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Research Papers

Design and Implementation of a Leg–Wheel Robot: TranslegOPEN ACCESS

[+] Author and Article Information
Zhong Wei

School of Instrument Science and Engineering,
Southeast University,
Nanjing 210096, China
e-mail: zwei371@163.com

Guangming Song

School of Instrument Science and Engineering,
Southeast University,
Nanjing 210096, China
e-mail: mikesong@seu.edu.cn

Guifang Qiao

School of Automation,
Nanjing Institute of Technology,
Nanjing 211167, China
e-mail: qiaoguifang@126.com

Ying Zhang

School of Automation,
Nanjing Institute of Technology,
Nanjing 211167, China
e-mail: zhangying295@126.com

Huiyu Sun

School of Instrument Science and Engineering,
Southeast University,
Nanjing 210096, China
e-mail: sunhuiyu2010@163.com

1Corresponding author.

Manuscript received October 20, 2016; final manuscript received April 19, 2017; published online June 22, 2017. Assoc. Editor: Shaoping Bai.

J. Mechanisms Robotics 9(5), 051001 (Jun 22, 2017) (9 pages) Paper No: JMR-16-1327; doi: 10.1115/1.4037018 History: Received October 20, 2016; Revised April 19, 2017

Abstract

In this paper, the design and implementation of a novel leg–wheel robot called Transleg are presented. Transleg adopts the wire as the transmission mechanism to simplify the structure and reduce the weight. To the best knowledge of the authors, the wire-driven method has never been used in the leg–wheel robots, so it makes Transleg distinguished from the existing leg–wheel robots. Transleg possesses four transformable leg–wheel mechanisms, each of which has two active degrees-of-freedom (DOFs) in the legged mode and one in the wheeled mode. Two actuators driving each leg–wheel mechanism are mounted on the body, so the weight of the leg–wheel mechanism is reduced as far as possible, which contributes to improving the stability of the legged locomotion. Inspired by the quadruped mammals, a compliant spine mechanism is designed for Transleg. The spine mechanism is also actuated by two actuators to bend in the yaw and pitch directions. It will be beneficial to the turning motion in the legged and wheeled modes and the bounding gait in the legged mode. The design and kinematic analyses of the leg–wheel and spine mechanisms are presented in detail. To verify the feasibility of Transleg, a prototype is implemented. The experiments on the motions in the legged and wheeled modes, the switch between the two modes, and the spine motions are conducted. The experimental results demonstrate the validity of Transleg.

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Introduction

According to the counterparts in the nature, the legged robots have the potentials to negotiate the rough terrain agilely [1]. Some advanced legged robots have been designed to achieve this goal, such as BigDog [2], LittleDog [3], Spot, and RoboSimian [4]. Although the wheeled robots cannot cross the rugged topography as the legged robots, they can perform high-speed, smooth, and energy-efficient locomotion on the flat ground [5]. To combine the advantages of the legged and wheeled robots, various leg–wheel robots with different structures and dimensions are proposed. The leg–wheel robots can be classified into two categories according to the way in which the wheel function is integrated into the leg–wheel robots.

One category of leg–wheel robots owns the separate wheel mechanisms. That is to say, the traditional wheels can be seen in the robots. For example, PAW [6], Hylos [7], Walk’n Roll [8], Roller-Walker [9], MHT [10], ATHELET [11], AirHopper [12], HIT-HYBTOR [13], Rolling-wolf [14], RT-Mover [15], Zero Carrier [16], and LegVan [17] all have a wheel on the tip of each leg. NOROS [18] possesses a wheel on each shank, and NOROS-II [19] mounts the wheel on the tip of each thigh. A leg–wheel robot designed by Guo et al. has one wheel on the tip of the leg, one on the tip of the thigh, and the other on the body [20]. Mounting the wheel on the leg will increase the weight of the leg and will lead to the instability of the legged locomotion. Therefore, a few robots only fix the wheels on the body. For instance, HyTRo-I [21] possesses four wheels on the body. A stair-cleaning robot proposed by Zhang et al. has four wheels distributed as HyTRo-I [22]. Wheeleg owns two wheels on the rear of the body and two legs on the front, and it looks like a cart [23]. Ottaviano and Rea developed a leg–wheel robot with the structure similar to Wheeleg [24]. Mantis 2.0 is equipped with four wheels and two rotating legs [25]. The wheels of these robots are designed to be active or passive in the light of different requirements. The active wheels can increase the flexibility of wheeled locomotion, while the passive ones can lighten the weight of the robots. However, whether the wheels are active or passive, mounted on the leg or the body, the weight of the robot will be increased.

The other category of leg–wheel robots has the coupled leg–wheel mechanism, which couples the leg with the wheel in function or structure. The spoke wheel without rim is one kind of such mechanism, and it acts as a wheel on the level ground and a leg on the rugged one. Whegs series [26] and IMPASS [27] are two typical robots with such mechanisms. Although the leg–wheel mechanisms of Loper [28] and ASGUARD [29] seem to be different from the spoke wheel, they are similar in function. The other kind of coupled leg–wheel mechanism is the transformable leg–wheel, which can change between the legged and wheeled structures according to the terrain. Wheel Transformer [30], Quattroped [31], Turboquad [32], LEON [33], and PEOPLER-II [34] have diverse transformable leg–wheels which transform in different ways. Tadakuma et al. [35] and She et al. [36] also designed two leg–wheel robots with different transformable leg–wheels. Compared with the spoke wheel without rim, the transformable leg–wheel is more flexible, but the structure becomes more complex.

Transleg proposed in this paper adopts four transformable leg–wheels, and the wire-driven method is utilized to reduce the complexity of the structure. In addition, the use of the wire-driven method allows the heavy actuators to be located far from the leg–wheels, which is beneficial to the stability of the legged locomotion [37]. Because of the advantages, the wires have been applied to actuate many robots, like quadruped robot [38], bipedal robot [39], robot fish [40], continuum robot [4145], hyper-redundant robot [46], and so on. Compared with the first category of leg–wheel robots, the structure of Transleg is simpler since it has no separate wheel mechanisms. Transleg owns two actuators for each leg–wheel, while some leg–wheel robots with spoke wheels, such as Whegs, Loper, and ASGUARD, have only one actuator for each spoke wheel. However, Whegs, Loper, and ASGUARD cannot select the contact points with the ground for the legs. To make up for this defect, IMPASS adds one actuator for each spoke, so four actuators are needed for each spoke wheel. Different from the legs of Wheel Transformer, Quattroped, Turboquad, PEOPLER-II, and the robot proposed by She et al., the legs of Transleg are inspired by the limbs of the quadruped mammals. However, they are much simplified, and only two pitch joins are reserved. The legs of LEON and the robot designed by Tadakuma et al. also mimic the biological legs, but the actuators are mounted on the legs, which leads to the instability of the legged locomotion. The characteristics of some leg–wheel robots referenced in this paper and Transleg are listed in Table 1.

Inspired by the quadruped mammals in the nature, a compliant wire-driven spine mechanism is designed for Transleg. The spine mechanism is actuated by two actuators and can bend in the yaw and pitch directions. It will contribute to the turning motion and bounding gait in the legged mode. Some quadruped robots have introduced the spine mechanism to improve the locomotion performance, such as Cheetah-I [47], Cheetah-Cub-S [48], Bobcat [49], Lynx [50], and Kitty [51]. The spines of Cheetah-I, Lynx, and Kitty use wires as the transmission mechanism, the one of Cheetah-Cub-S uses rigid bars, and Bobcat adopts direct-drive method. Moreover, Cheetah-I, Bobcat, and Lynx can just bend in the pitch direction, and Cheetah-Cub-S can only bend in the yaw direction. Though Kitty can bend in both two directions as Transleg, its spine mechanism is actuated by four actuators. The rest of this paper is organized as follows. Section 2 gives the detailed mechanical layouts of Transleg. Section 3 introduces the kinematic analyses. Section 4 presents the experimental validations. And the concluding remarks are given in Sec. 5.

