive ability [18]. The microstructure [19] of the adhesive material used in the robot's foot mechanism is shown in figure 3(h).

To complete attachment–detachment movements, the gecko uses active muscles in its toes to control eversion and adduction. The adhesive foot for the robot was designed as a passive mechanism to reduce the complexity of the gecko-inspired robot. The free ball joint (acting as a wrist) links the lower limb and the cylinder foot. The foot can move freely without considering the directional problem when the foot is attached to or detached from the substrate. The margin of the inner hole of the cylinder foot acts as a stopper (figure 3(g)), which limits the tilting angle of the lower-limb bar and improves the force application when the foot needs to attach and detach from the substrate. Such a hybrid soft-rigid mechanism exhibits appropriate flexibility and more promising features when used on this type of compact design climbing robot with a high payload. The detailed manufacture and performance test can be found in our previous work [17].

Figure 4 demonstrates the locomotion strategy of a real gecko. The stance phase is our focus here because attaching–detaching movements all occurred during this period. An overview of the climbing posture of a real gecko is shown in figure 4(a), where the high-speed camera captured three vivid periods (figure 4(b)) in one step of the gecko's locomotion.

Zoom In Zoom Out Reset image size

The attach, hold, and detach periods are defined according to the specific function of each period, from the start to the end of this step in the stance phase. The lower arm was tilted towards the forward direction from the attachment period to the detachment period. In this manner, the impact force transferred to the main trunk is reduced to better stabilise the locomotion of the gecko.

Attaching and detaching are two crucial periods that can determine the stability and continuity of a gecko's locomotion [21]. The left snapshot in figure 4(b) shows that at the beginning of the attachment period, the toes have an attaching angle with the substrate. Thereafter, the toes are attached to the surface using the rollout action (wherein effective adhesive area increases), while the heel of the foot is set as a fixed point. Detaching occurs at the end of the toes. As the toes gradually roll up, the effective adhesive area decreases. At the end of the detachment period, the entire foot leaves the substrate, and no adhesive force is generated. The vivid change in the effective area is observed from the attachment period until the end of the detachment period, as shown in figure 4(c).

Based on the gecko's locomotion strategy, one step of the gecko-inspired robot in the stance phase (figure 4(d)) is divided into the same three periods. During the hold period (figure 4(e)), the ball joint is in free mode, and the foot can stay at one point, merely rotating the lower arm towards the moving direction to push the body forward. During the attachment and detachment periods (figure 4(e)), the stopper limits the movement of the foot-ball joint, and the bottom adhesive material is controlled to gradually attach and detach from the substrate. Figure 4(f) demonstrates a change in the effective adhesive area of the robot foot comparable to the gecko (figure 4(c)).

A method for generating gecko-inspired leg movements is shown in figure 5(a). There were four steps in total. The first step was to observe the locomotion strategy of a real gecko and extract its leg movements (figure 4). The following three steps are realized below. The specific periods and movements of the robot were planned according to the locomotion strategy, which was extracted from the gecko. The complete period of the gecko-inspired robot in one step is illustrated in figure 5(b). As the timeline progresses, the attach and hold periods first occur, wherein the foot effective adhesive area starts to increase until the entire foot attaches to the climbing surface. Subsequently, one side leg waits for the other side leg to complete the detaching movement in the still stage of the hold period. After sufficient adhesive force is generated, the diagonal legs begin to push backward, thereby moving the body forward. The last two periods also start from the still stage of the hold period, in which the other side foot generates sufficient adhesive force. Thereafter, the foot detaches from the surface and swings to the start of the next moving step.

