In order to accomplish exploration missions in complex environments, a new type of robot has been designed. By analyzing the characteristics of typical moving systems, a new mobile system which is named wheeltracked moving system (WTMS) has been presented. Then by virtual prototype simulation, the new system’s ability to adapt complex environments has been verified. As the curve of centroid acceleration changes in large amplitude in this simulation, ride performance of this robot has been studied. Firstly, a simplified dynamic model has been established, and then by affecting factors analysis on ride performance, an optimization model for suspension parameters has been presented. Using NSGAII method, a set of nondominated solutions for suspension parameters has been gotten, and by weighing the importance of the objective function, an optimal solution has been selected to be applied on suspension design. As the wheeltracked exploration robot has been designed and manufactured, the property test has been conducted. By testing on physical prototype, the robot’s ability to surmount complex terrain has been verified. Design of the wheeltracked robot will provide a stable platform for field exploration tasks, and in addition, the certain configuration and suspension parameters optimization method will provide reference to other robot designs.
An exploration robot is usually used to work in complex environments. Its abilities related to obstacle climbing, flexible steering, and passive adaptation should be improved in order to perform exploration tasks smoothly [
The slope inclination angle that the robot can climb up should be no less than 35°; the height of barriers that it can cross over should be no lower than 160 mm, and the width of ditches should be no less than 100 mm.
The mass of the robot should not exceed 20 kg and can be carried by one man. And it should be designed with following dimensions: the length
The robot can passively adapt to different terrains and is easy to control.
In order to perform exploration missions in complex environments, it is very important to design the structure of the mobile system. By now, there are many types of mobile structures such as leg [
As different structures have their own characteristics and can adapt to diverse terrains, four typical structures have been analyzed in this paper, and according to the design objects, two new structures have also been proposed. Then, we select out a suitable structure for the field exploration robot based on the six mobile systems.
The rocker bogie mobile system has been used in space explorations [
This type of mobile system can be used for field explorations for it is easy to control, has characteristics of simple structures, and can move at high speeds. There is a differential balance mechanism in wheeledrocker bogie mobile robot. Using this mechanism, the rotation movement at left and right suspension rockers can be transferred to the bodywork. The mechanism makes the robot more stable and enables it to surmount obstacles and resist turnovers in a better way.
Because of the bogie connecting to the two front wheels, the height of the bogie should exceed the height of the obstacles, which is expressed as
The rocker bogie mobile system.
There are other forms derived from the sixwheel suspension system. As shown in Figure
Sixwheel positive and negative quadrilateral suspension system.
Sixwheeled and double crank slider suspension system.
Planetary wheeled mobile system [
The planetary wheeled mobile system.
Structure of the planetary wheeled system.
There are some forms derived from the tracked robot, as this type of mobile system can adapt to complex environments and has good ability of maneuverability. It has been widely used for field explorations. The MROBOTI was designed by Nanjing University of Science and Technology [
Structure of the tracked mobile system MROBOTI.
In this system, there are oscillating arms at both sides. The robot can adapt to different terrains due to the rotation of the oscillating arms which are interactive with the tracked wheels. Some other tracked mobile systems have structures that are different from the MROBOTI, but they all need to improve their passive adaption ability in complex terrains.
The wheellegged mobile system can adapt to complex environments by changing the posture of the legs. Its moving efficiency is improved because of the wheels installed at the end of the legs.
By mechanism synthesis [
The model of the sixwheellegged mobile system.
In this exploration robot, there are two assistant wheellegs in the head. As the assistant wheelleg is a fourbar linkage mechanism, it can rotate to the top of obstacles and help the robot to stride across complex terrains. However, this type of moving system can not adapt to uneven terrains actively, so we should search for a new moving system.
In order to combine advantages of the above mobile systems and to improve the passive adaption ability of the robot, we have designed a new type of moving system, called the wheeltracked mobile system (WTMS), as shown in Figure
Schematic diagram of the wheeltracked exploration robot.