Mechanical Layouts

Overall Design.

The prototype of Transleg in the legged and wheeled modes is shown in Fig. 1. The robot has four transformable leg–wheel mechanisms at the corners of the body. Therefore, Transleg can perform as a quadruped robot in the legged mode and a four-wheel vehicle in the wheeled mode. The body consists of two parts which are connected by a spine mechanism. The introduction and creation of the spine mechanism are inspired by the quadruped mammals in the nature. The spine plays a significant role in the locomotion of these animals, such as self-balance, bounding gait, and so on. Therefore, it is valuable to study on integrating the spine motions into the locomotion of the quadruped robot. Moreover, the spine can improve the turning performance in the wheeled mode. Due to the open architecture of Transleg, the controller, sensors, battery, and some other functional modules can be expediently integrated when needed. Transleg is driven by ten Dynamixel MX-64R actuators, which are controlled through the RS-485 communication. The wires used as the transmission mechanism are steel rope and PE nylon rope, which can be extended so little that they are assumed to be rigid. Now most components of Transleg are made from the toughened resin or cut from the carbon fiber composite material, the weight is 2.245 kg, and the dimensions are 331.20 mm × 252.00 mm × 195.42 mm (length × width × height). The leg–wheel and spine mechanisms are the two main mechanisms of Transleg, which will be carefully described later on.

Design of Leg–Wheel Mechanism.

As shown in Fig. 2(a), the two actuators driving the leg–wheel mechanism are mounted on the body, so the weight of the leg–wheel mechanism is largely reduced. To make the spine mechanism easy to understand, it is introduced in several parts.

Hip Joint.

The output shaft of actuator 1 is connected with the thigh, forming the hip joint. The thigh has a circle rim which is supported by two spokes and the thigh, and the hip joint is just at the center of the rim.

Knee Joint.

The shank is jointed with the thigh by a docking assembly, forming the knee joint. At the joint, a thrust ball bearing is used to decrease the friction and a torsion spring is mounted. The two ends of the torsion spring are, respectively, fixed at the thigh and the shank, so the knee joint can keep an initial angle.

Transmission Mechanism for Knee Joint.

A turnplate is connected with the output shaft of actuator 2, and one end of a wire is fixed on the turnplate. The wire crosses a hole whose entrance is at the center of the rim of the thigh. The other end of the wire is fixed on a rotary assembly which is mounted on the shank with a revolute pair. The foot is mounted at the end of the shank.

Rotary Assembly.

The rotary assembly is composed of a bearing pedestal, a flange bearing, and a dowel. One end of the wire is fixed on the dowel, which crosses a flange bearing. The flange bearing is fixed on the bearing pedestal, which is mounted on the shank with a revolute pair. The dowel will rotate when the wire is twisted in the wheeled locomotion. The revolute pair can make the dowel in a line with the wire.

Legged Mode.

The leg–wheel mechanism is in the legged mode when the shank is out of the rim of the thigh, as shown in Fig. 2(a). By actuating the two actuators mounted on the body coordinately, the hip and knee joints can rotate in the certain tracks, and the leg–wheel mechanism can perform the legged locomotion.

Wheeled Mode.

The leg–wheel mechanism can easily transform from the legged mode to the wheeled mode by actuating actuator 2 to pull the shank in the rim of the thigh, as shown in Fig. 2(b). In the wheeled mode, by keeping the knee joint static and driving actuator 1, the leg–wheel mechanism can perform the wheeled locomotion. In the wheeled locomotion, the hole rotates together with the rotating rim, and the turnplate keeps stationary.

Design of Spine Mechanism.

As shown in Fig. 3, the spine mechanism is driven by two actuators which are, respectively, mounted on the front and rear bodies. To make the spine mechanism easy to understand, it is introduced in several parts.

Mechanism for Bending in Pitch Direction.

The pitch actuator drives the spine to bend in the pitch direction, and it is mounted on the front body. The output shaft of the pitch actuator is connected with the pitch turnplate. The pitch turnplate has two fan-shaped wire spools on which two wires allocated up and down are mounted. The wires cross the guide holes on the spine joints, and the end of them is fixed on the tail end of the spine joints.

Mechanism for Bending in Yaw Direction.

The yaw actuator drives the spine to bend in the yaw direction, and it is mounted on the rear body. The output shaft of the yaw actuator is connected with the yaw turnplate. Two wires allocated left and right are mounted on the semicircular wire spool of the yaw turnplate. The wires cross the guide holes on the spine joints, and the end of them is fixed on the head end of the spine joints.

Spine Joints.

The tail and head ends of the spine joints are, respectively, fixed on the rear and front bodies. The spine joints are made up of vertebras and silicon pieces. The silicon pieces work as the intervertebral disks in the mammal. Between two vertebras, there are four silicon pieces. To see the inner structure of the spine joints, some silicon pieces are made transparent. The wires and silicon pieces are symmetrically allocated around the ball joints. In addition, the number of joins can be determined as needed. There are three ball joints in Fig. 3.

Bend in the Yaw and Pitch Directions.

When the pitch turnplate is driven to rotate clockwise or anticlockwise by the pitch actuator, the wire allocated up or down is pulled, and then the spine joints bend up or down. That is to say, Transleg bends in the pitch direction. Likewise, Transleg bends in the yaw direction, when the yaw turnplate is driven.

Kinematic Analyses

Motion of Leg–Wheel Mechanism.

Transleg is mainly propelled by the four leg–wheel mechanisms, and it can perform legged and wheeled locomotion. In the legged mode, Transleg works like a quadruped robot, which has the hip and knee joints in each leg. Therefore, all the typical gait of the quadruped robot, such as walking, trotting, bounding, pacing, and galloping, can be achieved.

Motion Tracks of Hip and Knee Joints.

In this paper, the trotting gait is applied to Transleg, and the motion tracks of the hip and knee joints are planned using the method proposed in Ref. [52]. With this gait, the diagonal legs of Transleg keep synchronous. If two synchronous legs are in the swing phase or the beginning of the swing phase, the other two must be in the stance phase or the beginning of the stance phase. In the swing phase, the hip joints move from back (PEP, short for posterior extreme position) to front (AEP, short for anterior extreme position), and the knee joints move to lift the shank up and then down. When the legs are in the extreme position, Transleg touches the ground with four legs, which means Transleg is in the balanced state. In the stance phase, the hip joints move from front to back, and the knee joints keep motionless. To simplify the control method, the cosine signal rather than the central pattern generator (CPG) is employed to control the motion of the hip joint. Then, the motion track of the hip joint is described as Display Formula

(1)${θHR(t)=aAH2(cos 2πT1t−1)a={1(FL,FR)−1(HL,HR)$

where θHR, AH, and T1 are, respectively, the angle displacement, swing amplitude, and swing cycle of the hip joint. FL, HR, HL, and FR denote the front-left, hind-right, hind-left, and front-right leg–wheel, respectively. The motion track of the knee joint is slightly modified on the basis of the one in Ref. [49] and is defined as Display Formula

(2)${θKR(t)={b(AH2−||θHR(t)|−AH2|)k(t)(swingphase)0(stancephase)k(t)=2AKAH(1+2AH||θHR(t)|−AH2|)b={1(FR,HL)−1(FL,HR)$

where θKR and AK are, respectively, the angle displacement and swing amplitude of the knee joint.

