**5. Risk factors**

In the present study, 80 of the pregnancies (70.7%) were without risk factors, and only 33 (29.3%) were under the influence of such. The risk factors were grouped into three categories: obstetric risk factors from past events, risk factors due to diseases of the mother, and exogenous risk factors.

The term of pregnancy termination is presented in **Figure 1**. Most interrupted pregnancies are between the 20th and 24th gestational weeks. Six pregnancies were carried to birth.

**6. Anthropometric characteristics of the fetuses**

the smallest fetus being 13 gestational weeks (**Figure 1**).

**7. System anomalies of the fetus**

**Figure 2.** Motives for pregnancy termination.

in **Table 1**.

**Distribution of lethal hydrocephalus by gender (sex ratio).** The genders were equally affected, but the mean weight of male fetuses (842.17 ± 115.2) was less than that of female fetuses (892.06 ± 101.1), without the difference being statistically significant (*u* = 0.51, *p* > 0.05). **Age of the fetus.** The average pregnancy term in the entire study is 24 ± 0.45 gestational weeks. The fetal expulsion in two-thirds of the cases occurred before the 24th gestational week, with

Correlations between Ultrasound and Pathology in Fetal Ventricular System Anomalies

http://dx.doi.org/10.5772/intechopen.71934

75

**Fetus weight.** The average weight of the fetuses is 865.99 ± 809.8 g with a range of 23–3800 g. It is worth noting that 50 fetuses (44.2%) weigh less than the corresponding gestational age.

The head, extremities, and respiratory system anomalies associated with FHLO are presented

The cardiovascular system abnormalities are a total of 32 and are from all groups. The digestive system abnormalities are 56 and are broken down into groups: mesenteric (affecting the small intestine and colon), parenchymal (affecting the liver and spleen), anal imperforation (affecting the terminal part of the intestines), gall bladder agenesis, and situs inversus. The parenchymal and mesenteric abnormalities are evenly distributed. The gender abnormalities are present in both male and female fetuses with a ratio of female to male of 8:7. Hermaphroditism was established in four (3.5%) fetuses. The fatal hydrocephalus-associated anomalies of the

cardiovascular, digestive, excretory, and genital systems are presented in **Table 2**.

**Motives for pregnancy termination.** Interruption of pregnancy due to medical reasons was performed in 87 cases (77%); spontaneous abortions were 13 (11.5%), and there was 1 voluntary abortion (0.9%). There were 2 live births (1.8%) and 2 stillbirths (1.8%). In eight of the cases (7%), there is no information on the motive for pregnancy interruption (**Figure 2**).

**Figure 1.** Term of pregnancy termination.

Correlations between Ultrasound and Pathology in Fetal Ventricular System Anomalies http://dx.doi.org/10.5772/intechopen.71934 75

**Figure 2.** Motives for pregnancy termination.

**5. Risk factors**

(1.8%), and epilepsy—3 (2.7%).

74 Congenital Anomalies - From the Embryo to the Neonate

**Figure 1.** Term of pregnancy termination.

In the present study, 80 of the pregnancies (70.7%) were without risk factors, and only 33 (29.3%) were under the influence of such. The risk factors were grouped into three categories: obstetric risk factors from past events, risk factors due to diseases of the mother, and exogenous risk factors.

**1. Obstetric risk factors.** This group includes spontaneous abortions—13 (11.5%), voluntary abortions—1 (0.9%), birth of a child with malformations—11 (9.8%), stillbirths—2 (1.8%),

**2. Endogenous risk factors.** The risk factors from the mother include maternal age, hypertension—1 (0.9%), diabetes mellitus—2 (1.8%), bronchial asthma—2 (1.8%), thalassemia—2

**3. Exogenous risk factors.** Exogenous risk factors for the pregnancy include pregnancies carried in geographical areas near mines and underground mineral water deposits and consanguineous marriages. In our study, the pregnancies from geographic regions with mining and underwater mineral water deposits were 5 (4.4%). Supplementation with folic acid is mandatory in Tunisia and Bulgaria. There were no women without folic acid supplementation.

The term of pregnancy termination is presented in **Figure 1**. Most interrupted pregnancies are

**Motives for pregnancy termination.** Interruption of pregnancy due to medical reasons was performed in 87 cases (77%); spontaneous abortions were 13 (11.5%), and there was 1 voluntary abortion (0.9%). There were 2 live births (1.8%) and 2 stillbirths (1.8%). In eight of the cases (7%), there is no information on the motive for pregnancy interruption (**Figure 2**).

between the 20th and 24th gestational weeks. Six pregnancies were carried to birth.

multifetal pregnancy—2 (1.8%), and multi-year sterility—4 (3.5%).


