Posture Control of a Four-Wheel-Legged Robot With a Suspension System

To achieve posture control and ride comfort (vibration isolation performance) of a robot in unstructured terrain, a novel four-wheel-legged robot (FWLR) with an actively-passively suspension system is first designed. In the suspension system, the active parts are responsible for posture control and the passive parts are responsible for vibration isolation. Then, a closed-loop and decoupled posture control model with 11 DOF are proposed, with which we designed the posture controller with a second-order low-pass filter (SLPF). To test the posture control performance of FWLR in unstructured terrain, both simulation and experiment are carried out, the simulation and experimental results show that the posture angles in unstructured terrain are reduced by 54.65% and 59% on average, respectively. In addition, the frequency response shows that the posture angles are reduced by more than 50% in low-frequency unstructured terrain. Finally, to validate the ride comfort of FWLR, dynamic models with different degrees of freedom (DOF) are established and simulated, and the results present that the ride comfort can be improved with the posture angular acceleration is reduced by 15.83% and 46.7% on average. Generally, with the actively-passively suspension system proposed in this article, FWLR can be equipped with excellent ride comfort and posture control in unstructured terrain. The research in this article has potential reference value and practical value for enriching the posture control of robots and vehicles.


I. INTRODUCTION
Wheel-legged all-terrain mobile robots (WLATMR) have the advantages of wheeled robots and legged robots [1] and have a wide range of applications in the fields of post-disaster rescue [2], [3], resource exploration [4], [5], precision agriculture [6] and other fields [7], [8]. Furthermore, WLATMR can replace people by working in extreme surroundings and thus reduce the dangers posed to humans. Therefore, posture control and ride comfort in an unstructured environment are two critical requirements of WLATMR [9], [10], and both of them are studied in this article.
There is no doubt that the posture of a robot can be changed in an unstructured terrain, thus, the off-road ability and stability are reduced. Therefore, posture control is a good way to solve these above problems, and the posture The associate editor coordinating the review of this manuscript and approving it for publication was Chua Chin Heng Matthew .
control of WLATMR has attracted considerable attention. For example, Ma et al. [11] proposed a wheel-legged all terrain mobile robot with active suspension and thus improved the pitch angle in unstructured terrain. Garcia et al. [12] described the locomotion control of a leg prototype, designed and developed to make a quadruped walk dynamically while exhibiting compliant interaction with the uneven terrain. Wei et al. [13] provided an approach to generate hopping pattern at stance phase and control it. The effectiveness of the proposed model and control scheme is verified through the simulation and experiments. He et al. [14] studied dynamics and posture control of a one-legged hopping robot with articulated leg. To ensure the controllability of the elastic underactuated mechanism, a dynamics synthesis method is proposed for designing the underactuated mechanism so that the dynamics of the system can be transformed into the strict feedback normal form. Cordes et al. [15] depicted the mechanical design of a rover, to realize posture control, kinematic considerations for movement constraints on the wheel contact points are presented. Iagnemma et al. [16] developed a novel rover with the ability to reconfigure its structure to improve posture in unstructured terrain. Wettergreen et al. [17] proposed a robot called Scarab, which can adjust the wheelbase and height to keep its drill in contact with the ground and can also adjust its posture to better adapt to uneven terrain. Wilcox et al. [18] showed a robot called ATHLETE, which is capable of efficient rolling mobility and walking mobility on extreme terrain. Similar studies include the robots Tri-star [19], Workpartner [20], and Mammoth [21].
Although posture control has been studied by many researchers, most of these methods have been tested in the laboratory, and the experimental terrains have been relatively simple. Furthermore, even if the accuracy of the model and algorithm is not high, it can achieve excellent performance, so the posture control of many robots has remained in the open-loop control or coupled state. However, if the robots are in unstructured terrain, the performance will be reduced. Moreover, since most wheel-legged robots have no elastic system, the traditional modelling method is to regard the robot as a multi-rigid-body, but for the robots with elastic elements in their structure, it will lead to huge error. For example, Luo et al. [22] depicted a wheel-legged robot with an elastic structure, and the simulation and experimental results showed that the robot achieved posture control and vibration isolation performance in unstructured terrain, but the control accuracy is affected since the elastic element is regarded as a rigid body. Jiang et al. [1] proposed a wheel-legged robot that can travel over unstructured terrain based on active posture control and passive spring-damping system, however, the spring-damping system is still regarded as a rigid body when modelling. Grand et al. [23], [24] showed a four-wheel-legged robot that has excellent off-road ability, and its posture is well controlled, but the experiment is carried out in moderate terrain. Bazeille et al. [25] studied the posture control of HyQ in unstructured terrain. However, its posture control mainly depends on environment perception, and its control accuracy is easily disturbed by the external environment.