Angle Displacement of Actuator Driving Knee Joint.

Because the knee joint is driven by the turnplate through wire, the relation between the rotation angle θTR of turnplate and the angle θK of knee joint should be derived. According to the geometries of the leg–wheel mechanism in Fig. 4(a), the relation between θTR and θK is

Display Formula

(3)${lXI=rC2+lT2+lF2−2rC2+lT2lF cos(θKI−arctanrClT)lX=rC2+lT2+lF2−2rC2+lT2lF cos(θK−arctanrClT)θTR=clXI−lXrTc={1(FR,HL)−1(FL,HR)$
where rC is the radius of the cylinder at the hip joint, lT is the distance from the hip joint to the knee joint, θKI is the initial angle of the knee joint, lF is the distance from the knee joint to the point where the rotary assembly is fixed, and rT is the radius of the turnplate. In addition, θKR and θK satisfy the following relation: Display Formula
(4)$θK=θKI−|θKR|$

Position of Hip Joint in AEP and PEP.

In the legged locomotion, the leg–wheel swings between the anterior extreme position (AEP) and the posterior extreme position (PEP), as shown in Fig. 4(b). When the leg–wheels are in the two positions, the distances from the four hip joints to the ground are the same, and Transleg is in the balanced state. To keep smooth moving, the quadruped robot usually starts from the balanced state, so the angle θHAEP of the hip joint in the AEP and the one θHPEP in the PEP should be figured out. According to the geometries in Fig. 4(b), θHAEP and θHPEP are expressed as Display Formula

(5)${θHAEP=arcsinlS sin(θKI−θ1)l1−AH2θHPEP=θHAEP+AH$

where lS is the distance from the knee joint to the center of the sphere surface of the foot. lS and θ1 are given by Display Formula

(6)${lS=lSP2+lSV2θ1=arctan(lSVlSP)l1=lT2+lS2−2lTlS cos(θKI−θ1)$

where lSP and lSV are, respectively, the projections of lS to the broadside and base of the shank. It is worth noting that the calculations of θHAEP and θHPEP are on the basis of the hypothesis that the leg–wheels touch the ground with the sphere surface of the foot. Hence, the swing amplitude of the hip joint AH should satisfy Display Formula

(7)${AH≤2(arcsinlS sin(θKI−θ1)l1−π+θKI+θ2)θ2=arcsinrFCrFS$

where rFC is the radius of the cylinder of the foot, and rFS is the radius of the sphere surface of the foot.

Wheeled Locomotion.

In the wheeled locomotion, only the hip joint is actuated, and the knee joint maintains the angle θKW. Therefore, the motion tracks of the hip and knee joints are Display Formula

(8)${θHR(t)=2πT2tθKR=0$

where T2 is the rotation cycle of the hip joint. According to the geometries in Fig. 4(c), θKW is described as Display Formula

(9)$θKW=arccoslEK2+lT2−rR22lEKlT−arccoslPlEK$

where lEK is the distance from the knee joint to the point where the edge of the foot overlaps with the rim of the thigh, rR is the radius of the rim of the thigh, and lP is the distance from the knee joint to the plane in which the circle edge of the foot is.

Switch Between Legged and Wheeled Modes.

To adequately take advantage of the mobility performance, Transleg should transform between the legged and wheeled modes according to the terrain. The selection of the transformation position is important to the transforming process. As noted above, Transleg is in the balanced state in the extreme position. Therefore, the extreme position is set as the transformation position in this paper. When Transleg transforms from the legged locomotion to the wheeled motion, the thigh keeps motionless in the extreme position and the shank moves until the foot is inside the rim of thigh. The angle displacement of the turnplate can be figured out by replacing θK with θKW in Eq. (3). When Transleg performs the inverse transformation, the thigh stops in the extreme position and the shank moves until the knee joint is in the initial angle θKI. The angle displacement of the turnplate is just the opposite value of the one obtained when Transleg transforms from the legged mode to the wheeled mode.

Motion of Spine Mechanism.

The spine mechanism is driven to bend in the yaw and pitch directions by two turnplates mounted on the output shafts of the actuators through wire. To control the spine mechanism well, the relations between the bending angles of spine joints in the yaw and pitch directions and the rotation angles of the actuators need to be figured out. The motion of the spine mechanism is driven by pulling the wires using the wire spool of the turnplate. Therefore, when the spine mechanism bends, the decrement of the length of the wire in the spine joints is equal to the length of the wire which the wire spool takes back. Because the wires are symmetrically allocated around the joints, the variations of the lengths of the wires in the spine joints are identical when the spine mechanism bends in the yaw and pitch directions with the same angle. Moreover, the distances of the adjacent vertebras are the same, and the silicon pieces are supposed to be identical. Hence, the bending angles of all the ball joints are the same, and the variations of the lengths of the wires between any two adjacent vertebras are equal.

Decrement and Increment of Length of Wire in Spine Joints.

According to the geometries in Fig. 5, the relation between the decrement lDE of the length of the wire in the spine joints and the bending angle α of one joint is

Display Formula

(10)${lDE=3(lI1−lT1)lT1=l22+lW2+lV2−2l2lW2+lV2 cos(αmax1−α)$
where lI1 and lT1 are, respectively, the lengths of the wires between the adjacent vertebras before and after the spine joints bend, lV is the distance from rotation center of the ball joint to the plane of the vertebral, and lW is the distance from rotation center of the ball joint to the wire. αmax1 is the maximum bending angle of spine joint, exceeding which the length of the wire between the adjacent vertebras increases. l2 and αmax1 are given by Display Formula
(11)${l2=lW2+(lI1+lV)2αmax1=arctanlI1+lVlW−arctanlVlW$

The maximum bending angle is also limited by the maximum angle αmax2 that the ball joint can rotate Display Formula

(12)$αmax2=π2−arcsinlCrB−arcsinrLrB$

where lC is the thickness of the cover which prevents the ball from being out, rB is the radius of the ball, and rL is the radius of the link of the ball joint. The maximum bending angle αmax is the smaller one between αmax1 and αmax2. When one ball joint bends with the angle α, the increment lIN of the length of the wire in the spine joints is Display Formula

(13)${lIN=3(lT2−lI1)lT2=l22+lW2+lV2−2l2lW2+lV2 cos(αmax1+α)$

where lT2 is the length of the wire between the adjacent vertebras after the spine joints bend.

Length of Wire Taken Back and Let Out by Yaw and Pitch Turnplates.

For the semicircular yaw turnplate, when it rotates with the angle β (β ≤ π/2), the length lTB1 of the wire taken back is Display Formula

(14)${lTB1=lT3−lI2lT3=lI22+2lW2−2lWlW2+lI22 cos(arctanlI2lW+β)$

where lT3 and lI2 are, respectively, the lengths of the wires between the turnplate and the spine joints after and before rotating. The length lLO1 of the wire let out is Display Formula

(15)$lLO1=βlW$

For the fan-shaped pitch turnplate, when it rotates with the angle γ, whose range is Display Formula

(16)$γ≤π−arcsinrPlI2−arcsinrPlW−arccoslWlI2$

the length lTB2 of the wire taken back is Display Formula

(17)${lTB2=lT4−lI3lT4=lI22+lW2−2lI2lW cos(arccoslWlI2+γ)lI3=lI22−lW2$

where rP is the radius of the pedestal of the turnplate, and lT4 and lI3 are, respectively, the lengths of the wires between the turnplate and the spine joints after and before rotating. The length lLO2 of the wire let out is Display Formula

(18)$lLO2=γlW$

Relation Between Bending Angle of Spine and Rotation Angles of Actuators.