Zoom In Zoom Out Reset image size

The planned moving sequence of the gecko-inspired robot in one step, as observed from the gecko (figures 2(c) and 4(b)), is illustrated in figure 5(c), wherein the curved arrows indicate the tendencies of the foot movement, and the black bar under the foot indicates the ground. Using the moving sequence defined above, the robot can realise continuous adhesive locomotion. Figure 5(d) depicts the hand-crafted moving trajectory of the robot foot and the corresponding moving sequence (figure 5(c)). The red arrows indicate the foot's movement direction. Subsequently, in the third step, the planned trajectory was mapped to the joint space of the limbs using the numerical kinematic method [24]. The mapping between the foot wrist position in a three-dimensional Cartesian space $(\boldsymbol{T}={[{P}_{x},{P}_{y},{P}_{z}]}^{\mathrm{T}})$ and the joint angle space $(\boldsymbol{q}={[{\theta }_{1},{\theta }_{2},{\theta }_{3},{\theta }_{4}]}^{\mathrm{T}})$ was done by equation (1). The error e between the desired foot tip position T _d and generated foot tip position T _c was used as a cost function (equation (2)).

$$\begin{equation}\boldsymbol{T}=\boldsymbol{f}(\boldsymbol{q})\end{equation} \tag{ 1 }$$

$$\begin{equation}\boldsymbol{e}={\Vert}{\boldsymbol{T}}_{\mathbf{d}}-{\boldsymbol{T}}_{\mathbf{c}}{\Vert}={\Vert}{\boldsymbol{T}}_{\mathbf{d}}-\boldsymbol{f}({\boldsymbol{q}}_{\mathbf{c}}){\Vert}\end{equation} \tag{ 2 }$$

e was optimized by using equations (3) and (4). The Jacobian matrix J can be calculated from the Denavit–Hartenberg (DH) parameters of the robot's limb (table A1 and figure A1). The positive scalar α was used as an update rate of the joint positions. It was set to 0.01. We assumed that the optimal wrist position can be obtained after e was smaller than 0.001, i.e. q _d ≅ q _c .

$$\begin{equation}\mathbf{\Delta }\boldsymbol{\theta }={\left(\frac{\partial \boldsymbol{e}}{\partial \boldsymbol{\theta }}\right)}^{\mathrm{T}}={\boldsymbol{J}}^{\mathbf{T}}(\boldsymbol{\theta })\boldsymbol{e}\end{equation} \tag{ 3 }$$

$$\begin{equation}{\boldsymbol{q}}_{\boldsymbol{c}}^{\boldsymbol{k}+\boldsymbol{1}}={\boldsymbol{q}}_{\boldsymbol{c}}^{\boldsymbol{k}}+\mathbf{\alpha }\mathbf{\Delta }\mathbf{\theta }.\end{equation} \tag{ 4 }$$

Figure 5(f) presents the output of the four joints of a single leg. The same joint movements were also applied to the other legs. By comparing the joint position change of the real gecko and the robot (figures 5(e) and (f)), the consistent tendency (increase or decrease) can be found in attach, hold, and detach periods. This demonstrates that the key movements in adhesive locomotion of the real gecko, such as attachment and detachment, have been successfully extracted for the robot. It is important to note that due to our simplified fixed body of the gecko-inspired robot, the still stages in the hold phase were additionally introduced (figure 5(f)) for stability enhancement. Specifically, adding the still stages can ensure firmly surface adhesion before pushing back and obtain a double stance phase before detaching.

The gecko's locomotion strategy, which includes efficient foot attachment and detachment, allows it to stably climb on various slope angles. Its leg structure with many DOFs provides it with additional body height adaptability. Gecko obstacle crossing experiments were carried out to preliminary investigate the body height adaptability when encountering a bump or an obstacle. A gecko was used for the experiments at different slope angles of 0°, 30°, 60°, and 90°, where an obstacle with different heights (10 mm and 20 mm) was placed on the slope. Figure 6(a) exemplifies the gecko's entire obstacle crossing process where the height of the obstacle was set to 20 mm on a slope of 60°. The whole process can be divided into the following periods. In period I, the gecko moved towards the obstacle with its normal body height (low centre of mass). In period II, it began to lift the body up when it detected or its front limb approached the obstacle. In periods III and IV, it maintained its relatively high body height. In period V, its body height began to drop immediately when the front limb crossed over the obstacle while the remaining body part just glided on the obstacle. In period VI, the entire crossing process was completed when the hind limb also crossed over the obstacle. Figure 6(b) shows the corresponding body height adaptation of the gecko during the whole obstacle crossing process. Figure 6(c) depicts all results from the experiments as a percentage of body height elevation at various slope angles and obstacle heights. There is a significant correlation between obstacle height and body height, indicating that the gecko increased its body height when the obstacle height was increased. It raised its body by approximately 35% and 75% on average to overcome an obstacle with heights of 10 mm and 20 mm, respectively. However, there is no clear correlation between slope inclination and body height elevation, i.e. the gecko lifted its body at a certain level with respect to the obstacle height and maintained nearly the same body height even when the slope angle was increased. According to the experimental results, the gecko adapted its body height just enough to clear the obstacle and gravity appeared to have no significant influence on its body adaption.