Importantly, if the impact force from the terrain is very huge, the posture can be affected and the ride comfort can be reduced, so achieving an excellent ride comfort in unstructured terrain is an another essential requirement for a wheel-legged robot, and the most effective approach is to equip a vibration isolation system [26], [27]. The reasons for equipping robots with a vibration isolation system are as follows: 1) A chatter or bouncing between the tyres and the terrain can occur in the moment of abrupt contacts, causing a temporary loss of contact force. 2) Substantial acceleration from the terrain can damage the weakest mechanical components of the robot (e.g. actuator), especially in extremely unstructured terrain.
3) Impact energy caused by the terrain can be significantly absorbed by equipping with a suspension system, thereby enhancing the ride comfort performance while achieving all-terrain driving. Generally, it is necessary to equip a vibration isolation system for all-terrain mobile robots, but traditional wheellegged robots rarely feature vibration isolation system. For example, CDRDA developed a hybrid wheel-legged robot by including hydraulic joints and electric wheels [28], although the hydraulic mechanism can absorb part of the impact force, there is still a huge impact force on the robot in unstructured terrain. Sun et al. [29] presented a decoupled control method based on kinematic models of an amphibious reconfigurable robot called eQuad. Therefore, the proposed robot can walk with a unique gait by eliminating the swing phase of each legs, and it has a balanced posture in unstructured terrain because all legs are in contact with the terrain while walking. However, due to the lack of vibration isolation system, the joint force is huge, which limits its application. Nakajima et al. [30] proposed a basic control method for a wheel-legged robot moving on unexplored rough terrains. Based on the proposed control algorithm, the posture of the robot is well controlled, but due to the lack of vibration isolation system, the unstructured terrain will have huge impact on the joints and body.
Although few scholars pay attention to the vibration isolation of WLATMR, some researchers had tried to equip elastic components for wheeled robots, legged robots and wheeled vehicles. For example, Xie et al. [31] proposed a robust control method for wheeled vehicles with active suspension, the simulation results show that the vertical acceleration, pitch acceleration and roll acceleration are reduced by 23.07%, 13.24% and 19.63%, respectively. Zhu et al. [32] used semi-active suspension and fuzzy control method to achieve the posture control of wheeled vehicle. The simulation results show that the roll angle is reduced by approximately 30% and the ride comfort is improved when changing lanes. Zheng et al. [33] designed a semi-active suspension for a wheeled vehicle based on MR damper. The posture control is realized by fuzzy control, and the simulation results present that the pitch and roll angles are reduced by approximately 30% and the vibration isolation performance is enhanced under the steering condition. To solve the problems of energy-saving control, non ideal actuator, and actuator fault tolerance, the nonlinear characteristics of active suspension are studied based on finite-time control [34], bioinspired control [35] and adaptive control [36]. The simulation and experimental results show that the dynamic system performance of the suspension and the ride comfort of the wheeled vehicle are improved.
In addition, Tharakeshwar and Ghosal [37] added a suspension system for a wheeled robot to increase ride comfort performance and stability. Chen et al. [38], [39] improved the ride comfort performance of a hexapod robot by adding rubber to the feet, thus realizing gait planning and posture control. Li et al. [40] designed a quadruped robot with LCS (Linkage-Cable-Spring) mechanism, and achieved excellent ride comfort and posture control performance. These studies provide reference for the research of vibration isolation and ride comfort of wheel-legged robots.
Overall, the traditional WLATMR seldom involves vibration isolation system, and the research on ride comfort is seldom considered, In addition, the modeling method of posture control usually regards the robot as a rigid body. These problems limit the development of WLATMR. Based on the above analysis, a wheel-legged robot with suspension system is proposed, and its posture control and ride comfort are studied.
In this article, to solve the problem of posture control and vibration isolation of WLATMR, a four-wheel-legged all terrain mobile robot with actively-passively suspension system called FWLR is proposed. Each leg of FWLR has an independent passive vibration isolation system and active posture control system that does not interfere with each other. The passive system mainly comprises a spring-damping, and the active system is mainly composed of an actuator, both of which are connected in series, as shown in Fig. 1. Relying on the passive vibration isolation system, FWLR can continuously keep the tyres in contact with the ground all the time, and absorb the ground impact from the terrain. By relying on the active system, FWLR can reconfigure its posture by actuators. Thus the posture control performance and ride comfort can be effectively improved by the actively-passively suspension system proposed in this article.
In this article, to validate the posture control performance in unstructured terrain, a closed-loop and decoupled posture control model with 11DOF is proposed, with which the LQR posture controller with SLPF is designed. In addition, the terrain estimation model based on a gyroscope is presented. To verify the posture control performance, both simulation and experiment are carried out and compared, the results show that FWLR has good posture control ability. Besides, to validate the ride comfort of FWLR, the dynamic models with different DOF are established and compared, and the results show that the ride comfort can be improved by the actively-passively suspension.
This article is organized as follows. The next section provides the design of the prototype. The posture control is established in Section 3. The ride comfort is completed in Section 4. The conclusions are presented in Section 5.

