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Article

Bionic Design of Multi-Toe Quadruped Robot for Planetary Surface Exploration

1
Lab of Locomotion Bioinspiration and Intelligent Robots, College of Mechanical and Electrical Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
2
Large Space Structures GmbH, Hauptstr. 1e, D-85386 Eching, Germany
*
Author to whom correspondence should be addressed.
Submission received: 11 August 2022 /Revised: 9 September 2022 /Accepted: 16 September 2022 /Published: 20 September 2022
(This article belongs to the SectionMachine Design and Theory)

Abstract

:
To increase the knowledge and exploit new resources beyond the Earth, planetary surface exploration on the Moon or Mars attracts significant attention around the globe. Due to the fact that these planetary surfaces are widely covered by soil-like materials, various structures of planetary rovers have been proposed to adapt to the terrains. Nonetheless, the traditional rover structures, such as wheeled and leg-wheeled, have shown limitations in moving on granular soils. To improve the mobility, this paper proposes a multi-toe quadruped robot inspired by the desert chameleon animal. The key features are that each bionic foot possesses four toes to stabilize them on granular materials. Moreover, a bionic flexible spine is designed to coordinate with walking and turning gaits and to make the robot approach an animal-like mobility. To assess the robot performances, kinematics analysis and analytical modeling of foot, leg, and spine movements are carried out. The results demonstrate that this robot can effectively walk and turn in accordance with the adopted gaits. Finally, field tests of moving over sands have been conducted. It shows that the robot can stably walk and turn on sands, which indicates that it is adaptable to planetary granular terrains.

    1. Introduction

    In the context of planetary and lunar exploration, various rovers have been developed and also operated on Mars and on the Moon over the past 25 years, following initial lunar rovers in the early 1970s. In the US, the Jet Propulsion Laboratory (JPL) conceived, developed, and operated a line of so-called Rocker-Bogie suspension, six-wheeled rovers for Mars exploration, and NASA’s Johnson Space Center is currently developing the VIPER rover for the polar regions of the Moon [1]. The European Space Agency has completed the development of the ExoMars Rover for Mars, which features metallic flexible wheels [2]. China has successfully operated the YuTu and YuTu-2 rovers on the Moon [3] and ZhuRong on Mars [4]. The United Arab Emirates is prepared to send the Rashid microrover to the moon [5]. Planetary surface exploration operations over the past few years were dominated by science objectives such as field geology and geochemical analyses involving the sampling of soils and rocks. In the future, instrument deployment and infrastructure construction [6] will become important additional objectives and capabilities. For conducting these tasks, a series of planetary surface rovers have to be utilized. Because the lunar and Martian surfaces are covered with granular materials, and the surface gravities are significantly lower than for Earth [7], researchers mainly proposed four types of rover structures to be suited to such environments, namely, wheeled [4,8], crawler [9], legged [10,11], and leg-wheeled [12,13].
    The wheeled structure robots are the most common structure for planetary rovers due to their high flexibility, fast speed, and simple structure. Nonetheless, wheeled robots, if not designed properly, can be quite limited in gradeability and soft soil performance. For instance, the Martian robot Spirit became permanently immobilized in soft areas [14]. In comparison, crawler robots have much lower ground pressure than wheeled systems and can therefore achieve superior mobility on soft terrain. However, the crawler robot results in insufficient maneuverability in cornering and avoiding obstacles, and consuming high energy. The legged and leg-wheeled robot of NASA’s Athlete [13] adopted the structures of animal legs, such that they have higher maneuverability in cornering and avoiding obstacles [15]. However, the feet of the current legged robots utilize flat plates or spheres [16], as the development thrust of legged vehicles so far has been towards mobility over rough, hard surfaces. In addition, the body of legged robot prototypes are typically rigid, which is adverse to adjust the stride for accelerating and turning. Overall, there has been little work so far on legged robots suited for soil-like terrain where they promise to exhibit a slope climbing capability beyond that of wheeled rovers.
    The bionic design of mobile robots provides an effective approach to improve the mobility with respect to various mobility environments [10,17]. For instance, to improve the adaptability to granular and uneven surface terrains, many successful bionic feet have been studied, e.g., the bionic ostrich foot [18,19], bionic goat foot [20], and bionic hook claw foot [21]. By adopting the structures and mechanisms of mobile animals, the robot mobility for similar movement conditions can be significantly improved. The planetary surfaces have similar terrains as that of deserts on the earth. Therefore, the excellent mobility of desert animals, such as the desert chameleon, can be investigated for the bionic design of planetary surface robots. For moving on sands, the excellent mobility of desert animals is achieved by the coordination of feet, legs, and spine. Therefore, to improve the mobility of planetary robots for granular terrain, the structure of foot, leg, and spine desert quadruped animals can be adopted.
    On the basis of the foot, leg, and spine structure and mechanisms of the desert chameleon, this paper contributes a bionic quadruped robot for improving the adaptability to planetary surface environments. The kinematics analysis of the bionic feet, legs, and spine are carried out. The coordination motions between the robot’s feet, legs, and spine are numerically modeled. Furthermore, field tests of walking and turning over sand surfaces were conducted. This work has shown that the bionic quadruped robot is of high adaptability to planetary surface terrains.

