When stability function   0 sϕ > ,the robot will be considered  stabilization, when  0 sϕ ≤ , the robot will be overturn. Stabilization boundary of the robot is defined that the minimum of iθ  should be greater than zero according to the stability function. Ⅲ. TRACTION ANALYSIS  Fig.4 shows traction characteristic analysis of the wheel-legged robot iV — iiiVWU =× , the local wheel-ground points coordinate system ( , , , ) iiiiiR PU VW = , which satisfies the right-hand rule. if —Contact force vector for iP ,which is decomposed as  (, , ) iuiviwif fff = along with the part coordinate system,  wif －normal vector of contact plane,； uif －tangent vector for if ； vif －ponderance for if along with direction of axle .  Fig.4 Traction characteristic analysis velocity of iP  is shown with symbol (/ ) iW VP R , physics meaning for each ponderance of   (, , ) iuiviwif fff =  follows： (/ )0 wi i W fVP R = , expresses continuum contact between wheels and ground, (/ )0 ui i W fVP R = , expresses nonskidding on direction X , (/ )0 vi i W fVP R = , expresses nonskidding on directionY , Contact complexion between each wheel and ground can be controlled by driving { } 1234 ,,, αααα , therefore, (, , ) iuiviwif fff =  can be changed based on the change of contact position by controlling   iα , which is the function of iα . It can be found from driving power of robot that normal vector wif and  tangent vector uif   affect its traction characteristic, therefore, traction characteristic is evaluated by slide ratio iS , which is defined the ratio between tangent vector and normal vector:   22ui viiwif fSf+=                             （2） Traction efficiency relates to skid characteristic  of each wheel-ground contact point,  minishing  skid equals to letting  iS  be the least, therefore, to each wheel-ground contact point iP，increasing its driving characteristic means to let iS  be the least, to the robot increasing its driving characteristic means to let the maximum iS  be the least, then driving characteristic function can be defined :  { } min max( ) fiS φ =             
（3）  The meaning of this function is that the maximum iS  is set to the least. Stability control steps are as follows: (1) During  the current control period, the  value of each iα can be  measured  by encoders of arm，or can be calculated with robot gesture information such as Roll angle ϕ , Pitch angle ψ  and Yaw angle θ   measured by  sensors located on the robot body. (2) Combining measurement value of  iα  and kinetics model, decomposed  vector of  contact force  (, , ) ui vi wif ff  can be calculated, utilizing equation 22ui viiwif fSf+= , then the contact point max iP of the maximum iS  can be found. (3) The value of iα   is set to the target value when iS  is calculated to be the least value. (4) The control value iα  can be achieved with measurement and target value of iα , then motor of wheel-leg joint atmax iP   is controlled correspond. Ⅳ. CONTROL FOR COUPLED OPTIMIZATION A.  Function of Coupled Optimization For a given set of posture parameter p (which depends on the particular design of the vehicle), the aim of the optimization process is to find the optimal posture vector p which minimizes an objective functionΦ . Control method for coupled optimization is advanced based on the analysis of the stability function and the driving characteristic function; coupled optimization control function can be expressed with weighed mean-square-root sum of stability function and driving characteristic function: 22 121 ()nn SfiiP KKSθΦ= + ∑∑            （4）                Where iS is a function of if  , iθ  is a function of ir  (the vector connecting the CoG to each contact point), and sK ,fK   are constant positive weighting factors. Minimizing this function leads us to maximize all iθ  (i.e., the margin stability) and to minimize all  iS (i.e. the robot slippage). It  can be found from above analysis that  changes of (, , ) iuiviwif fff = and  ,( 1,2,3,4) ii θ = follows with change of  iα , wif 、 uif 、 vif  、 iθ are the functions about iα , therefore , coupled optimization control function  () P Φ  is expressed with iα  which can be controlled by adjusting. However, in order to evaluate the objective function, we need information about the local terrain map to define the contact points iP and the associated normal vectors. As the terrain map is generally unknown, iP  and normal vectors have to be evaluated online. Thus, the main drawback of this method lies on its practical issues: measurement of the contact normal and computational cost of the online optimization process. Thus, for the practical implementation of the posture control algorithm on the robot, a suboptimal solution is proposed in the next section. B.  