In this mobile system, both left and right rocker suspensions are connected to the bodywork through a differential balance mechanism, which can decrease the pitching angle of the bodywork and, accordingly, reduce impacts coming from rough terrains. Compared to the track system, this compound system can reduce the ground contact area and thus can improve the steering performance. Since the new system has the above characteristics, it is suitable for field exploration tasks.
In order to validate the locomotion ability of the wheeltracked exploration robot in rough terrains, we build a 3D simulation model of the robot by using Recurdyn and carry out the dynamic simulation in a virtual environment, as shown in Figure
Virtual prototype of the wheeltracked exploration robot.
We can see from the simulation that the passing ability of the wheeltracked exploration robot is better and its components work well without interference. In this simulation, the maximum height of barriers is 180 mm, the maximum width of the channel is 150 mm, and the maximum angle of the slope is 40°. This simulation verifies that the new system is able to adapt to complex environments.
From the simulation we also get the acceleration curve of body center mass in vertical direction, as shown in Figure
Acceleration curve of the bodywork centroid in vertical direction.
From the curve we see that the acceleration change in amplitude is large, which is mainly caused by uneven road conditions. In order to provide a good environment for automotive instruments and equipment, parameters of the wheeltracked mobile robot’s suspension should be optimized to get a stable platform for field explorations.
Ride performance is an important vehicle property. For a vehicle, good ride performance can make passenger comfortable, ensure goods not to be damaged in transportation, and prolong components’ fatigue life. In the exploration robot, good ride performance is also very important for exploration tasks. Therefore, making study on the ride performance of the wheeltracked exploration robot is very important to improve its exploration abilities.
Firstly, we should analyze the factors infecting the ride performance of the wheeltracked exploration robot. When the robot walking on an uneven road, the road roughness and the robot’s speed will be the input of this system. The input is then transferred by the vibration system which consists of rear wheel, front wheel, suspension and unsprung mass, and other elastic and damping components. Finally, the acceleration at centroid position is obtained as the output, and how to control the body output acceleration in a certain circumscription should be discussed.
The structure of the wheeltracked robot should be simplified as it is a complex vibration system. Figure
3D dynamic simplification model of the wheeltracked exploration robot.
The wheeltracked exploration robot is a symmetrical system, so the vibration system can be simplified into a plane model, as shown in Figure
Plane model of the wheeltracked exploration robot.
In Figure
To establish the vibration equation for
As pointed in literature [
From Figure
Assume that the maximum rotate angle of the front bearing wheel is
Motion position of the bearing wheel.
Figure
Vibration model of the front wheel.
The Kinetic equation for the front wheel system can be expressed as
Then, (
Assume that the ratio of the spring stiffness
Frequency response function can be defined as the road displacement excitation function about the displacement
Given
Using the linear relationship between
At the same time, the suspension system of the rear wheel can be simplified as vibration system that has two degrees of freedom, as shown in Figure
Vibration model of the rear wheel.
Using the same method, the amplitudefrequency characteristic of
In the WTMS, there are two inputs
By calculation, the selfspectral density of robot centroid can be written as
Pavement power spectral density is mainly used to describe the statistical characteristics of road roughness. According to GB703187 “Vibration Input of Vehicles—Pavement Roughness Representation” [
This expression is complex to calculate because the mean square value of body acceleration is
Between the wheels and the ground exists a relative dynamic load due to the influence of uneven incentives. If the dynamic load exceeds the gravity load, the pressure acting on the ground from the wheels will be negative, which will generate influences on the adhesion and the robot can not move ahead. To improve the adhesion ability, the dynamic load acting on wheels should be controlled reasonably. Because the adhesion ability on the front wheel acts as a decisive role in the whole robot system, the dynamic load on the front track wheel needs to be investigated.
The relative load is defined as
From (
From the balance position of robot bodywork, the maximum compression stroke of suspension allowed is the limit travel
According to the structural design, spring damper of the connection position, which connects arm suspension and front track wheel suspension, creates a certain angle with vertical direction. In the simplified vibration model, the deformation in the vertical direction, which is equivalent dynamic deflection
When the maximum of equivalent dynamic deflection
Assuming
Similarly, the amplitudefrequency characteristic of front wheel track suspension equivalent dynamic deflection to road input can be calculated in the same way as follows:
Thus, the maximum limit travel of the rear wheel is
The robot suspension flexibly connects bodywork, the front wheel and rear wheel flexibly, and it can transfer the force and torque between the bodywork and the wheels. The suspension can also reduce the impact and vibration of bearing system caused by uneven pavement, so as to ensure the ride performance of the robot and provide a stable work platform for the vehicle instrument and equipment.