    2. Structure Design

    The structures of the robot can directly affect the mobility of the planetary surface exploration rovers. To achieve high adaptability on planetary granular terrains, this section firstly presents the analysis of biological structures of the desert chameleon. Referring to the analysis, the bionic structure design of a quadruped robot is presented.

    2.1. Biological Structure Analysis

    The desert chameleon is a quadruped animal that can efficiently move in granular sands, as shown inFigure 1. The foot pad contains the outer main toes and inner separated auxiliary toes. The foot and toe pads can increase the contact area with respect to granular sands to prevent subsidence. Each foot has a flexible ankle that connects to all toes, and each toe tip has a claw. When grasping sand, the toes and claws bend down. In this manner, the sands are stabilized and a higher contact force can be achieved. During walking, the thigh of the leg swings forward whilst the shank moves inward and outward to adjust strides. Synchronously, the flexible spine swings with the change of strides so as to assist movements.

    2.2. Bionic Structure Design

    The quadruped robot described in this paper is divided into the three sections, i.e., the feet, legs, and spine (Figure 2). The foot pad contains three main toes and one auxiliary toe. Each toe consists of a joint and a claw at the end of the toe. Both sides of each toe also adopt a webbing planar pad. The claw is connected to the toe joint through a rotor. All claws of each foot are connected to the ankle by a rope. A steering gear, which is to drag the rope, is placed between the ankle joint and the foot pad. When the toe grasps a soft surface, the rope is driven by the steering gear [19], as illustrated inFigure 2b, so that the claw and the toe joint bend inward to grasp the surface. For the retrieving of the toe, a torsion spring is applied. The ankle is composed of a ball joint and a spring, which will be passively rotated as the foot contacts an uneven terrain. The joints of the leg adopt a hinged structure [22,23] and three steering gears connected via specific shapes of brackets [24,25] that form three degrees of freedom, as shown inFigure 2c. The upper steering gear is to produce forward motion by the leg. The other two motors connect both the thigh and the shank to enable their up–down motions [26].
    For the flexible spine of the symmetrical structure (Figure 2d), eight springs are used to be deformed in synchronization with the leg movements [27,28]. Each end of the spine adopts two motors that connect the structures of two legs. The middle part is connected by a multi-functional bracket, forming two degrees of freedom with up–down and left–right rotation. The middle segment has a torsion degree of freedom by using a single-axis steering gear and a bearing structure. The bearing is fixed in the middle of the flange rod to connect the front and back parts so as to achieve the torsion motion of the spine. For the five gears, the spine totally produces five degrees of freedom. During movements, the spine can actively bend and twist under the control of the steering gears. Based on the analysis of three sections, the quadruped robot structural model and the overall sizes are shown in theFigure 3.

    3. Theoretical Analysis

    To evaluate mobility in accordance with predetermined trajectories, a kinematic study of the feet, legs, and spine of the quadruped robot is carried out. Moreover, the gaits plan for walking and turning is illustrated. By adopting planned gaits, the stable movement of the robot can be realized through the coordination motions of the spine and leg [29].