II. PROTOTYPE DESIGN A. DESIGN CONCEPT
A good way to improve the performance of a robot in unstructured terrain is to use structure optimization [41], [42], therefore, according to the principle diagram shown in Figs. 1(a), a wheel-legged structure with an actively-passively suspension system is designed in Figs. 1(b), and the real model of the novel wheel-legged is depicted in Figs. 1(c). The suspension system is mainly composed of an actuator and a springdamping, the posture control of FWLR is achieved by four actuators, and the length of the output of the actuator is treated as the input of the control system. Moreover, to improve the ride comfort in unstructured terrain, the spring-damping system is connected in series with the actuator, and this design makes it possible for FWLR to have both posture control and ride comfort at the same time. In this article, the posture control is achieved by the active system, and the excellent ride comfort is equipped by the combination of the posture control and the passive system.

B. STRUCTURE PARAMETERS
As illustrated in Fig. 2, FWLR consists of the body, battery, controller, actuators, motor drivers, legs, spring-damping, etc. FWLR is a symmetrical structure, and the specific parameters are illustrated in Tab. 1. The virtual and real model are shown  in Figs. 2(a) and 2(b), respectively, and the balanced posture in unstructured terrain is shown in Figs. 3(a) and 3(b).
The proposed robot can traverse over unstructured terrains by the actively-passively suspension system proposed in this article. The advantages of the suspension system are shown below: 1) The posture is controlled by four actuators, which ensures the pitch and roll of the robot can be decoupled, thus it is convenient for posture control. 2) The combination of passive system and active system can achieve the advantages of both approaches, therefore, the ride comfort and posture control performance of the robot in unstructured terrain can be enhanced at the same time. Overall, this article presents a novel wheel-legged robot with the posture and ride comfort that can be improved according to the terrain.