Zoom In Zoom Out Reset image size

To overcome the complex environment with stability and adaptability, geckos require exteroceptive feedback (i.e. vision) and neural systems to detect and then enact locomotion and adaptation strategies. For the gecko-inspired robot, the locomotion strategy described above was encoded using a general neural control framework.

To enable adhesion and obstacle-overcoming abilities in the gecko-inspired robot, CPG-based neural control was used, comprised of four primary layers: sensory input, CPG, premotor neurons, and motor neurons. The sensory layer transmits input signals to adapt the body height of the robot, which enables closed-loop control with exteroceptive feedback for the robot. The signals from the sensory layer are transmitted to the CPG layer, which generates basic periodic patterns that drive the robot joint movements. To satisfy the requirements of efficient foot attachment and detachment behaviour as described above, basic periodic joint movement signals must be shaped to obtain more complex joint patterns. For this purpose, a RBF-based premotor network in the premotor neuron layer was employed to shape or transform the CPG periodic patterns into complex patterns. In this manner, the neural control network can realise the basic joint movements of the robot with efficient foot adhesion. The shaped joint movement signals are finally sent to the motor neuron layer. Different delaylines between the legs were implemented to shift the joint signals between the legs. This was done to achieve a trot gait. The details of each layer are presented below. An overview of the neural network connections is presented in figure 7(a).

Zoom In Zoom Out Reset image size

The sensory layer receives infrared (IR) signals from two IR sensors, IR1 and IR2, which are installed on the front and back of the robot, respectively (figure 7(a)). The scaled IR signals, which are mapped into a range from 0 (no obstacle) to 1 (obstacle detected), are transmitted to the sensory preprocessing unit, which uses the below step functions and logistic OR-like gate to control the robot body height.

$$\begin{equation}{i}_{1,2}(t)=\begin{cases}1,\quad \hfill & {i}_{1,2}(t) > 0.5\hfill \\ 0,\quad \hfill & {i}_{1,2}(t)< 0.01\hfill \end{cases}\end{equation} \tag{ 5 }$$

$$\begin{equation}\mathit{I}\mathit{R}(t)=\begin{cases}1,\quad \hfill & \quad \text{if}\ {i}_{1}(t)=1,\ {i}_{2}(t)=0\hfill \\ 0,\quad \hfill & \quad \text{if}\ {i}_{1}(t)=0,\ {i}_{2}(t)=0\hfill \\ -2,\quad \hfill & \quad \text{if}\ {i}_{1}(t)=0,\ {i}_{2}(t)=1\hfill \end{cases}.\end{equation} \tag{ 6 }$$

Here, i_1,2 are the sensor signals obtained from the front and back IR sensors. The value of 0.01 is set for the lower threshold, and a value lower than 0.01 indicates that no obstacle is found. The value of 0.5, which is set for the upper threshold, and a value higher than 0.5, indicating that an obstacle is detected (the distance between the sensors and obstacle is approximately 5 cm). The threshold value set was used to prevent the noise generated by the sensors (equation (5)). The sensor signals are converted into three states: state 1 (i₁(t) = 1, i₂(t) = 0), state 2 (i₁(t) = 0, i₂(t) = 0), and state 3 (i₁(t) = 0, i₂(t) = 1). The conversion is expressed by equation (6), which is directly applied to adapt the motor neurons (M_12,22 and M_14,24) (figure 7(a)) of joint 2 and joint 4 of all legs in the motor layer to adaptively increase or decrease the body height of the robot. A value of 1 lifts the body up, a value of 0 sustains the present body height, and a value of −2 reduces the body height. Here, we set the speed of the body drop to two times (IR = −2) faster than the body lift up (IR = 1). The rationale for this decision is that when a robot encounters an obstacle, the body height must avoid surpassing the obstacle height too much to save energy and to maintain the movement stability. Additionally, when the robot crosses the obstacle, it should return to a normal posture as soon as possible to increase the stability of locomotion.