    3.1. Kinematics

    The foot motion is a combination of active toe movement and passive ankle movement. Toe movement includes grasping and retrieving actions (Figure 4). The bending of the claw is driven by the steering gear in the pad via a rope. The maximum bending angle (θ) is about 90°. Due to that, all claws in a foot are driven by one gear, so the bending angles of the claws are approximately equal. The ankle generates passive rotations of various directions subjected to contacted uneven surfaces.
    In correspondence to the leg structure, as shown inFigure 2c, the schematic diagram of the established coordinate system of the robot leg is shown inFigure 5. The leg contains the three segments of base section, thigh, and shank, and three joints of waist, hip, and knee. The D-H parameter method [30] is used to analyze the leg forward motion. The establishment of each coordinate system adopts the rules for the bar and the corkscrew rule [30]. The D-H parameters of the leg of the robot are shown inTable 1.
    According to the D-H coordinate system and the parameters inTable 1, the pose matrix ( T01,T12,T23,) between the two rods can be obtained using Equation (1):
     Tn−1n=Rot(Z,θn)Trans(an,0,dn)Rot(X,αn)
    Using the pose matrix, the position equation curve of the leg end (O3) relative to the base joint coordinate system is obtained. The inverse kinematics of a single leg corresponds to the coordinates of the endpoint of the leg relative to the base joint. The leg joint is solved by the pose matrix obtained from the forward kinematics. The relationships between the angle of each leg joint and the leg end position are calculated as:
    {θ1=tan−1(PyPx)θ2=sin−1PzL22 + 2L2L3cosθ3 + L32 − tan−1L3sinθ3L2 + L3cosθ3θ3 = −cos−1((cosθ1)2(Pz2 − 2Pz + L12) + Px2 − 2PxL1cosθ1 − (cosθ1)2(L22 + L32)2L2L3(cosθ1)2)
    In this research, the lengths of each part of robot leg are respectivelyL1=41 mm,L2=74 mm, andL3=150 mm. The Monte Carlo [31,32] method is used to predict the mapping of the joint space to the workspace. Through the forward kinematics solution, a series of random variables within the range of joint angles and a set of joint space vectors are randomly generated. Then, the distribution of the workspace of a robot leg can be obtained. The obtained angle ranges of the three leg joints of waist, hip, and knee are respectively−pi/2≤θ1≤pi/2,−pi/2≤θ2≤pi/2, and−5pi/6≤θ3≤5pi/6. The foot reachable space can be solved using the Robotics-Toolbox 10.3 [33].Figure 6 displays the calculated reachable positions (blue cloud) for a leg. The three joints of the waist and knee, and the three length of base section, shrank, and thigh are also denoted. The reachable spaces of the leg for X, Y, and Z-axes are respectively (−15,265), (−265,265), and (−224,224).
    Knowing the positions of the robot foot in each axis, the angles of each joint can be solved, which are then used as the input signal to determine the robot leg movement in accordance with the established coordinate system. In this manner, the trajectory of the robot foot can be designated. Using the initial coordinate of the foot as the center of the new coordinate system, the planning trajectory of a semi-circular curve can be assigned. In this work, the length of a thigh part of legy =L1 +L2 = 115 mm. The foot moves forward 40 mm each stride and the trajectory curve is expressed as:
    (x − 20)2+z2=400 (z>0)
    By convertingx,y, andz into time expressions, and substituting them into the basic coordinate systemO0, the foot positionsPx,Py andPz as functions of timet can be obtained by,
    {Px=20−20cos(t)(0≤t≤2π)Py=115Pz=20sin(t) (0≤t≤π), 0(π≤t≤2π)
    SubstitutingPx,Py, andPz into each joint (Equation (2)), the angle change of each joint with regard to one time cycle can be calculated, as shown inFigure 7. It is seen that the angle of the waist joint initially increases, and after reaching a peak, it gradually decreases to zero and completes one cycle. This means that the forward motion by the waist joint has been initiated. At the peak of the curve, the forward velocity decreases to zero, then the motion reverses. The angle for the hip joint increases to the peak value at a quarter period. Then, it gradually decreases to zero at the half period and maintains zero until the end. This means that the hip joint firstly swings upwards and gradually returns to the initial position at the half period after reaching the maximum angle. The angle for the keen joint initially changes with an opposite curve compared to the hip joint. Note that before the half cycle, the motion reverses and achieves an angle of about 2.8° according to Equation (2), then gradually decreases to zero. This indicates that the knee joint experiences an opposite motion compared to the hip joint in the swing phase, which is to enable the vertical lift motion of the foot. Moreover, the reverse motion of the knee joint can cooperate with the waist joint which guarantees the linear trajectory in the completion of a cycle.
    The swing movement of the robot spine accompanies the movement of its legs. Meanwhile, the swing of the spine enhances the stride, such that the speed of the robot is increased. In order to adapt to such moving characteristics of this robot, the triangle gait is adopted. Denoting the maximum curvature of the spineθ, the swing angle changing with time can be expressed as,
     θ={0(0≤t≤pi/2,pi≤t≤3∗pi/2)pi∗θ∗sin(t−pi/2)/360(pi2≤t≤pi)pi∗θ∗sin(t−pi)/360(3∗pi2≤t≤2∗pi) 