Because lDE is equal to lTB1 and lTB2, the relations between the bending angle αS (αS = 3α) in the yaw and pitch directions and the rotation angles of the actuators (β and γ) can be obtained, combining Eqs. (10), (14), and (17). It should be noted that the decrement lDE of the length of the wire in the spine joints is a little smaller than the increment lIN. To make the spine mechanism work normally, the length of the wire let out should be longer than the one taken back. Therefore, the yaw and pitch turnplates are designed to be semicircular or fan-shaped.

Simulation Validations

The simulations were done to verify the validity of the theory of the leg–wheel motion and the feasibility of the design of the leg–wheel mechanism. In the simulation, Transleg performed legged locomotion for five gait cycles, transformation from legged to wheeled mode, wheeled locomotion for one cycles, transformation from wheeled to legged mode, and legged locomotion for five gait cycles in turn. To avoiding the complex wire simulation, the control signals were directly applied to the hip and knee joints. What’s more, the control signals needed in the simulation are the angle displacement relative to the initial position. The tracks of the hip and knee joints in Eqs. (1) and (2) start from the extreme position where Transleg is in the balanced state. Hence, the extreme position is set as the initial state as well as the transformation position for Transleg. The control signals and some necessary parameters can be obtained by the equations in Sec. 3.1. The values of the geometries of Transleg are shown in Table 2.

In this simulation, θKI is set as 140 deg, so AH is not larger than 19 deg according to Eq. (7). Set AH as 18 deg, and θHAEP and θHPEP are calculated as 15.44 deg and 33.44 deg according to Eq. (5). At t = 0 in Eq. (1), the FL and HR leg–wheels are in the PEP, and the FR and HL ones are in the AEP. Set the hip and knee joints of the four leg–wheels of Transleg with the corresponding initial angles. AK, T1, and T2 are set as 10 deg, 0.5 s, and 2 s. In addition, θKW is 43.23 deg, and the time for the mode transformation is set as 2 s. Therefore, the control signals directly applied on the hip and knee joints of the four leg–wheels can be achieved through Eqs. (1) and (2). They are shown in Fig. 6. The snapshots of the simulation video using these control signals are shown in Fig. 7.2 The simulation results show that the control signals and parameters obtained pursuant to the equations in Sec. 3.1 are right, and the leg–wheel mechanism can work well.

Experimental Validations

To further validate the effectiveness of the design of Transleg, two experiments on the motions of the prototype were conducted. Currently, Transleg is controlled by the program running on an external laptop through a RS-485 serial connection, and the power is provided by an external power supply.

Leg–Wheel Motions.

In one experiment, Transleg was controlled to do the legged locomotion, legged to wheeled mode motion, forward and backward wheeled locomotion, wheeled to legged mode motion, and legged locomotion successively. The actuators used in the prototype can work in three modes: wheeled, joint, and multiturn modes. Only the wheeled and joint modes are used here. In the wheeled mode, the actuators are controlled by assigning the moving speed and direction and can run endlessly, while they are controlled through the absolute angle position and have an operating angle range of 360 deg in the joint mode. Therefore, the knee joint of the prototype can be controlled in the joint mode using the signal obtained by Eq. (2) after mapping to the rotation angle of the turnplate by Eq. (3) and adding the initial angle. The initial angle is the angle position of the corresponding actuator when Transleg is in the extreme position. The hip joint in the legged locomotion can be controlled using the track in Eq. (1) after adding the initial angle in the joint mode, while it needs to be controlled in the wheeled mode by specifying the moving speed. The experimental results are shown in Fig. 82.

Spine Motions.

In the other experiment, Transleg was controlled to bend the spine without any leg–wheel motion. Pursuant to Eqs. (11), (12), and the geometry values in Table 1, the maximum bending angle αmax is 33.1 deg. When each ball joint rotates 33.1 deg, lDE in Eq. (10) is 42.1 mm. In addition, the maximum of β is 90 deg and that of γ is 85.4 deg. When they are in the maximum angles, the lengths of the wire taken back are, respectively, 36.3 mm and 36.7 mm, and the ball joint rotates 26.1 deg and 26.4 deg. Therefore, the maximum rotation angle of each ball joint is 26.1 deg in the yaw direction and 26.4 deg in the pitch direction. That is to say, Transleg can bend with the maximum angle 78.3 deg in the yaw direction and 79.2 deg in the pitch direction. Set the rotation angle of each ball joint 0–26.1 deg, and then the bending angle of the spine joins is 0–78.3 deg.

According to Eqs. (10), (13), (14), (17), and (18), the relations between the bending angles of spine joints in yaw and pitch directions and the rotation angles of actuators, the increments and decrement of wire in the spine joints, and the length of wire let out by the yaw actuator and the pitch actuator can be figured out, as shown in Fig. 9. The decrement of the length of the wire (lDE) in the spine joints is smaller than the increment (lIN), and the difference is incremental with the increasing bending angle. This will cause the spine mechanism to fail to work. To deal with this problem, the yaw and pitch turnplates are designed to be semicircular or fan-shaped, which makes the turnplates let out longer wire than take back. As shown in Fig. 9, the wires let out by the turnplates (lLO1 and lLO2) are obviously longer than that lIN needs when the bending angle is big. In fact, when the bending angle is small, the wires let out by the turnplates are a little shorter than 0.04 mm, which is small enough to be ignored. In this experiment, the yaw and pitch turnplates were actuated to rotate with different angles in two directions relative to the initial position where the spine is straight. The experimental results of the spine motion are shown in Fig. 10.2 The angles in this figure were measured with a protractor when Transleg was kept static. The results show that the turnplates collided with each other when Transleg bended with 45 deg, which is the actual maximum bending angle in the yaw direction.

Conclusions

Transleg proposed in this paper is a wire-driven leg–wheel robot. The leg–wheel mechanism is its main propelling mechanism, and it can transform between the legged and wheeled modes. Only two actuators are used to actuate each leg–wheel, which has the hip and knee joints in the legged mode and the active revolution joint in the wheeled mode. Hence, Transleg can perform almost all the legged and wheeled locomotion. The spine mechanism is its one characteristic, and it can bend in the yaw direction with the maximum angle 45 deg and in the pitch direction with 79.2 deg. The spine mechanism adopts the ball joint, whose number is extensible. In the present prototype, three ball joints exist. The experiments on the trotting gait and spine motion are conducted, and the results demonstrate the validity of Transleg. In the future, we will further optimize the structure of Transleg, study on its multimode locomotion, and apply the advanced control method to it.

Acknowledgements

The research reported in this paper was conducted at the Robotic Sensor and Control Lab, School of Instrument Science and Engineering, Southeast University, Nanjing, Jiangsu, China. The authors thank all the members of the lab for their great support.

This work was partially supported by the Nature Science Foundation of China under Grant No. 61375076 and the Jiangsu Provincial Key Laboratory of Remote Measurement and Control Technology under Grant No. 2242015k30005.