Coupled Optimization Control  During the coupled optimization control, stability should be judged firstly, if   0 sϕ ≤ , stability should be controlled，otherwise, driving traction characteristic should be controlled, (1) Stability control: joint angle is controlled to stabilize status according to the difference between target angle and measurement angle which can be calculated with the robot gesture information.  (2) Traction  control： control steps are as the above introduced in driving power analysis. Stability control steps are as follows in Fig.5:  (1) Corresponding relation list should be set firstly used to conserve the weighed coefficients sK ,fK , roll angle ϕ , pitch angle ψ  and yaw angleθ , considering  yaw angleθ  does not affect the stability of robot ,therefore , sK ,fK  corresponding roll angle ϕ  and pitch angle ψ are conserved in the list. During this step, target joint angles with stability status are set as 0 iα ( 10 α 、 20 α 、 30 α 、 40 α ), when robot moves on the flat, target joint angle adopts the beforehand-enactment 0 iα ( 10 α 、 20 α 、 30 α 、 40 α ), when moves on the slope , target joint angle equal  the sum of  advanced enactment 0 iα  and pitch angle ψ . Corresponding relation list setting rules are as follows: when all of the roll angle ϕ and  pitch angle ψ are less than beforehand-enactment 0 iα , sK  should be the least, but cannot equal  zero , when each of  the roll angle ϕ and  pitch angle  ψ  is higher than beforehand-enactment 0 iα ,fK  should equal  zero. (2) the roll angle  ϕ and  pitch angle  ψ  should be achieved termly with sensors , then  look  up  the corresponding relation list to get the value of sK  ,fK , (3)during every control period , joint angle iα  of each wheel leg can be calculated with the robot gesture which can be advanced with sensors located on the robot or encodes on the motors  (4) 1 θ ， 2 θ ， 3 θ  and 4 θ  can be calculated with  the gesture information and  geometry relation between contact point  iP and center of mass G, then determine min{ , 1, 2, , } siin ϕθ = = ⋅⋅⋅  and fK ,If 0 fK = or 0 fK ≠  and  0 sϕ ≤ ,executes the next step (5) to control its stability, if  0 fK ≠  and  0 sϕ > ，executes the step (6) to control its driving traction. (5) After having determined the robot to be instability, the difference between measurement value in step (3) and target angle in step (1) is set as the control value of the joint angle. During the control period, joint angle of one leg is controlled, and one control process has been finished. During the next three control periods, three other legs will be controlled. (6) After having determined the robot to be stability,  decomposing vector  (, , ) ui vi wif ff  at contact point iP  can be achieved with the measurement value of joint angle and kinetics model，then iS  can be calculated with equation 22ui viiwif fSf+= ,from which wheel-ground contact point max iP  corresponding to the max iS  can be found . (7) The value of joint angle with the minimum  () P Φ  calculated is set as the target value for max iP  in step (6) (8) The wheel leg joint at max iP  is controlled based on the control value achieved from measurement value and target value, since then one control process has been finished. Control system has been advanced based on the above analysis which controls every motor with Fuzzy Neural Network to change coupled optimization function.  The control system (Fig.6) consists of four parts such as apperceive system, organization and coordination unit, decision-making unit and execution unit and the work process is as follows:  The original gesture, locomotion parameters such as roll angleϕ , pitch angleψ , yaw angleθ  and force information can be achieved with apperceive system, which are transformed and transferred to decision-making unit by coordination unit, then decision-making is transferred to corresponding motor. 1 θ ， 2 θ ， 3 θ  and 4 θ  can be calculated with apperceive information by decision-making unit. determine  min{ , 1, 2, , } siin ϕθ = = ⋅⋅⋅  and fK , if 0 fK = or 0 fK ≠  and  0 sϕ ≤ , executes stability control, if 0 fK ≠  and  0 sϕ > ，executes driving traction control. Corresponding relation list settingWheel-leg angle settingRoll angle and  pitch angle AchevedLookuping corresponding relation listEach measurement valueof joint angle calculated123θ1~θ4 calculatedΦs<0? ,Kf=0?0 fK =0 fK ≠ 0 sφ <0 sφ ≥ 0 fK ≠ or 移动机器人英文文献和中文翻译(2):http://www.youerw.com/fanyi/lunwen_42976.html