    3.2. Gait Planning

    After the motions of the legs and spine have been determined, the gaits for the robot movements can be planned.Figure 8a–h illustrates the change of the tripod gait for a full cycle, in which the black square represents the support phase; the white square denotes the swing phase; the white square means the revolute joint of the robot spine; the dashed triangle represents the stable area; the pointM represents the center of mass. At the first step ofFigure 8a, the spine bends to the right 30° about its initial position. The right front and hind legs maintains the same angle at 70° with respect to the spine. The left hind leg and spine forms an angle of 130°. The left front leg is perpendicular to the spine. Then, the left hind leg moves forward 40° and arrives at the posture ofFigure 8b. Subsequently, the left front leg moves forward 40° and all feet begin to contact the ground (Figure 8c). Next, the spine retrieves to straight status (Figure 8d) and completes a half cycle. For the other half cycle, the spine and legs perform symmetrical motions. During the cycle, the center of mass changes within the triangle of the three contact feet. In this way, the robot can obtain as much stability margin as possible when going straight [34].
    Figure 9a–e shows the turning gait for the quadruped robot. At the beginning, the left front leg and right front leg maintains 70° with respect to the spine. The left hind leg of the robot steps backward 20° (Figure 9a). Then, the right hind leg lifts up whilst the posterior spine swings to the right (Figure 9b). Next, the right front leg moves forward 20° (Figure 9c) and the left front leg lifts up while the anterior spine swings to the left (Figure 9d). Finally, all the four legs touch ground and accomplish one cycle, resulting in a rotation angle of about 18°. It is also seen that the center of mass falls in the triangle of the three contact feet for the full cycle, which guarantees the turning stability. By following such a turning gait, a full turning and a small turning radius can be expected [35].
    To summarize, this section elaborated on the kinematics analysis and gait plan of walking and turning. The reachable workspace of a robot leg was determined and the trajectory of the robot foot was designated using a semi-circular curve. The center of mass for the two types of gaits can be maintained inside triangles, which promotes high stability for the robot walking and turning movements. These theoretical analyses provide the basis for the analytical modeling of the robot motions.

    4. Analytical Modeling

    To explicitly illustrate the pre-determined motions of the robot, this section presents the multi-body modeling of the robot motion by adopting the results of the theoretical analysis. The software Adams® [36] is used to simulate the kinematics of the robot movements. Moreover, the coordination movements between the feet, legs, and spine are investigated via simulating walking and turning motions.