References

Ajallooeian, M. , Pouya, S. , Sproewitz, A. , and Ijspeert, A. J. , 2013, “ Central Pattern Generators Augmented With Virtual Model Control for Quadruped Rough Terrain Locomotion,” IEEE International Conference on Robotics and Automation (ICRA), Karlsruhe, Germany, May 6–10, pp. 3321–3328.
Wooden, D. , Malchano, M. , Blankespoor, K. , Howard, A. , Rizzi, A. A. , and Raibert, M. , 2010, “ Autonomous Navigation for BigDog,” IEEE International Conference on Robotics and Automation (ICRA), Anchorage, AK, May 3–7, pp. 4736–4741.
Zucker, M. , Ratliff, N. , Stolle, M. , Chestnutt, J. , Bagnell, J. A. , Atkeson, C. J. , and Kuffner, J. , 2011, “ Optimization and Learning for Rough Terrain Legged Locomotion,” Int. J. Rob. Res., 30(2), pp. 175–191.
Satzinger, B. W. , Lau, C. , Byl, M. , and Byl, K. , 2015, “ Tractable Locomotion Planning for RoboSimian,” Int. J. Rob. Res., 34(13), pp. 1541–1558.
Morin, P. , and Samson, C. , 2008, Springer Handbook of Robotics, Springer, Berlin, Chap. E.
Sharf, I. , 2010, Brain, Body and Machine, Springer, Berlin, pp. 299–310.
Grand, C. , Benamar, F. , Plumet, F. , and Bidaud, P. , 2004, “ Stability and Traction Optimization of a Reconfigurable Wheel-Legged Robot,” Int. J. Rob. Res., 23(10–11), pp. 1041–1058.
Adachi, H. , and Koyachi, N. , 2001, “ Development of a Leg-Wheel Hybrid Mobile Robot and Its Step-Passing Algorithm,” IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Maui, HI, Oct. 29–Nov. 3, Vol. 2, pp. 728–733.
Endo, G. , and Hirose, S. , 2012, “ Study on Roller-Walker—Improvement of Locomotive Efficiency of Quadruped Robots by Passive Wheels,” Adv. Rob., 26(8–9), pp. 969–988.
Thomson, T. , Sharf, I. , and Beckman, B. , 2012, “ Kinematic Control and Posture Optimization of a Redundantly Actuated Quadruped Robot,” IEEE International Conference on Robotics and Automation (ICRA), Saint Paul, MN, May 14–18, pp. 1895–1900.
Wilcox, B. H. , 2012, “ ATHLETE: A Limbed Vehicle for Solar System Exploration,” IEEE Aerospace Conference (AERO), Big Sky, MT, Mar. 3–10, pp. 1–9.
Tanaka, T. , and Hirose, S. , 2008, “ Development of Leg-Wheel Hybrid Quadruped ‘AirHopper’ Design of Powerful Light-Weight Leg With Wheel,” IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Nice, France, Sept. 22–26, pp. 3890–3895.
Huang, B. , Wang, P. , and Sun, L. , 2006, “ Behavior-Based Control of a Hybrid Quadruped Robot,” Sixth World Congress on Intelligent Control and Automation (WCICA), Dalian, China, June 21–23, Vol. 2, pp. 8997–9001.
Luo, Y. , Li, Q. , and Liu, Z. , 2014, “ Design and Optimization of Wheel-Legged Robot: Rolling-Wolf,” Chin. J. Mech. Eng., 27(6), pp. 1133–1142.
Nakajima, S. , 2011, “ RT-Mover: A Rough Terrain Mobile Robot With a Simple leg–Wheel Hybrid Mechanism,” Int. J. Rob. Res., 30(13), pp. 1609–1626.
Yuan, J. , and Hirose, S. , 2004, “ Research on Leg-Wheel Hybrid Stair-Climbing Robot, Zero Carrier,” IEEE International Conference on Robotics and Biomimetics (ROBIO), Shenyang, China, Aug. 22–26, pp. 654–659.
Szrek, J. , and Wójtowicz, P. , 2010, “ Idea of Wheel-Legged Robot and Its Control System Design,” Bull. Pol. Acad. Sci.: Tech. Sci., 58(1), pp. 43–50.
Xu, K. , and Ding, X. , 2013, “ Typical Gait Analysis of a Six-Legged Robot in the Context of Metamorphic Mechanism Theory,” Chin. J. Mech. Eng., 26(4), pp. 771–783.
Ding, X. , Li, K. , and Xu, K. , 2012, “ Dynamics and Wheel’s Slip Ratio of a Wheel-Legged Robot in Wheeled Motion Considering the Change of Height,” Chin. J. Mech. Eng., 25(5), pp. 1060–1067.
Guo, L. , Chen, K. , Zhao, D. , Wu, D. , Liu, Z. , and Bing, Y. , 2009, “ Study on a Wheel-Legged Hybrid Mobile Robot,” Manuf. Autom., 31(10), pp. 1–6 (in Chinese).
Lu, D. , Dong, E. , Liu, C. , Xu, M. , and Yang, J. , 2016, “ Generation and Analyses of the Reinforced Wave Gait for a Mammal-Like Quadruped Robot,” J. Intell. Rob. Syst., 82(1), pp. 51–68.
Zhang, L. , Yang, Y. , Gu, Y. , Sun, X. , Yao, X. , and Shuai, L. , 2016, “ A New Compact Stair-Cleaning Robot,” ASME J. Mech. Rob., 8(4), p. 045001.
Lacagnina, M. , Muscato, G. , and Sinatra, R. , 2003, “ Kinematics, Dynamics and Control of a Hybrid Robot Wheeleg,” Rob. Auton. Syst., 45(3), pp. 161–180.
Ottaviano, E. , and Rea, P. , 2013, “ Design and Operation of a 2-DOF Leg–Wheel Hybrid Robot,” Robotica, 31(8), pp. 1319–1325.
Bruzzone, L. , and Fanghella, P. , 2016, “ Functional Redesign of Mantis 2.0, a Hybrid Leg-Wheel Robot for Surveillance and Inspection,” J. Intell. Rob. Syst., 81(2), pp. 215–230.
Boxerbaum, A. S. , Klein, M. A. , Bachmann, R. , Quinn, R. D. , Harkins, R. , and Vaidyanathan, R. , 2009, “ Design of a Semi-Autonomous Hybrid Mobility Surf-Zone Robot,” IEEE/ASME International Conference on Advanced Intelligent Mechatronics (AIM), Singapore, July 14–17, pp. 974–979.
Hong, D. , Jeans, J. B. , and Ren, P. , 2009, “ Experimental Verification of the Walking and Turning Gaits for a Two-Actuated Spoke Wheel Robot,” IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), St. Louis, MO, Oct. 10–15, pp. 402–403.
Herbert, S. D. , Drenner, A. , and Papanikolopoulos, N. , 2008, “ Loper: A Quadruped-Hybrid Stair Climbing Robot,” IEEE International Conference on Robotics and Automation (ICRA), Pasadena, CA, May 19–23, pp. 799–804.
Eich, M. , Grimminger, F. , Bosse, S. , Spenneberg, D. , and Kirchner, F. , 2008, “ Asguard: A Hybrid-Wheel Security and SAR-Robot Using Bio-Inspired Locomotion for Rough Terrain,” International Workshop on Robotics for Risky Interventions and Surveillance of Environment, Benicàssim, Spain, Jan. 7–8, pp. 774–779.