III. POSTURE CONTROL A. DYNAMIC MODEL
Compared to traditional robots, the existence of springdamping system makes the control system more complex, and FWLR can not be regarded as a rigid system. Therefore, an 11 DOF dynamic model considering the suspension system and linear quadratic regulator (LQR) algorithm are built to achieve the posture control in unstructured terrain, and the pitch angle and roll angle are decoupled with closedloop control. In addition, to fully leverage the advantages of actuators and realize the controllability of the system, two second-order low-pass filters (LPF) in series are established, as shown in Fig. 4, Equation. (1-8) describe the dynamic model, among which, Eqs. (6-7) refer to the corresponding filter model. In this section, the roll and pitch angles are used to describe the posture of the robot.
The equation of the vertical motion of the body is given by The equation of the pitch motion of the body is given by The equation of the roll motion of the body is given by The equations of the vertical motion of the links, i = (1∼4) is given by The equations of the vertical motion of the tyres, i = (1∼4) is given by For the system in hand, the second order LPF equations are: with

B. LQR ALGORITHM
The purpose of this section is to reduce the change in posture angles of FWLR in unstructured terrain, therefore, the θ and ϕ shown in Eq. (9) are set as the state variables, and the control input, disturbance vector, and system state equations are shown in Eqs. (10)(11)(12), respectively. The performance indexes of posture control are provided in Eqs. (13)(14), and the Riccati equation and the control input (u) that minimizes J 1 and J 2 are depicted in Eqs. (15)(16). The state vector is given by The control input is given by The disturbance vectors is given by The state equation is given bẏ The performance indexes of posture control, i = (1∼4) is given by The Reccati equation is given by The control input u that minimizes J 1 and J 2 is given by among which, in the performance indexes, ρ 1 , ρ 2 , ρ 3 , ρ 4 , ρ 5, ρ 6 , and ρ 7 are weighting factors. The tyre deflections, ti , suspension deflections, bi , integral of posture angles, d , pd , control input, ai , and posture angles, p , pp are given in Eqs. (17)(18)(19)(20)(21)(22)(23), respectively.
Because the LQR algorithm needs disturbance information from the terrain, and it can be estimated by the posture angles fed back by the gyroscope on the body. Figs. 5(a) shows the flow chart of terrain estimation, and Eqs. (24)(25) represent the proposed terrain model, as long as the posture angles of FWLR are fed back, the terrain can be estimated.

C. CO-SIMULATION AND EXPERIMENT 1) POSTURE TRACKING
To validate the validity of the proposed model and algorithm, posture tracking of FWLR with the co-simulation of ADAMS and MATLAB is carried out. The control principle is that the robot adjusts its posture according to the desired posture angles.
The simulation results are compared with the experimental results below.
To realize the comparison of the simulation and experiment of posture tracking, a control loop shown in Figs. 6(a) is built, and the corresponding controller depicted in Figs. 6(b) is designed. The Kvaser controller in this article is implemented on a PC in the MATLAB environment via the communication mode of the controller area network (CAN). All the investigated parameters can be measured and displayed in MATLAB, the controller mainly includes four modules:   The parameter values in the experiment are the same as those in the co-simulation. In the experiment of posture tracking, the sampling rate of all sensors, devices and measurement system is 0.001s, the speed of FWLR is 0m/s, and the desired posture is θ = −0.026, ϕ = 0.040. The experimental principle is that the desired posture is input into the control system firstly. The control signals are then sent to the corresponding actuator, and the posture of FWLR is adjusted by the output of actuators. Finally, the posture angles are fed back by the gyroscope installed in FWLR, and the angles will be compared with the desired angles until the posture tracking is achieved.
The comparison between the simulation and experiment of posture tracking is shown in Fig 7. The results illustrate that the steady-state values are consistent with the desired values, the steady-state time is approximately 0.5s, and the overshoot is very small. Generally, the validity of the model and algorithm is validated by the simulation and experiment. In addition, the simulation can achieve the steady state faster than the experiment, because there are errors in the experiment, and the main errors are as follows: 1) White noise of gyroscope.
2) Measurement and machining error. For example, it is difficult to achieve the moment of inertia of the robot accurately, but it has a great influence on the posture angles of the robot.