    4.1. Foot Trajectory Simulation

    The foot movements are critical functions for the robot to move on granular sands, which can be studied from the toe and ankle trajectories. The simulation parameters refer to the experimental materials for fabricating the robot, i.e., the foot structures are printed using resin materials, and their parameters are determined referring to the manual data [37]; the spring material is manganese steel. The torsional spring stiffness can be estimated using Equation (6) [38,39],
    k=Ed43667Dn
    whereE is the Young’s Modulus of the spring,d is the diameter of the spring, andn is the number of the spring cycles. In this work,E = 2.02 × 105 MPa,D = 4 mm andn = 3, resulting ink = 4.6 N∙mm/°.
    The torsional spring dampingC can be calculated by Equation (6),
    C=Fv=kαLv
    whereF is the damping force, v is the velocity of spring oscillator,α is the torsion angle, andL is the arm distance. Hereby,k = 4.6 N∙mm/°,α = 90°, andL = 20 mm. Then,C is estimated at 2.1 N∙mm∙s/°.
    To simplify the modeling, the rope is not modeled. To simulate the effect by the rope, a constant forceF = 15 N is applied on the ropes connecting the claw, which is denoted inFigure 10a. The torsion springs are added at each joint of the toe. The simulation parameters and their values are listed inTable 2. In addition, the simulation utilizes the integral solver GSTIFF, the integral format I3, a maximum number of iterations at 25, and a surface tolerance of 200. The simulation step size is set at 0.1 s [36]. Using these settings, the expected foot grasping motion as that in reality can be obtained.
    Figure 10a shows the trajectories (red curves) of the toes bending down to grab. It has been obtained that when the force is exerted, the toe grabs downward. When the force is not exerted, the toe recovers to the initial state under the action of torsion springs. The bending angle is about 90°, which is consistent with theoretical calculations.Figure 10b shows the trajectory for swing phase of the foot. In the simulation of the rotational angle of each foot joint, the theoretical analysis of Equation (2) is applied. The correctness of the leg kinematics can be verified by comparing the simulation trajectory with the theoretical analysis of the motion trajectory in Equation (3), which is shown inFigure 11.
    Figure 11 presents the displacements of the foot, respectively, inX0,Y0, andZ0 directions. The values in theX0 direction represents the forward displacement, which is measured at 39.94 mm. The deviation from the theoretical value is 0.06 mm. The value for theY0-axis differs by 0.04 mm compared to the theoretical value. The values for theZ0 direction is measured as 21.18 mm, which deviates by 1.18 mm from the theoretical value. These deviations for theX0,Y0, andZ0 axes may be attributed to measurement errors of the curves or the position errors when applying drive torques on the joints. Nonetheless, the overall error is small, and thus it is obtained that the simulations can reasonably predict the motions of the robot leg [40].

    4.2. Mobility Simulation

    Using the adopted gait plan, the simulations of the walking and turning performances of the robot can be carried out. These simulations involve the contact between robot feet and ground surface. The contact algorithm uses the contact–impact force model [41,42]. The materials and friction parameters are determined by referring to the ASTM manual [37]. The contact parameters for assessing walking and turning are given inTable 3. Other simulation parameters are the same as those for assessing foot motions.
    Figure 12 presents the simulations of the robot walking motions in one cycle in accordance with the tripod gait. It demonstrates that the legs can cooperate with the spine of the robot during forward motion. The eight movements are consistent with the walking gait described inFigure 8. In theFigure 12a,h,d1 andd2 represent the distances between the initial and final step. It gives 110 mm forward distance for one cycle. The swing amplitudes of the robot spine is around 70 mm. The deviation of the center of mass with respect to the Y direction is 9 mm in each cycle, which is caused by the deviations of the coordination movements between the leg and spine.
    To observe the walking characteristics for a long period,Figure 13 plots the variations of the center of the robot mass in the X, Y, and Z (vertical direction) directions over four cycles. The value for X has increased by 430 mm, as expected. For the horizontal line in each cycle, it means that the spine is static (the center of mass is unchanged) whilst the legs are moving. The fluctuating feature means that robot moves forward with spine swinging. The fluctuations of Y displacements represent the swing amplitudes of the spine. The deviation of the center of mass in the Z-axis direction is 13 mm, which is induced by the motion variations of the legs. Nonetheless, such deviations are considered small and would not affect the motion stability [43].
    Figure 14 shows the simulations of the robot turning motion in accordance with the turning gait for a cycle. It demonstrates that, through the coordination of the feet, legs, and spine, the sequence motions, as those of turning gait, are obtained. The average angle is 18° for each cycle. The result is expected based on the theoretical parameters for the turning gait planning.
    To further analyze the turning characteristics, the trajectory curve of the center of mass of the robot over five cycles corresponding to a quarter circle of spine rotation is shown inFigure 15. The variations for the displacements in X and Y directions are, respectively, 124 and 126 mm. Similar values are approximated based on the theoretical analysis for gait planning. The curve for the motions in the X direction in the first cycle is relatively flat. However, the fluctuations of the curves gradually intensify over the rest of the four cycles. This is because the displacements for the center of mass follow approximately an arc in the X–Y plane. As a result, the motion in the Y direction exhibits opposite changes, which is to complement the arc curve. The displacement in the Z direction is minor during turning, as anticipated. It is noted that around 20 cycles are required for simulating a full circle of rotation, which leads to that the center of mass deviates about 11 mm from the initial position. This deviation is caused by the accumulated errors of movements from the feet, legs, and spine. The radius of the turning circle is about 175 mm, which is approximately equal to half of its body size. Therefore, the deviations of the center of mass is relatively small for such robot sizes, which concludes that the robot can a turn for a small turning radius [44].
    To sum up, this section presented the simulations of the foot movements based on the applied theoretical analysis. Additionally, the robot motion for walking and turning are resembled using gait plans. The overall errors between simulations and theoretical analysis are small, and thus the simulations have successfully resembled the robot motions.