The CPG layer (figure 7(a)) consists of two discrete-time recurrent neurons (C1 and C2), and the activities of neurons are presented in equation (7) and (8).

$$\begin{equation}{c}_{1}(t)=\mathrm{tanh}\left({w}_{11}{c}_{1}(t-1)+{w}_{12}{c}_{2}(t-1)\right)\end{equation} \tag{ 7 }$$

$$\begin{equation}{c}_{2}(t)=\mathrm{tanh}\left({w}_{22}{c}_{2}(t-1)+{w}_{21}{c}_{1}(t-1)\right).\end{equation} \tag{ 8 }$$

The alternate activation and inhibition between the two-neuron centres can provide the robot with basic period signals. The frequency of the outputs can be adjusted by adjusting the weight values of the neurons. Here, the weights are set for w₁₁ = w₂₂ = 1.01 and w₂₁ = −w₁₂ = 0.0182. This weight setup followed the analysis of the CPG neurodynamics described in [25]. Thus, one period (350 time steps) of the CPG output signals can generate adequate central points to control and shape the final joint movement signals for foot attachment and detachment.

The outputs of the CPG are transmitted to the RBF layer, which consists of three sublayers: input (receiving the signals from the CPG layer), kernel (shaping the CPG signals), and outputs (linearly combining the kernel outputs). Neural activation can be acquired using equation (9).

$$\begin{equation}{h}_{i}(t)=\mathrm{exp}\left(-\frac{{\left({c}_{1}(t)-{\mu }_{1,i}\right)}^{2}+{\left({c}_{2}(t)-{\mu }_{2,i}\right)}^{2}}{s}\right)\quad i\in \left[1,n\right],\quad \end{equation} \tag{ 9 }$$

where h_i (t) represents the specific kernel in the layer. c₁(t) and c₂(t) are the output values from the CPG layer. μ_1,i and μ_2,i are the kernel centres obtained from one period of c₁ and c₂, respectively. n determines the number of centres, that is, the number of kernels. Here, n = 80, which is set to maintain a sufficient complexity of signals but not too large for computation. The denominator of this equation is s (s = 0.001), which can determine the width of each kernel output. The signals from the kernels were linearly added using simple linear neurons (equation (10)).

$$\begin{equation}{O}_{j}(t)=\sum\limits _{i=1}^{n}{w}_{ij}{h}_{i}(t)\quad i\in \left[1,n\right],\enspace j\in \left[1,m\right].\end{equation} \tag{ 10 }$$

w_ij represents the weights used to scale and combine the transmitted signals between the RBF hidden/kernel and output layers. Here, O_j represents the output signals, which are transmitted to different groups of motor neurons in the motor layer. The motor neurons finally send the motor commands to control the joint angles of the legs as a position control. The gecko-inspired robot has four legs, that is, m = 4. The connections of the premotor neuron layer are also shown in figure 7(a). The final patterns of the neural control network outputs were shaped through w_ij , which uses the delta-learning rule to train (equation (11)).

$$\begin{equation}{\Delta}{w}_{ij}=\alpha \left({T}_{j}(t)-\sum\limits _{i=1}^{n}{w}_{ij}{h}_{i}(t)\right)\quad i\in \left[1,n\right],\enspace j\in \left[1,m\right].\end{equation} \tag{ 11 }$$

The extracted locomotion strategy with foot attaching and detaching movements in a three-dimensional Cartesian space was successfully applied to the robot joint space (see section 3.1 and figure 5). Here, the planned joint positions (T_j (t)) of the gecko-inspired robot were used as the target signals for training the RBF network. α represents the learning rate, which was empirically set to 0.1. Figure 7(b) demonstrates the entire training process for a single joint. Figure 7(c) shows the loss of the training process (calculated from the squared error) with varying RBF neurons. We observed that the minimal network with 80 RBF neurons has the lowest acceptable loss (approximately 0.07). As a result, we used this size for robot control.