*2.1. Propagation of Ultrasonic Waves in Linear-Elastic Material*

Generally, an anisotropic body, e.g., crystal of defined symmetry, can be the solid medium. The propagation of waves in the anisotropic medium, particularly velocity, depends on the direction relative to the axis of coordinates usually related to the crystallographic arrangement that corresponds to the given symmetry. Hooke's law [15] describes elastic properties of the anisotropic arrangement in the linear relationship between the stress tensor σij and the deformation tensor εkl in the following way:

$$
\sigma\_{i\bar{j}} = \mathcal{c}\_{i\bar{j}k\bar{l}}\varepsilon\_{k\bar{l}} + \mathcal{c}\_{i\bar{j}k\bar{l}m\bar{u}}\varepsilon\_{k\bar{l}}\varepsilon\_{m\bar{u}} + \dots \tag{1}
$$

where: σi—components of stress state, εkl—components of deformation state.

Both quantities are symmetric tensors of second rank, which means they can have six independent components. Coefficients *c*ijkl and *c*ijklmn are constants of elasticity of second or third rank, respectively. They are symmetric tensors of fourth and sixth rank, respectively. The linear theory of elasticity assumes

materials are elastic, and the relationship between stress and deformation is linear. All constants of elasticity of third order or higher are neglected. Even for such a simplification, the number of tensor components *c*ijkl defining elastic properties is 36, but the number of independent components is 21. In the case of orthotrophic materials with three mutually perpendicular planes of symmetry, elastic properties are described by nine independent constants of elasticity in the following form:

$$c\_{ij} = \begin{bmatrix} c\_{11} & c\_{12} & c\_{13} & 0 & 0 & 0\\ c\_{12} & c\_{22} & c\_{23} & 0 & 0 & 0\\ c\_{13} & c\_{23} & c\_{33} & 0 & 0 & 0\\ 0 & 0 & 0 & c\_{44} & 0 & 0\\ 0 & 0 & 0 & 0 & c\_{55} & 0\\ 0 & 0 & 0 & 0 & 0 & c\_{66} \end{bmatrix} \tag{2}$$

Regarding isotropic materials with the infinite number of axes of symmetry planes, elastic properties can be comprehensively described by two independent constants of elasticity *c*12 and *c*44. Other matrix coefficients (2) can be expressed as linear combinations using the Lamé coefficients:

$$\mathfrak{c}\_{11} = \mathfrak{c}\_{22} = \mathfrak{c}\_{33} = \lambda + 2\mu,\ \mathfrak{c}\_{12} = \mathfrak{c}\_{23} = \mathfrak{c}\_{23} = \lambda,\ \mathfrak{c}\_{44} = \mathfrak{c}\_{55} = \mathfrak{c}\_{66} = \mu. \tag{3}$$

The force acting on any volume element in the solid medium, in which the disturbance is observed, can be expressed as the gradient of stress caused by the disturbance [1]. The Equation of the particle motion representing the equilibrium state between the restoring force and the inertial force is expressed by the following Equation:

$$
\rho\_0 \frac{\partial^2 \underline{\xi}\_i}{\partial t^2} = \frac{\partial T\_{ij}}{\partial \mathbf{x}\_j} \to \rho\_0 \frac{\partial^2 \underline{\xi}\_i}{\partial t^2} = c\_{ijkl} \frac{\partial^2 \underline{\xi}\_k}{\partial \mathbf{x}\_j \partial \mathbf{x}\_l} \tag{4}
$$

where: ρ0—density of the body in the tensionless state. The expression (4) contains the equations of three components of the displacement, which describe components of the wave equation of vector quantity ξ described by three components. Assuming that coordinates of the plane harmonic wave are expressed by the relationship ξ = ξ0*ei*(ω*t*−*kr*), Equation (4) can be expressed as:

$$-\omega^2 \rho\_0 \underline{\varsigma}\_{0i} = -c\_{i\bar{j}k} k\_j k\_l \underline{\varsigma}\_{0k} \rightarrow \left( c\_{i\bar{j}k} k\_j k\_l - \delta\_{ik} \omega^2 \rho\_0 \right) \underline{\varsigma}\_{ok} = 0 \tag{5}$$

where: ω is the wave frequency, *kj*, *kl*,—wave vector (towards *j, l*), ξ0i, ξ0k—coordinates of the plane harmonic wave (towards *i*, *k*).