The evaluation of ride performance of the robot can be achieved by optimizing spring stiffness and damping constant of damping element of suspension based on the mission execution conditions. Therefore, establishing an ideal ride performance evaluation system of robot is the basis of optimizing suspension parameters. In order to make a scientific evaluation of ride performance, the establishment of suspension parameter optimization model of the wheeltracked robot, the ascertainment of corresponding design variables, and the objective function and the constraint conditions are all necessary.
As the quality of bodywork and front wheel track is given, and the equivalent stiffness coefficient between track wheel and ground is approximately constant, the stiffness coefficient and damping coefficient of the suspension will have an impact on the maximum of body acceleration and dynamic load. In order to improve the ride performance, the suspension spring stiffness coefficient and damping element of the wheels should be optimized. And the design variables of robot suspension are determined to be the equivalent stiffness coefficient of the suspension spring in front wheel track
Generally, the ground condition on which the wheeltracked robot works is complicated and harsh. However, with the designed autonomous obstacle avoidance system of robot, the real ground condition is good. Therefore, the ground condition of robot chosen is level
According to the above analysis, the mean square value of the body acceleration with random road input, the mean square value of the front wheel track dynamic load, and the influence of suspension dynamic deflection on ride performance of the wheeltracked robot are, respectively, calculated and analyzed. Besides, according to the analysis of suspension mechanics, the improvement direction of the wheel dynamic load is consistent with the improvement direction of body acceleration in low frequency, while in high frequency, they improve in the opposite direction. The improvement direction of the wheel dynamic load is opposite to the improvement direction of the dynamic direction.
Therefore, those evaluation indexes of the robot ride performance are irreconcilable in the optimization process of suspension parameters. According to the analysis of factors influencing the properties, the evaluation statistics of the robot are ascertained as the effective value
Performance parameters of the wheeltracked robot.
Name of relevant parameters  Parameter values  Unit 

Suspension quality of front wheel ( 
10.5  kg 
Suspension quality of rear wheel ( 
13.5  kg 
Quality of front wheel track ( 
5.5  kg 
Quality of rear wheel ( 
2.5  kg 
The equivalent stiffness coefficient of the front wheel track relative to ground ( 

N/m 
The stiffness coefficient of the rear wheel track relative to ground ( 

N/m 
The equivalent stiffness coefficient of the spring before optimization of the position connecting the front wheel and suspension ( 

N/m 
The equivalent damping coefficient of the damping element before optimization of the position connecting the front wheel and suspension ( 
164  Ns/m 
The equivalent stiffness coefficient of the spring before optimization of the position connecting the rear wheel and suspension ( 

N/m 
The equivalent damping coefficient of the damping element before optimization of the position connecting the rear wheel and suspension ( 
200  Ns/m 
In order to maintain mechanical safety, machinery, and practicality in the structural design, the design variables and system state variables must satisfy certain conditions. Those conditions are the constraints. The constraints of design variables of the wheeltracked robot are as follows.
The natural frequency of bodywork for the WTMS is
Reducing the natural frequency
According to the provided processing conditions, the damping ratio range which may be chosen of damping element is fixed. The front robot suspension spring damping ratio
Ratio
Parameter optimization of the suspension system is a multiobjective constrained optimization problem, and the objective function is a nonlinear function. The traditional method to deal with this kind of multiobjective optimization problem is to construct an effect function and then convert the multiobjective optimization problem into a single objective optimization problem. Although the method to solve single objective optimization problem is mature, this optimization process cannot guarantee the optimality of Pareto.