    5. Experimental Tests

    On the basis of the results, the experiments testing the robot movements can be conducted. This section presents the manufacture of this robot prototype. The mobility for walking and turning is experimentally demonstrated with respect to granular surfaces. For applying the quadruped robot to planetary surface exploration, the limitations and future work are discussed.

    5.1. Manufacture

    The quadruped robot is composed of mechanical structures and an electronic control system. The mechanical structures contain the resin materials of the feet, legs, and spine fabricated by a 3D printer, and eight springs made of manganese steel. The electronic control system contains 25 steering gears, a control panel, and a battery.Figure 16 presents the diagram of the robot control design. The steering gear control panel will receive the signals from the control center. Using a high-accuracy potentiometer, the deviations of the rotation angles are transferred to the steering gear where the positions and voltages are adjusted to obtain the prescribed rotation angles. The steering gear adopts an asynchronous serial bus communication and the port can send and receive data via different lines. In this manner, simple and long-distance communication can be realized, and the complexity of the wiring is also greatly reduced.
    The selections of the electronic components are given as follows. The control center utilizes Raspberry PI 4B (4×ARM, Cortex-A53, 1.5 GHz,4G-DDR4, Cambridge, England) [45], which adopts wireless technology for remote control. The power supply voltage is a lithium battery with a voltage of 12 V. The 25 steering gears are all LX-224 serial bus, and the steering gear control board is used to assist in controlling the central interface and the power supply pressure. Through the selections of electrical appliances and mechanical parts described above, the entire robot body can be fabricated.

    5.2. Mobility Tests

    To validate the mobility of the robot, the motions of the toes must be tested for grasping granular materials.Figure 17 shows the grabbing action of the toes on a sand surface. In the initial state, the toes remain extended when the torsion spring is in the relaxing state (Figure 17a). When the steering gear drives the rope, the torque is exerted on each toe, and the toes maximally bend down about 90° (Figure 17b). The passive retraction of the toes are obtained after the tension is released (Figure 17c).
    Figure 18 shows a series of sequence postures of the robot when it moves on a granular sand surface according to the walking gait. The black arrow represents the walking direction. The blue curves denotes each motion of the spine during the whole cycle. The total walking distance isd ≈ 80 mm for the whole cycle, which takes about 16 s, and thus the average speed is 5 mm/s. In correspondence to the postures inFigure 18, the movements of each leg in their time periods are shown inFigure 19. The black stripe stands for the swing phase whilst the white stripe stands for the support phase. LH and LF, respectively, denote the movements of the left hind and left front legs. RF and RH mean the right front and hind leg. The periods (d,e) and (h,a) indicate that no movements are occurring. By comparing the tests to the simulations, it is obtained that the consistent motions are achieved. This distance is smaller compared to the simulation results, which is ascribed to extra resistance to the drives when the fine sand particles are introduced to the mechanical parts.
    Figure 20 shows the robot turning motion for one cycle, in which the blue curves denotes the status of spine, and the black curved arrow stands for the rotation direction. It is found that the robot can achieve a rotation angleθ ≈ 18° for each cycle, which takes about 5 s.Figure 21 shows the turning status for a quarter of the locomotion cycle. The two perpendicular directions represent the robot head at the beginning and the end (t = 35 s) after completing a quarter cycle. It shows that the rotation trajectory forms a circle whose center is the center of robot mass and the diameter is the robot length. The center of mass deviates from initial position by 10 mm for a circle rotation. These values are slightly smaller than the simulation results. This is also associated with the involvement of dusts in the mechanical parts, which reduces the foot strides and spine flexibility.
    Thus far, the structure, theoretical analysis, analytical modeling, and experimental tests have been conducted. It has been shown that the quadruped robot can effectively grasp the sand to prevent sinking, such that it can move stably on the sand surfaces, promoting significant potential for adapting to planetary granular terrains. Nevertheless, limitations and further improvements are required toward planetary surface exploration applications, which are discussed below.