Kim, Y. S. , Jung, G. P. , Kim, H. , Cho, K. J. , and Chu, C. N. , 2014, “ Wheel Transformer: A Wheel-Leg Hybrid Robot With Passive Transformable Wheels,” IEEE Trans. Rob., 30(6), pp. 1487–1498.
Chen, S. C. , Huang, K. J. , Chen, W. H. , Shen, S. Y. , Li, C. H. , and Liu, P. C. , 2014, “ Quattroped: A Leg–Wheel Transformable Robot,” IEEE/ASME Trans. Mechatron., 19(2), pp. 730–742.
Chen, W. H. , Lin, H. S. , and Lin, P. C. , 2014, “ TurboQuad: A Leg-Wheel Transformable Robot Using Bio-Inspired Control,” IEEE International Conference on Robotics and Automation (ICRA), Hong Kong, China, May 31–June 7, p. 2090.
Rohmer, E. , Reina, G. , Ishigami, G. , Nagatani, K. , and Yoshida, K. , 2008, “ Action Planner of Hybrid Leg-Wheel Robots for Lunar and Planetary Exploration,” IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Nice, France, Sept. 22–26, pp. 3902–3907.
Okada, T. , Mahmoud, A. , Botelho, W. T. , and Shimizu, T. , 2012, “ Trajectory Estimation of a Skid-Steering Mobile Robot Propelled by Independently Driven Wheels,” Robotica, 30(1), pp. 123–132.
Tadakuma, K. , Tadakuma, R. , Maruyama, A. , Rohmer, E. , Nagatani, K. , Yoshida, K. , Ming, A. , Shimojo, M. , Higashimori, M. , and Kaneko, M. , 2010, “ Mechanical Design of the Wheel-Leg Hybrid Mobile Robot to Realize a Large Wheel Diameter,” IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Taipei, Taiwan, Oct. 18–22, pp. 3358–3365.
She, Y. , Hurd, C. J. , and Su, H. J. , 2015, “ A Transformable Wheel Robot With a Passive Leg,” IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Hamburg, Germany, Sept. 28–Oct. 2, pp. 4165–4170.
Bryson, J. T. , Jin, X. , and Agrawal, S. K. , 2016, “ Optimal Design of Cable-Driven Manipulators Using Particle Swarm Optimization,” ASME J. Mech. Rob., 8(4), p. 041003.
Spröwitz, A. T. , Ajallooeian, M. , Tuleu, A. , and Ijspeert, A. J. , 2014, “ Kinematic Primitives for Walking and Trotting Gaits of a Quadruped Robot With Compliant Legs,” Front. Comput. Neurosci., 8, p. 27. [PubMed]
Tsusaka, Y. , and Ota, Y. , 2006, “ Wire-Driven Bipedal Robot,” IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Beijing, China, Oct. 9–15, pp. 3958–3963.
Zhong, Y. , Li, Z. , and Du, R. , 2013, “ The Design and Prototyping of a Wire-Driven Robot Fish With Pectoral Fins,” IEEE International Conference on Robotics and Biomimetics (ROBIO), Shenzhen, China, Dec. 12–14, pp. 1918–1923.
Zhang, K. , Qiu, C. , and Dai, J. S. , 2016, “ An Extensible Continuum Robot With Integrated Origami Parallel Modules,” ASME J. Mech. Rob., 8(3), p. 031010.
Gravagne, I. A. , Rahn, C. D. , and Walker, I. D. , 2003, “ Large Deflection Dynamics and Control for Planar Continuum Robots,” IEEE/ASME Trans. Mechatron., 8(2), pp. 299–307.
Webster, R. J. , and Jones, B. A. , 2010, “ Design and Kinematic Modeling of Constant Curvature Continuum Robots: A Review,” Int. J. Rob. Res., 29(13), pp. 1661–1683.
Burgner-Kahrs, J. , Rucker, D. C. , and Choset, H. , 2015, “ Continuum Robots for Medical Applications: A Survey,” IEEE Trans. Rob., 31(6), pp. 1261–1280.
Kato, T. , Okumura, I. , Song, S. E. , Golby, A. J. , and Hata, N. , 2015, “ Tendon-Driven Continuum Robot for Endoscopic Surgery: Preclinical Development and Validation of a Tension Propagation Model,” IEEE/ASME Trans. Mechatron., 20(5), pp. 2252–2263.
Yang, Y. , Chen, Y. , Li, Y. , and Chen, M. Z. , 2016, “ 3D Printing of Variable Stiffness Hyper-Redundant Robotic Arm,” IEEE International Conference on Robotics and Automation (ICRA), Stockholm, Sweden, May 16–21, pp. 3871–3877.
Hyun, D. J. , Seok, S. , Lee, J. , and Kim, S. , 2014, “ High Speed Trot-Running: Implementation of a Hierarchical Controller Using Proprioceptive Impedance Control on the MIT Cheetah,” Int. J. Rob. Res., 33(11), pp. 1417–1445.
Weinmeister, K. , Eckert, P. , Witte, H. , and Ijspeert, A. J. , 2015, “ Cheetah-Cub-S: Steering of a Quadruped Robot Using Trunk Motion,” IEEE International Symposium on Safety, Security, and Rescue Robotics (SSRR), West Lafayette, IN, Oct. 18–20, pp. 1–6.
Khoramshahi, M. , Sprowitz, A. , Tuleu, A. , Ahmadabadi, M. N. , and Ijspeert, A. J. , 2013, “ Benefits of an Active Spine Supported Bounding Locomotion With a Small Compliant Quadruped Robot,” IEEE International Conference on Robotics and Automation (ICRA), Karlsruhe, Germany, May 6–10, pp. 3329–3334.
Eckert, P. , Spröwitz, A. , Witte, H. , and Ijspeert, A. J. , 2015, “ Comparing the Effect of Different Spine and Leg Designs for a Small Bounding Quadruped Robot,” IEEE International Conference on Robotics and Automation (ICRA), Seattle, WA, May 26–30, pp. 3128–3133.
Zhao, Q. , Nakajima, K. , Sumioka, H. , Hauser, H. , and Pfeifer, R. , 2013, “ Spine Dynamics as a Computational Resource in Spine-Driven Quadruped Locomotion,” IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Tokyo, Nov. 3–7, pp. 1445–1451.
Zhang, X. L. , Duan, G. H. , Zheng, H. J. , Zhao, L. Y. , and Cheng, Z. F. , 2003, “ Bionic Design of the Quadrupedal Robot and Motion Simulation,” IEEE International Conference on Robotics, Intelligent Systems and Signal Processing (RISSP), Changsha, China, Oct. 8–13, pp. 137–141.
Topics: Robots , Wire , Actuators , Design , Wheels , Yaw , Knee , Rotation
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References