Expression (5) is the system of homogeneous algebraic equations, which due to unknown ξ0k is described in the following form:

$$\begin{cases} c\_{1\bar{\jmath}1}k\_ik\_l - \alpha^2 \rho\_0 \vert \not\xi\_{10} + c\_{1\bar{\jmath}2}k\_ik\_l \not\xi\_{20} + c\_{1\bar{\jmath}3}k\_ik\_l \not\xi\_{30} = 0\\ c\_{2\bar{\jmath}1}k\_ik\_l \not\xi\_{10} + \left(c\_{2\bar{\jmath}2}k\_ik\_l - \alpha^2 \rho\_0\right) \not\xi\_{20} + c\_{2\bar{\jmath}3}k\_ik\_l \not\xi\_{30} = 0\\ c\_{3\bar{\jmath}1}k\_ik\_l \not\xi\_{10} + c\_{3\bar{\jmath}2}k\_ik\_l \not\xi\_{20} + \left(c\_{3\bar{\jmath}21}k\_ik\_l - \alpha^2 \rho\_0\right) \not\xi\_{30} = 0 \end{cases} \tag{6}$$

The system of equations is fulfilled when the determinant of the coefficients is equal to 0. The equation of third degree relevant to ω2 is the solution for the determinant. The equation contains three roots that correspond to three different waves with mutually perpendicular displacements. When the simplest case of the isotropic body and waves travelling along one axis (x3), the determinant of the Equation (6) takes the following form:

$$
\begin{vmatrix}
 c\_{44}k^2 - \alpha^2 \rho\_0 & 0 & 0 \\
 0 & c\_{44}k^2 - \alpha^2 \rho\_0 & 0 \\
 0 & 0 & c\_{11}k^2 - \alpha^2 \rho\_0
\end{vmatrix} = 0\tag{7}
$$

By solving the determinant, the following equation is obtained:

$$\left(c\_{44}k^2 - \alpha^2\rho\_0\right)^2 \left(c\_{11}k^2 - \alpha^2\rho\_0\right) = 0\tag{8}$$

It has two roots equal to ω2 1 = ω2 2 = *c*44*k*2 ρ0 , and the third one equal to ω2 3 = *c*11*k*2 ρ0 . Taking into account that *k* = ω/*C* (where *C* is wave velocity), the following roots are obtained:

$$\mathbf{C}\_1 = \mathbf{C}\_2 = \sqrt{\frac{c\_{44}}{\rho\_0}}, \mathbf{C}\_3 = \sqrt{\frac{c\_{11}}{\rho\_0}} \tag{9}$$

A solution to this issue indicates the propagation of three waves in the body. Two of them are characterized by mutually perpendicular oscillations and the same velocity *C*1 = *C*2 = *cT* is known as transverse waves as *c*44 is the shear. The third wave with the velocity *c*p is the longitudinal wave because *c*11 is constant related to the component of the normal deformation. Taking into account relationships between material constants, the following expression is obtained:

$$c\_T = \sqrt{\frac{\mu}{\rho\_0}}, c\_p = \sqrt{\frac{\lambda + 2\mu}{\rho\_0}}\tag{10}$$

Constants λ and μ can be introduced into the system of Equations (4) by replacing coefficients *c*ijkl. Then, the system of equations broken down into components is for the isotropic body as follows:

$$\begin{array}{l} \rho\_0 \frac{\partial^2 \xi\_1}{\partial t^2} = (\lambda + 2\mu) \frac{\partial^2 \xi\_i}{\partial x\_1 \partial x\_i} + \mu \frac{\partial^2 \xi\_1}{\partial x\_1 \partial x\_i} \\ \rho\_0 \frac{\partial^2 \xi\_2}{\partial t^2} = (\lambda + 2\mu) \frac{\partial^2 \xi\_i}{\partial x\_2 \partial x\_i} + \mu \frac{\partial^2 \xi\_2}{\partial x\_2 \partial x\_i} \\ \rho\_0 \frac{\partial^2 \xi\_3}{\partial t^2} = (\lambda + 2\mu) \frac{\partial^2 \xi\_i}{\partial x\_3 \partial x\_i} + \mu \frac{\partial^2 \xi\_2}{\partial x\_2 \partial x\_i} \end{array} \tag{11}$$

When the medium is incompressible (no changes in volume), the above equations give the wave equation for transverse waves in the following vector form:

$$\frac{\partial^2 \xi}{\partial t^2} = \frac{\mu}{\rho\_0} \nabla^2 \xi \tag{12}$$

where ∇2 is the Laplace operator of the second order in *n-* dimensional Cartesian coordinate system expressed as: ∇2 = Δ = ∂2 ∂*x*2 *i* + ∂2 ∂*x*2 *j* + ∂2 ∂*x*2 *k* + ... + ∂2 ∂*x*2 *n* .