    5.3. Discussion

    This work presents a model of a bionic quadruped robot. Under the earth’s surface environment, the mobility experiments of the robot on the granular surface were carried out. It demonstrates that this robot is able to stably walk and turn on granular materials. Because the bionic foot can grasp sands to solidify the surface, the slope climbing behavior on soil is expected to be better than for wheeled vehicles or the legged robots star1ETH [46] and Lemur3 [10], which have no flexible toes. To make the robot approach animal-like mobility, a bionic flexible spine is designed to coordinate with walking and turning gaits, which significantly enhances the adaptability on uneven terrains.
    Compared to the Bezier curve [47], polynomial curve [48], and composite curve, the applied foot trajectories in this work (Equation (4)) are relatively simple for controlling motion. However, the adopted equation may result in a high impact force between the foot and ground terrains. Further work of applying optimal trajectories for adapting different terrains will be arranged. To improve the walking efficiency for the planetary surface, the contact models between the robot foot and different granular terrains should be applied [49]. Meanwhile, the feedback control is expected to be used for adjusting the foot movements based on the contact forces by the toes and pads in regard to different terrains.
    For space exploration, the sizes of this robot will be adjusted. The mobility affected by the lower gravities on planetary surfaces has to be clarified [50,51]. The regolith and terrains of planetary surfaces vary for different locations. Therefore, the mobility tests on different granular materials and different slope terrains are essential to be carried out. In addition, the materials will also be replaced to resist the thermal and radiational environments. Moreover, sealing and dust prevention measures must be taken because dust particle involvements can cause extra friction and wear of components, which can severely deteriorate the functions of the robot [8]. Last, but not least, the power supply system for the planetary robot should be used [52,53].

    6. Conclusions

    To improve rover mobility for planetary surface exploration, this paper proposed a bionic quadruped robot based on the desert chameleon animal. The kinematics of the robot foot, leg, and spine were theoretically analyzed. Robot locomotion performances were analytically predicted using the theoretical analysis and gait planning. Experimental tests of the prototype demonstrated that the bionic robot can stably walk and turn on granular sand surfaces with the bionic foot. It is expected that the slope climbing behavior of the robot on soil is better than for wheeled vehicles. The bionic active flexible spine functions to coordinate with walking and turning gaits, which significantly enhances the adaptability on uneven terrains. Accordingly, the bionic quadruped robot is adaptive to the granular surfaces similar to planetary terrains, and thus it is of high potential for the application toward planetary surface exploration.

    Author Contributions

    G.C. and L.R. conceptualized, reviewed, and edited the manuscript; the data processing and original draft preparation were accomplished by L.Q. The experimental methodology was formulated by B.W.; A.J. was responsible for the robot validation tests. All authors have read and agreed to the published version of the manuscript.

    Funding

    This research was funded by the project of Foreign Culture and Education Experts (Ministry of Science and Technology), grant number G2021181006L, and the Foundation Research Project of Jiangsu Province Natural Science Fund, grant number BK20190415.

    Institutional Review Board Statement

    Not applicable.

    Informed Consent Statement

    Not applicable.

    Data Availability Statement

    Not applicable.

    Conflicts of Interest

    The authors declare no conflict of interest.