The motor layer (figure 7(a)) directly transfers the signals to the physical joints. Equations (12) and (13) describe the detailed parameter settings among the motor layer.

$$\begin{equation}{M}_{1,j}(t)=\begin{cases}{O}_{j}(t),\quad \hfill & j=1,3\hfill \\ {O}_{j}(t)+\mathrm{I}\mathrm{R}(t),\quad \hfill & j=2,4\hfill \end{cases}\end{equation} \tag{ 12 }$$

$$\begin{equation}{M}_{2,j}(t)={M}_{1,j}(t+\tau )\quad j=1,2,3,4.\end{equation} \tag{ 13 }$$

M_1,j (t) and M_2,j (t) indicate the signals that are transmitted to the real servo motors in the robot. Because we used a trot gait for the robot, the left front and right hind legs used the same motor signals (M_1,j (t)). The delayline τ can shift the signals to derive the trot gait. It was set to 175 time steps (half of the CPG signal period). The shifted signals are directly used as commands in the right front and left hind legs. In addition, the sensory layer signals flow into the two depression and extension joints (joint 2 and joint 4) to adapt to the body height while the robot moves to overcome an obstacle. The pseudocode for the implementation of neural control (equations (5)–(13)) is shown in table A2. All parameters in the neural control (described above) together with their values and descriptions, are summarised in table A3.

To better understand the dynamics of animals and robots, which can contribute to adhesive features, the ground reaction force was measured and analysed. A force-measuring array [26] consisting of 16 independent force sensors, ranging from 0 to 1.5 N with a resolution of 0.1% of full scale (FS), was used to detect the ground reaction force on the three axes of the real gecko. In this experiment, one gecko (Gekko gecko) was used. It climbed 2–3 times for each slope. In total, we used data from five successful runs for each slope in our analysis.

A comparable test of the gecko-inspired robot was conducted on a similar force testing platform [17], but on a larger scale. It consisted of 20 independent 3D force sensors. Each force sensor ranged from −50 N to 50 N on the X- and Y-axes, and −60 to 60 N on the Z-axis. The sensor resolution was 0.1% FS. The comparison groups were set when the gecko and gecko-inspired robot were made to climb on the ground (horizontal plane), 30° slope, and 45° slope. For consistency of the experiments, each robot experiment was conducted five times. The force data of the geckos in the front and hind limbs are shown in figures 8(a, I) and A2(a, I), respectively. The value was computed using the component force along the Y-axis (shear force) divided by the component force along the Z-axis (normal force). A significant increase was observed with the increase in slope angle. This phenomenon is similar to the visualised 3D force profiles displayed in figure 8(b). The force data of the gecko-inspired robot in the front and hind limbs (figures 8(c, I) and A2(b, I)) also show that the proportion of shear force in the resultant force gradually increased, which was consistent with the changing trend of the gecko force data. The visualised 3D force profiles of the robot's front and hind limbs (figure 8(d)) also exhibit the same tendency as the gecko force profiles (figure 8(b)). Furthermore, the gecko and robot's normalized force ranges in the Y–Z plane are analysed and illustrated in figures 8(a, II–IV) and (c, II–IV) for the front limbs, and figures A2(a, II–IV) and (b, II–IV) for the hind limbs. It can be seen that the gecko and the robot had quite similar force ranges for climbing on the ground, ranging from 60° to 120° (around the normal force along the Z-axis). The force ranges shifted towards the shear force along the Y-axis when climbing on the 30° and 45° slopes. In principle, climbing stability can be obtained by increasing the shear force contribution and decreasing the normal force contribution as the slope angle increases [27].