Multiobjective genetic algorithm simulates the evolution process, which processes a population and generates a large number of noninferior solutions in an optimization process, so that it can find the approximate Pareto optimal solution of multiobjective optimization problems. In addition, it is a simple, general, good robustness, parallel search algorithm for global optimization processing mechanism. Pareto solutions can be defined as follows: if
By analysis, we use NSGAII method to optimize parameters of the suspension. As the design variables, objective function and constraint conditions have been described, the operation parameter should be set, and constraint conditions should be processed before the implementation of genetic algorithm optimization.
Formula ① is linear constraints which can be converted to
After setting operating parameters and processing constraint condition, the design variables are optimized by NSGAII method. The genetic algorithm meets the termination conditions and the evolution stops after 239 generations. The individual average distance is shown in Figure
The individual average distance in the process of evolution.
From Figure
Figure
Pareto frontier.
The initial design variable
According to the above analysis, the optimization results meet the design requirement and will be referred to as the suspension design parameters of WTMS. Due to the above analysis of the stiffness and damping coefficients which are equivalent, those equivalents should be converted in the actual structure design.
According to the proposed design program and optimization parameters on the suspension system, an experimental prototype has been manufactured, shown in Figure
Physical prototype for wheeltracked exploration robot.
Trench crossing test of the wheeltracked robot was performed by gradually increasing the distance between two objects. The front track wheel can smoothly cross the trench, but because of the size restrictions of the rear wheel, it becomes difficult to cross the trench gradually. After testing, the maximum width of the trench that the robot can smoothly cross is 150 mm, and the maximum height of barriers that can be spanned is 180 mm, which are both identical with simulation. Climbing test was carried out on indoor oblique board. The robot climbing performance is tested by changing the angle between the board and the floor. In the process of increasing board slope, the robot’s climbing difficulty increases gradually. When the angle of the slope is greater than 42°, the climbing movement appears as the phenomenon of slipping obviously. As the maximum angle in numerical simulation is 40°, the robot’s adhesion ability on the slope is improved compared to simulation. This is because the contact area on the track is larger than 3D model actually. It also shows that the bodywork is smooth in the rugged road, reflecting the robot ride performance is still good on uneven pavement condition, but further tests will be done to verify the ride performance of new suspension systems.
In this paper, a new mobile type of wheeltracked system has been designed, and by using virtual prototype, the property of this robot has been verified preliminarily. However, the ride performance of the mobile system was found to be poor by simulation, then suspension parameters optimization has been done, and, at last, the new type robot has been manufactured and the tests have been carried out. The result is as follows:
The typical mobile system has been analyzed, and by combining the advantages of these systems, the wheeltracked mobile system has been designed. Virtual simulation shows that the maximum height of barriers that the robot can cross is 180 mm, and the maximum width of the channel that can be crossed is 150 mm, and the wheeltracked structure project can satisfy the basic exploration requirements.
The rear wheel system and the front wheel system have been simplified; then the plan model for wheeltracked system has been established, which provides new ways for the establishment of dynamic models for complex suspension systems.
Based on the system’s dynamic model, ride performance of the exploration robot has been analyzed, and the optimization model has been established. By using NSGAII method, key parameters for suspension system have been obtained. Comparing to initial suspension parameters, effective value of bodywork acceleration
According to the design structure and optimization parameters for the suspension, physical prototype has been processed and tests have been carried out accordingly. By the tests, the maximum width of the trench that the robot can smoothly cross is identical to prototype simulation, while the climbing test shows the maximum angle of the slope that can be climbed up is 42°, which is larger than the numerical value in prototype simulation.
The authors declare that there is no conflict of interests regarding the publication of this paper.
This work was supported by Grant no. LQ15E050004 (study on the stability of mobile robot for seafloor exploration, supported by Natural Science Foundation of Zhejiang Province). Some of the simulation analysis was supported by Grant no. 2014A610081 (a fourlegged climbing wall robot based on Flexible Biomimetic adsorption unit, supported by Natural Science Foundation of Ningbo). The experiment work was also supported by Natural Science Foundation of Jiangsu Province (BK20130999), the Natural Science Foundation of Colleges and Universities in Jiangsu Province (13KJB460012), and the China Science Foundations (61203327, 51405243). The authors would like to express appreciation for their assistance and attention.