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    Machines 10 00827 g001 550
    Figure 1. Desert chameleon.
    Figure 1. Desert chameleon.
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    Figure 2. Bionic structures of the (a) foot, (b) broken-out section of foot structure, (c) leg, (d) and spine.
    Figure 2. Bionic structures of the (a) foot, (b) broken-out section of foot structure, (c) leg, (d) and spine.
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    Figure 3. Structure of quadruped robot inspired by desert chameleon.
    Figure 3. Structure of quadruped robot inspired by desert chameleon.
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    Figure 4. Diagram of a toe grasping motion.
    Figure 4. Diagram of a toe grasping motion.
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    Figure 5. Schematics of D-H coordinate system of robot leg.
    Figure 5. Schematics of D-H coordinate system of robot leg.
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    Figure 6. Workspace diagram of a robot leg.
    Figure 6. Workspace diagram of a robot leg.
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    Figure 7. Leg joint angle position diagram.
    Figure 7. Leg joint angle position diagram.
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    Figure 8. Tripod gait; (a–h) eight movements.
    Figure 8. Tripod gait; (a–h) eight movements.
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    Figure 9. Turning gait; (a–e) five movements.
    Figure 9. Turning gait; (a–e) five movements.
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    Figure 10. (a) Toe trajectory; (b) Foot trajectory.
    Figure 10. (a) Toe trajectory; (b) Foot trajectory.
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    Figure 11. Simulation prediction of robot foot trajectories.
    Figure 11. Simulation prediction of robot foot trajectories.
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    Figure 12. Tripod gait; (a–h) eight movements in one locomotion cycle.
    Figure 12. Tripod gait; (a–h) eight movements in one locomotion cycle.
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    Figure 13. Variance of mass center as the spine swings.
    Figure 13. Variance of mass center as the spine swings.
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    Figure 14. Turning gait; (a–e) five movements in one locomotion cycle.
    Figure 14. Turning gait; (a–e) five movements in one locomotion cycle.
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    Figure 15. Center of mass trajectory for turning gait.
    Figure 15. Center of mass trajectory for turning gait.
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    Figure 16. Diagram of robot control design.
    Figure 16. Diagram of robot control design.
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    Figure 17. Toe grasping test. (a) Touching surface; (b) Grasping sands; (c) Retrieving to initial.
    Figure 17. Toe grasping test. (a) Touching surface; (b) Grasping sands; (c) Retrieving to initial.
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    Figure 18. Tripod gait test; (a–h) eight movements in one locomotion cycle.
    Figure 18. Tripod gait test; (a–h) eight movements in one locomotion cycle.
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    Figure 19. The motion of each leg and corresponding time for one locomotion cycle.
    Figure 19. The motion of each leg and corresponding time for one locomotion cycle.
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    Figure 20. Turning gait test; (a–e) five movements in one locomotion cycle.
    Figure 20. Turning gait test; (a–e) five movements in one locomotion cycle.
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    Figure 21. Turning performances for a quarter locomotion cycle.
    Figure 21. Turning performances for a quarter locomotion cycle.
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    Table
    Table 1. D-H parameters of the robot leg.
    Table 1. D-H parameters of the robot leg.
    LinkAngleTorsional AngleDistanceLength
    nθnαndnan
    1θ190°0L1
    2θ20°0L2
    3θ30°0L3
    Table
    Table 2. Simulation parameters for assessing foot motion.
    Table 2. Simulation parameters for assessing foot motion.
    Torsional Spring StiffnessTorsional Spring DampingResin DensityResin Young’s ModulusResin Poisson Ratio
    4.6 N·mm/°2.1 N·mm·s/°1150 Kg/m32.65 GPa0.42
    Table
    Table 3. Contact parameters for assessing walking and turning.
    Table 3. Contact parameters for assessing walking and turning.
    StiffnessForce IndexDampingPenetration DepthStatic Friction CoefficientDynamic Friction CoefficientStatic Friction VelocityDynamic Friction Velocity
    1150 N/mm20.68 N·s/mm0.1 mm0.80.60.1 mm/s10 mm/s
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    Chen, G.; Qiao, L.; Wang, B.; Richter, L.; Ji, A. Bionic Design of Multi-Toe Quadruped Robot for Planetary Surface Exploration.Machines2022,10, 827. https://doi.org/10.3390/machines10100827

    AMA Style

    Chen G, Qiao L, Wang B, Richter L, Ji A. Bionic Design of Multi-Toe Quadruped Robot for Planetary Surface Exploration.Machines. 2022; 10(10):827. https://doi.org/10.3390/machines10100827

    Chicago/Turabian Style

    Chen, Guangming, Long Qiao, Bingcheng Wang, Lutz Richter, and Aihong Ji. 2022. "Bionic Design of Multi-Toe Quadruped Robot for Planetary Surface Exploration"Machines 10, no. 10: 827. https://doi.org/10.3390/machines10100827

    APA Style

    Chen, G., Qiao, L., Wang, B., Richter, L., & Ji, A. (2022). Bionic Design of Multi-Toe Quadruped Robot for Planetary Surface Exploration.Machines,10(10), 827. https://doi.org/10.3390/machines10100827

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