Ajallooeian, M. , Pouya, S. , Sproewitz, A. , and Ijspeert, A. J. , 2013, “ Central Pattern Generators Augmented With Virtual Model Control for Quadruped Rough Terrain Locomotion,” IEEE International Conference on Robotics and Automation (ICRA), Karlsruhe, Germany, May 6–10, pp. 3321–3328.
Wooden, D. , Malchano, M. , Blankespoor, K. , Howard, A. , Rizzi, A. A. , and Raibert, M. , 2010, “ Autonomous Navigation for BigDog,” IEEE International Conference on Robotics and Automation (ICRA), Anchorage, AK, May 3–7, pp. 4736–4741.
Zucker, M. , Ratliff, N. , Stolle, M. , Chestnutt, J. , Bagnell, J. A. , Atkeson, C. J. , and Kuffner, J. , 2011, “ Optimization and Learning for Rough Terrain Legged Locomotion,” Int. J. Rob. Res., 30(2), pp. 175–191.
Satzinger, B. W. , Lau, C. , Byl, M. , and Byl, K. , 2015, “ Tractable Locomotion Planning for RoboSimian,” Int. J. Rob. Res., 34(13), pp. 1541–1558.
Morin, P. , and Samson, C. , 2008, Springer Handbook of Robotics, Springer, Berlin, Chap. E.
Sharf, I. , 2010, Brain, Body and Machine, Springer, Berlin, pp. 299–310.
Grand, C. , Benamar, F. , Plumet, F. , and Bidaud, P. , 2004, “ Stability and Traction Optimization of a Reconfigurable Wheel-Legged Robot,” Int. J. Rob. Res., 23(10–11), pp. 1041–1058.
Adachi, H. , and Koyachi, N. , 2001, “ Development of a Leg-Wheel Hybrid Mobile Robot and Its Step-Passing Algorithm,” IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Maui, HI, Oct. 29–Nov. 3, Vol. 2, pp. 728–733.
Endo, G. , and Hirose, S. , 2012, “ Study on Roller-Walker—Improvement of Locomotive Efficiency of Quadruped Robots by Passive Wheels,” Adv. Rob., 26(8–9), pp. 969–988.
Thomson, T. , Sharf, I. , and Beckman, B. , 2012, “ Kinematic Control and Posture Optimization of a Redundantly Actuated Quadruped Robot,” IEEE International Conference on Robotics and Automation (ICRA), Saint Paul, MN, May 14–18, pp. 1895–1900.
Wilcox, B. H. , 2012, “ ATHLETE: A Limbed Vehicle for Solar System Exploration,” IEEE Aerospace Conference (AERO), Big Sky, MT, Mar. 3–10, pp. 1–9.
Tanaka, T. , and Hirose, S. , 2008, “ Development of Leg-Wheel Hybrid Quadruped ‘AirHopper’ Design of Powerful Light-Weight Leg With Wheel,” IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Nice, France, Sept. 22–26, pp. 3890–3895.
Huang, B. , Wang, P. , and Sun, L. , 2006, “ Behavior-Based Control of a Hybrid Quadruped Robot,” Sixth World Congress on Intelligent Control and Automation (WCICA), Dalian, China, June 21–23, Vol. 2, pp. 8997–9001.
Luo, Y. , Li, Q. , and Liu, Z. , 2014, “ Design and Optimization of Wheel-Legged Robot: Rolling-Wolf,” Chin. J. Mech. Eng., 27(6), pp. 1133–1142.
Nakajima, S. , 2011, “ RT-Mover: A Rough Terrain Mobile Robot With a Simple leg–Wheel Hybrid Mechanism,” Int. J. Rob. Res., 30(13), pp. 1609–1626.
Yuan, J. , and Hirose, S. , 2004, “ Research on Leg-Wheel Hybrid Stair-Climbing Robot, Zero Carrier,” IEEE International Conference on Robotics and Biomimetics (ROBIO), Shenyang, China, Aug. 22–26, pp. 654–659.
Szrek, J. , and Wójtowicz, P. , 2010, “ Idea of Wheel-Legged Robot and Its Control System Design,” Bull. Pol. Acad. Sci.: Tech. Sci., 58(1), pp. 43–50.
Xu, K. , and Ding, X. , 2013, “ Typical Gait Analysis of a Six-Legged Robot in the Context of Metamorphic Mechanism Theory,” Chin. J. Mech. Eng., 26(4), pp. 771–783.
Ding, X. , Li, K. , and Xu, K. , 2012, “ Dynamics and Wheel’s Slip Ratio of a Wheel-Legged Robot in Wheeled Motion Considering the Change of Height,” Chin. J. Mech. Eng., 25(5), pp. 1060–1067.
Guo, L. , Chen, K. , Zhao, D. , Wu, D. , Liu, Z. , and Bing, Y. , 2009, “ Study on a Wheel-Legged Hybrid Mobile Robot,” Manuf. Autom., 31(10), pp. 1–6 (in Chinese).
Lu, D. , Dong, E. , Liu, C. , Xu, M. , and Yang, J. , 2016, “ Generation and Analyses of the Reinforced Wave Gait for a Mammal-Like Quadruped Robot,” J. Intell. Rob. Syst., 82(1), pp. 51–68.
Zhang, L. , Yang, Y. , Gu, Y. , Sun, X. , Yao, X. , and Shuai, L. , 2016, “ A New Compact Stair-Cleaning Robot,” ASME J. Mech. Rob., 8(4), p. 045001.
Lacagnina, M. , Muscato, G. , and Sinatra, R. , 2003, “ Kinematics, Dynamics and Control of a Hybrid Robot Wheeleg,” Rob. Auton. Syst., 45(3), pp. 161–180.
Ottaviano, E. , and Rea, P. , 2013, “ Design and Operation of a 2-DOF Leg–Wheel Hybrid Robot,” Robotica, 31(8), pp. 1319–1325.
Bruzzone, L. , and Fanghella, P. , 2016, “ Functional Redesign of Mantis 2.0, a Hybrid Leg-Wheel Robot for Surveillance and Inspection,” J. Intell. Rob. Syst., 81(2), pp. 215–230.
Boxerbaum, A. S. , Klein, M. A. , Bachmann, R. , Quinn, R. D. , Harkins, R. , and Vaidyanathan, R. , 2009, “ Design of a Semi-Autonomous Hybrid Mobility Surf-Zone Robot,” IEEE/ASME International Conference on Advanced Intelligent Mechatronics (AIM), Singapore, July 14–17, pp. 974–979.
Hong, D. , Jeans, J. B. , and Ren, P. , 2009, “ Experimental Verification of the Walking and Turning Gaits for a Two-Actuated Spoke Wheel Robot,” IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), St. Louis, MO, Oct. 10–15, pp. 402–403.
Herbert, S. D. , Drenner, A. , and Papanikolopoulos, N. , 2008, “ Loper: A Quadruped-Hybrid Stair Climbing Robot,” IEEE International Conference on Robotics and Automation (ICRA), Pasadena, CA, May 19–23, pp. 799–804.
Eich, M. , Grimminger, F. , Bosse, S. , Spenneberg, D. , and Kirchner, F. , 2008, “ Asguard: A Hybrid-Wheel Security and SAR-Robot Using Bio-Inspired Locomotion for Rough Terrain,” International Workshop on Robotics for Risky Interventions and Surveillance of Environment, Benicàssim, Spain, Jan. 7–8, pp. 774–779.
Kim, Y. S. , Jung, G. P. , Kim, H. , Cho, K. J. , and Chu, C. N. , 2014, “ Wheel Transformer: A Wheel-Leg Hybrid Robot With Passive Transformable Wheels,” IEEE Trans. Rob., 30(6), pp. 1487–1498.
Chen, S. C. , Huang, K. J. , Chen, W. H. , Shen, S. Y. , Li, C. H. , and Liu, P. C. , 2014, “ Quattroped: A Leg–Wheel Transformable Robot,” IEEE/ASME Trans. Mechatron., 19(2), pp. 730–742.
Chen, W. H. , Lin, H. S. , and Lin, P. C. , 2014, “ TurboQuad: A Leg-Wheel Transformable Robot Using Bio-Inspired Control,” IEEE International Conference on Robotics and Automation (ICRA), Hong Kong, China, May 31–June 7, p. 2090.
Rohmer, E. , Reina, G. , Ishigami, G. , Nagatani, K. , and Yoshida, K. , 2008, “ Action Planner of Hybrid Leg-Wheel Robots for Lunar and Planetary Exploration,” IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Nice, France, Sept. 22–26, pp. 3902–3907.
Okada, T. , Mahmoud, A. , Botelho, W. T. , and Shimizu, T. , 2012, “ Trajectory Estimation of a Skid-Steering Mobile Robot Propelled by Independently Driven Wheels,” Robotica, 30(1), pp. 123–132.
Tadakuma, K. , Tadakuma, R. , Maruyama, A. , Rohmer, E. , Nagatani, K. , Yoshida, K. , Ming, A. , Shimojo, M. , Higashimori, M. , and Kaneko, M. , 2010, “ Mechanical Design of the Wheel-Leg Hybrid Mobile Robot to Realize a Large Wheel Diameter,” IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Taipei, Taiwan, Oct. 18–22, pp. 3358–3365.
She, Y. , Hurd, C. J. , and Su, H. J. , 2015, “ A Transformable Wheel Robot With a Passive Leg,” IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Hamburg, Germany, Sept. 28–Oct. 2, pp. 4165–4170.
Bryson, J. T. , Jin, X. , and Agrawal, S. K. , 2016, “ Optimal Design of Cable-Driven Manipulators Using Particle Swarm Optimization,” ASME J. Mech. Rob., 8(4), p. 041003.
Spröwitz, A. T. , Ajallooeian, M. , Tuleu, A. , and Ijspeert, A. J. , 2014, “ Kinematic Primitives for Walking and Trotting Gaits of a Quadruped Robot With Compliant Legs,” Front. Comput. Neurosci., 8, p. 27. [PubMed]
Tsusaka, Y. , and Ota, Y. , 2006, “ Wire-Driven Bipedal Robot,” IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Beijing, China, Oct. 9–15, pp. 3958–3963.
Zhong, Y. , Li, Z. , and Du, R. , 2013, “ The Design and Prototyping of a Wire-Driven Robot Fish With Pectoral Fins,” IEEE International Conference on Robotics and Biomimetics (ROBIO), Shenzhen, China, Dec. 12–14, pp. 1918–1923.
Zhang, K. , Qiu, C. , and Dai, J. S. , 2016, “ An Extensible Continuum Robot With Integrated Origami Parallel Modules,” ASME J. Mech. Rob., 8(3), p. 031010.
Gravagne, I. A. , Rahn, C. D. , and Walker, I. D. , 2003, “ Large Deflection Dynamics and Control for Planar Continuum Robots,” IEEE/ASME Trans. Mechatron., 8(2), pp. 299–307.
Webster, R. J. , and Jones, B. A. , 2010, “ Design and Kinematic Modeling of Constant Curvature Continuum Robots: A Review,” Int. J. Rob. Res., 29(13), pp. 1661–1683.
Burgner-Kahrs, J. , Rucker, D. C. , and Choset, H. , 2015, “ Continuum Robots for Medical Applications: A Survey,” IEEE Trans. Rob., 31(6), pp. 1261–1280.
Kato, T. , Okumura, I. , Song, S. E. , Golby, A. J. , and Hata, N. , 2015, “ Tendon-Driven Continuum Robot for Endoscopic Surgery: Preclinical Development and Validation of a Tension Propagation Model,” IEEE/ASME Trans. Mechatron., 20(5), pp. 2252–2263.
Yang, Y. , Chen, Y. , Li, Y. , and Chen, M. Z. , 2016, “ 3D Printing of Variable Stiffness Hyper-Redundant Robotic Arm,” IEEE International Conference on Robotics and Automation (ICRA), Stockholm, Sweden, May 16–21, pp. 3871–3877.
Hyun, D. J. , Seok, S. , Lee, J. , and Kim, S. , 2014, “ High Speed Trot-Running: Implementation of a Hierarchical Controller Using Proprioceptive Impedance Control on the MIT Cheetah,” Int. J. Rob. Res., 33(11), pp. 1417–1445.
Weinmeister, K. , Eckert, P. , Witte, H. , and Ijspeert, A. J. , 2015, “ Cheetah-Cub-S: Steering of a Quadruped Robot Using Trunk Motion,” IEEE International Symposium on Safety, Security, and Rescue Robotics (SSRR), West Lafayette, IN, Oct. 18–20, pp. 1–6.
Khoramshahi, M. , Sprowitz, A. , Tuleu, A. , Ahmadabadi, M. N. , and Ijspeert, A. J. , 2013, “ Benefits of an Active Spine Supported Bounding Locomotion With a Small Compliant Quadruped Robot,” IEEE International Conference on Robotics and Automation (ICRA), Karlsruhe, Germany, May 6–10, pp. 3329–3334.
Eckert, P. , Spröwitz, A. , Witte, H. , and Ijspeert, A. J. , 2015, “ Comparing the Effect of Different Spine and Leg Designs for a Small Bounding Quadruped Robot,” IEEE International Conference on Robotics and Automation (ICRA), Seattle, WA, May 26–30, pp. 3128–3133.
Zhao, Q. , Nakajima, K. , Sumioka, H. , Hauser, H. , and Pfeifer, R. , 2013, “ Spine Dynamics as a Computational Resource in Spine-Driven Quadruped Locomotion,” IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Tokyo, Nov. 3–7, pp. 1445–1451.
Zhang, X. L. , Duan, G. H. , Zheng, H. J. , Zhao, L. Y. , and Cheng, Z. F. , 2003, “ Bionic Design of the Quadrupedal Robot and Motion Simulation,” IEEE International Conference on Robotics, Intelligent Systems and Signal Processing (RISSP), Changsha, China, Oct. 8–13, pp. 137–141.