2) POSTURE CONTROL IN UNSTRUCTURED TERRAIN
The posture tracking of FWLR is validated by co-simulation and experiment, however, it is carried out under the condition that the robot does not move. To further validate the posture control ability of FWLR, a driving system and unstructured terrains are developed for FWLR, with purpose of testing the posture control performance of FWLR in unstructured terrain. In this subsection, the co-simulation and experiment of posture control in unstructured terrain are studied. The co-simulation of ADAMS and MATLAB with the comparison of posture control is carried out, and the simulation principle is as follows. Firstly, the posture angles in unstructured terrain are measured by the gyroscope. Secondly, the terrain information is estimated according to the angles, and the corresponding control signals are sent to the corresponding actuators. Finally, the posture control of FWLR in unstructured terrain is achieved as the adjustment of actuators. The virtual unstructured terrain built in ADAMS is shown in Figs. 8(a), and the co-simulation model built in MATLAB is shown in Figs. 8(b).
In the simulation, the speed of FWLR is 1m/s, the performance index is J 2 , and the comparison of posture con- trol is presented in Fig. 9 and Tab. 2. The results showed that the model and algorithm proposed in this article can improve the posture control ability of FWLR in unstructured terrain, in which the improvement proportion of the pitch angle is 58.2%, the roll angle is 51.1%, and the average improvement is 54.65%.
To further verify the correctness of posture control of FWLR in unstructured terrain, an experiment is carried out based on the simulation. The controller used in the experiment is basically the same as that shown in Fig. 6, but the difference between them is that the performance index is J 2 shown in Eq (14). In the experiment, the sampling rate of all sensors, devices and measurement system is 0.001s, the speed of FWLR is 1m/s, and the desired posture is θ = 0, ϕ = 0. VOLUME 8, 2020 The obstacle size of the terrain is 1m × 0.4m × 0.075m. The flow chart and unstructured terrain are depicted in Figs. 10(a) and 10(b), respectively, and the experimental results are shown in Fig. 11 and Tab. 2. The results show that the model and algorithm proposed in this article can obviously improve the performance of posture control in unstructured terrain, in which the improvement proportion of the pitch angle is 54%, the roll angle is 64%, and the average improvement is 59%. In addition, the experimental results and simulation results are basically the same, and the main errors in the experiment are as follows: 1) The moment of inertia of the robot is difficult to measure accurately.
2) The terrain model is linearized, which leads to errors between the estimated terrain and the actual terrain.
3) The maximum working speed of the actuator is 125mm/s, which limits the response of the control system.

3) FREQUENCY RESPONSE FOR RANDOM ROADS
To verify the posture control performance of FWLR in different terrain, the frequency response in random terrain is analyzed with the co-simulation of ADAMS and MATLAB.
In the simulation, the vibration platform is built in ADAMS, and the random terrain is input by a vibration platform. The random terrain is obtained by Eq. (26) (shown in Fig. 13), and the parameter settings are depicted in [43], [44].
where z j (t) represents the input of the vibration platform to each wheel, j = (LF, RF, LR, RR). w i (t) represents the input of random white noise, i = (1 ∼ 4). f 0 represents the lower cut-off frequency, f 0 = 0.01Hz. G 0 represents the road roughness coefficient, G 0 = 5×10 −6 (m 3 /cycle). v represents the speed of FWLR, v = 1m/s. The co-simulation model of frequency response is built in Fig. 14, and the comparison of posture angles is shown in Fig. 15. The results show that the pitch angle is reduced by more than 60%, and the roll angle is reduced by more than 50% within 5Hz. This shows that the proposed LQR controller can effectively improve the posture control performance of FWLR in low-frequency unstructured terrain. On the other hand, the following two reasons can also explain the validity of the frequency response.
1) The actively-passively suspension proposed in this article is a series slow active suspension, which is suitable for posture control of low-frequency unstructured terrain within 6Hz. 2) In addition, the LPF shown in Eqs. (6-7) is included in the posture control model, this means that the posture control can be achieved in low-frequency terrain. Overall, the novel suspension and LQR controller proposed in this article can improve the posture control performance FWLR in low frequency unstructured terrain.

IV. PERFORMANCE OF RIDE COMFORT (VIBRATION ISOLATION PERFORMANCE)
Posture control and ride comfort are two key factors that affect the off-road performance of the robot in unstructured terrain. The posture control of FWLR is realized by the proposed suspension system, control model, and algorithm in this article. In this subsection, the influence of the actively-passively suspension system on the ride comfort of the robot is studied, and the pitch angular acceleration and roll angular acceleration are regarded as two evaluation indexes of ride comfort [45].