Zoom In Zoom Out Reset image size

A performance test of the gecko-inspired robot was necessary to validate the robot in terms of its structure and control. The fundamental climbing abilities with surface adhesion were tested using a series of slope-climbing experiments (figures 9(a) and (c)).

Zoom In Zoom Out Reset image size

The robot was able to climb a maximum slope angle of approximately 60° with a success rate of 20%, as shown in figure 9(b). The success rates of the robot when it climbed at different speeds and slope-tilting angles are shown in figure 9(b). A complete climbing distance of at least 80 cm on the platform, without dropping or slipping conditions, was counted as one successful trial. The success rate was computed as the ratio of successful trials to the total number of trials (five trials in total) for one specific experiment. The results show that the gecko-inspired robot exhibited a fast climbing motion (1.76 cm s⁻¹) on a 30° slope; however, the success rate decreased when the slope angle became steeper. The robot can stably climb at a medium speed (1.07 cm s⁻¹) on the 45° slope. In addition, at a low speed (0.625 cm s⁻¹), the robot can climb the maximum slope angle (60°) with a success rate of 20%. A video of this experiment can be seen at http://manoonpong.com/Nyxbot/ Video3.mp4.

The obstacle-overcoming ability of the gecko-inspired robot is shown in figure 9(d). The success rate of obstacle crossing decreased dramatically as the slope tilting angle increased. The gecko-inspired robot can cross over an obstacle with a height of 6 cm (approximately 77% of body height) on the ground. The maximum slope angle for the gecko-inspired robot to overcome the obstacle was approximately 30°, with an obstacle height of 3 cm (approximately 38% of body height) (figure 9(c)). Figure 9(a) displays snapshots of the gecko-inspired robot climbing on slope angles of 0°, 15°, 30°, 45°, and 60°. The snapshots of the gecko-inspired robot crossing over different heights of obstacles at slopes of  0°, 15°, 30°, and 45° are shown in figure 9(c). A video of this experiment can be seen at http://manoonpong.com/Nyxbot/Video4.mp4.

The autonomous obstacle-crossing experiment with exteroceptive sensory feedback was performed to demonstrate the adaptability of the body height of the gecko-inspired robot, following the gecko obstacle-overcoming strategy (figure 6). Figure 10(a) shows the entire process of autonomous robot obstacle crossing. The colour bar marks the limb state of the gecko-inspired robot, and the different moving postures of the robot are shown in these snapshots. The robot climbed on a slope with a tilting angle of 15°. When it approached an obstacle with a height of 3 cm, the IR sensor (IR1), installed on the front of the robot, detected the obstacle and sent a signal to the neural control network. Immediately, the robot began to elevate itself (I, II, and III periods) until no obstacles were detected by the front IR sensor. The robot then crossed over the obstacle by sustaining its body height (IV and V periods). When the hind leg moved away from the obstacle, the entire crossing process was completed, and the hind IR sensor (IR2), installed on the back of the robot, detected the obstacle. Thereafter, the robot dropped to its normal height (VI period). Body height adaptation of the robot during the whole crossing process is shown in figure 10(b). The signals from IR sensors are shown in figure 10(c). The pitch-angle signal of the inertial measurement unit (IMU) installed on the robot body shows the posture change of the robot, during climbing with the trot gait (figure 10(d)). The undulation of the pitch angle was caused by the undulation of the body of the gecko-inspired robot.

Zoom In Zoom Out Reset image size

An increase in the pitch angle implies that the robot encounters an obstacle and has started to lift its body up (III and IV periods). The inverse pitch angle indicates that more than half of the robot's body has already crossed the obstacle, and the remaining body was laid on the obstacle, such that the robot body tilted downward (negative rotational direction) (V periods). The pitch angle dropped to normal when the robot recovered to its normal height (VI periods). The proprioceptive signals obtained from the joint position sensors in the motors of the robot are shown in figure 10(e). The signals indicate the changes in the elevation (i.e. the joint 2 angles shifting downward) and depression (i.e. the joint 2 angles shifting upward) of the robot's body at the corresponding timing. The corresponding footfalls are shown in figure 10(f). The robot used a trot gait throughout the crossing process.