Figures

Fig. 1

Prototype of Transleg in the (a) legged and (b) wheeled modes

Fig. 2

Schematic diagram of the leg–wheel mechanism in the (a) legged and (b) wheeled modes. The numbers denote: ① body, ② hip joint, ③ actuator 1, ④ thigh, ⑤ rim, ⑥ spoke, ⑦ knee joint, ⑧ shank, ⑨ docking assembly, ⑩ thrust ball bearing, ⑪ torsion spring, ⑫ turnplate, ⑬ actuator 2, ⑭ wire, ⑮ hole, ⑯ rotary assembly, ⑰ foot, ⑱ bearing pedestal, ⑲ flange bearing, and ⑳ dowel.

Fig. 3

Schematic diagram of the spine mechanism. The numbers denote: ① pitch actuator, ② front body, ③ pitch turnplate, ④ wire, ⑤ tail end, ⑥ spine joints, ⑦ yaw actuator, ⑧ rear body, ⑨ yaw turnplate, ⑩ head end, ⑪ vertebra, ⑫ silicon piece, and ⑬ ball joints.

Fig. 4

Geometries of leg–wheel mechanism for explaining (a) the relation between the rotation angle of turnplate and the angle of knee joint, (b) the angles of hip joint in anterior extreme position and posterior extreme position, and (c) the angle of knee joint in the wheeled mode

Fig. 5

Geometries of spine mechanism for explaining (1) the relation between the bending angle of Transleg in the yaw direction and the rotation angle of the yaw actuator, and (2) the relation between the bending angle of Transleg in the pitch direction and the rotation angle of the pitch actuator

Fig. 6

Control signals actuating Transleg to perform legged and wheeled locomotion and switch between the two locomotion modes. (FLH, FRH, HLH, and HRH, respectively, denote hip joint of front-left, front-right, hind-left, and hind-right leg–wheel; FLK, FRK, HLK, and HRK, respectively, denote knee joint of front-left, front-right, hind-left, and hind-right leg–wheel).

Fig. 7

Snapshots of Transleg performing legged, wheeled, and transformation motion in the simulation

Fig. 8

Snapshots of Transleg performing legged, wheeled, and transformation motion in the experiment

Fig. 9

Relations between the bending angles of spine joints in yaw and pitch directions and the rotation angles of actuators, the increments and decrements of wires in the spine joints, and the length of wire let out by the yaw actuator and the pitch actuator (solid lines and dotted lines are, respectively, relative to the left and right coordinates)

Fig. 10

Snapshots of Transleg performing spine motion

Tables

Table 1 Characteristics of some leg–wheel robots referenced in this paper and Transleg
Note: nA denotes the number of actuators for each leg–wheel, nLD denotes the number of active DOFs for the leg, nWD denotes the number of active DOFs for the wheel. “/” denotes “or”, indicating the leg–wheels of the robot have different numbers of actuators or DOFs.
Table 2 Values of the geometries of Transleg

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