A. INFLUENCE OF ACTIVE SYSTEM (POSTURE CONTROL) ON RIDE COMFORT
To validate the influence of the posture control on the ride comfort of FWLR, the flow chart and co-simulation model are presented in Figs. 16(a) and 16(b), respectively. The values of the parameters in the simulation are the same as those shown in subsection III, and the speed is also 1m/s.  The comparison is shown in Fig. 17. The results show that the pitch angular acceleration and the roll angular acceleration are reduced obviously with the posture control, and the specific results are presented in Tab. 3. In conclusion, the posture angular acceleration is reduced by 15.83% on average, which enhances the vibration isolation performance of FWLR.

B. INFLUENCE OF PASSIVE SYSTEM (SPRING-DAMPING)ON RIDE COMFORT
In this subsection, the influence of the passive system on ride comfort is studied, because the passive system is part of the proposed actively-passively suspension, and the vibration isolation system is rarely used in traditional robots. In the simulation, the posture cannot be changed, so the 7 DOF and 3 DOF dynamic model shown in Figs. 18(a) and 18(b), respectively, can be used to compare the influence of the passive system on ride comfort [46], [47], and the corresponding equations are shown in Eqs. (27)(28)(29)(30)(31)(32)(33)(34)(35). The 7 DOF model represents the robot with the spring-damping system that is regarded as an elastic component, and the 3 DOF model represents the robot with the spring-damping system that is regarded as a rigid body. In the simulation, the ramp terrain is input to each tyre, the slope of the terrain is 1, −1,1 and −1, respectively, and the interval time of input is 1s.
The flow chart and simulation model are presented in Figs. 19(a) and 19(b), respectively, and the results are shown in Figs. 20(a) and 20(b). The results illustrate that the posture angular acceleration is significantly reduced by 46.7% on average, which means the passive system of the proposed suspension can effectively improve the ride comfort of FWLR in unstructured terrain. These findings occur because the ground impact is absorbed by the passive system, and the impact energy is dissipated into the air in the form of thermal energy.
Overall, both the active system and passive system of the suspension proposed in this article can improve the ride comfort of the robot in unstructured terrain.

1) 7 DOF MODEL
The equations of the vertical motion of the tyres, i = (1∼4) is given by The equation of the vertical motion of the body is given by The equation of the pitch motion of the body is given by The equation of the roll motion of the body is given by The matrix expression of 7 DOF is given by 2) 3 DOF MODEL The equation of vertical motion of the body is given by The equation of the pitch motion of the body is given by The equation of the roll motion of the body is given by The matrix expression of 3 DOF is given by

V. CONCLUSION
This article for the first time proposed and developed a novel reconfigurable hybrid wheel-legged mobile robot. The posture control and ride comfort of FWLR in unstructured terrain can be achieved by the actively-passively suspension system of each leg at the same time. The suspension system is composed of an actuator and spring-damping system, respectively, and they are connected in series. In addition, the design concept of FWLR is universal, it can be used for the design of other types of robots and vehicles The closed-loop and decoupled dynamic model of posture control is formulated, with which the LQR controller with SLPF is proposed. The simulation and experimental results show that the posture angles in unstructured terrain are significantly reduced by more than 50%. On the other hand, the frequency response is analyzed, the results present that the posture angles are reduced by more than 50% in low-frequency unstructured terrain. In addition, the ride comfort performance of FWLR is validated by different dynamic models proposed in this article, the results indicate that both the posture control and passive system of FWLR can improve the ride comfort by more than 15% and 40%. Overall, the novel wheel-legged robot, control model and algorithm proposed in this article can improve the problems of posture control and ride comfort of traditional robots.
The research of this article has positive reference significance and potential practical value for developing the mechanism design and promoting the engineering application of wheel-legged robots. The future work of this research is to realize automatic driving and keep balanced posture in unstructured terrain by equipping with environment sensing system.