Assuming the irrotational medium, the wave equation for longitudinal waves is as follows:

$$\frac{\partial^2 \xi}{\partial t^2} = \frac{\lambda + 2\mu}{\rho\_0} \nabla^2 \xi \tag{13}$$


**3.3 Stage 3**

<9> After *stage 2*, the link height of *Robot A* is set at a low position (**Figure 6**). <10> *Operator A* makes *Robot A* stop, and *Operator B* makes *Robot B* move forward. As a result, the front wheels of *Robot B* are lifted. <11> Both robots move forward. <12> The operators recognize that the front wheels of *Robot B* have passed over the step edge. The operators manipulate each joystick to adjust the difference between

*Cooperative Step Climbing Using Connected Wheeled Robots and Evaluation of Remote… DOI: http://dx.doi.org/10.5772/intechopen.90162*

the speeds of the robots, so that the front wheels of *Robot B* are placed on the upper level of the step. Here, in stages 3 and 4, if *Robot B* is faster than *Robot A*, the tilt of *Robot B* increases. If *Robot A* is faster than *Robot B*, then the tilt of *Robot B* decreases.

### **3.4 Stage 4**

<13> The operators make the robots continue to move forward. The back wheels of *Robot B* come into contact with the step. <14> *Robot A* pulls *Robot B*. *Robot A* supports the climbing of *Robot B* and *Robot A* prevents *Robot B* from tipping over backward. <15> *Robot B* climbs up onto the step. <16> Once the rear wheels of *Robot B* have reached the upper level of the step, the operators stop each robot.

### **4. Theoretical analysis**

When *Robot A* climbs a step, the body of the robot inclines, and its front wheels are lifted due to the difference in velocity between the two connected robots. When the robots are manipulated by the operators, the step climbing ability greatly influences the manipulation time.

In this section, we clarify the relationships among the robot incline, the velocity, and the manipulation time.

### **4.1 Relationships among the manipulation time, the velocity, and the height of the front wheels required to climb the step**

In **Figure 10**, Σ*B* is the basic coordinate system for the robots, where *p*0 is the origin as well as the contact position between the rear wheels of *Robot B* and the ground. In addition, *pi* (*i* = 1–5) are the joints (*p*1, axis of the rear wheels of *Robot B*; *p*2, link position of *Robot B*; *p*3, link position of *Robot A*; *p*4, axis of the rear wheels of *Robot A*; *p*5, axis of the front wheels of *Robot A*; *p*6, tread position of the front wheels of *Robot A*).

The position vectors for the joints in the coordinate system Σ*B* are expressed as *Bpi*¼ *xi yi* � �*T* (*i* = 1–6). In the local coordinate system, for the case in which Σ*i* is parallel to Σ0, 0*p*1 ¼ ½ � 0*RB T*, 1*p*2 ¼ ½ � *lB* þ *lLBhLB T*, 2*p*3 ¼ ½ � *d* 0 *T*, 3*p*4¼ ½ � *lLA* �*hLA T*, 4*p*5 ¼ ½ � *lA* �*RA* þ *rA T*, and 5*p*6 ¼ ½ � *rA* 0 *T* (**Figure 10**). Then, *ϕi* is the angle between Σ*i* and Σ*i*�1, and Σ1 is parallel to Σ0 in *stage 1*. Thus,

$$
\phi\_1 = 0 \tag{1}
$$

The incline of *Robot A*, P3 *k*¼1*ϕi*, is

$$\sum\_{k=1}^{3} \phi\_i = \phi\_2 + \phi\_3 \tag{2}$$

Here, Σ4 is always parallel to Σ3:

$$
\phi\_4 = 0 \tag{3}
$$

In the basic coordinate system Σ*B*, the homogeneous transformation matrix *BT*4 is as follows:

supports the climbing of *Robot A*, and *Robot B* prevents *Robot A* from tipping over backward. <7> *Robot A* climbs up onto the step. <8> Once the rear wheels of *Robot*

<9> After *stage 2*, the link height of *Robot A* is set at a low position (**Figure 6**). <10> *Operator A* makes *Robot A* stop, and *Operator B* makes *Robot B* move forward. As a result, the front wheels of *Robot B* are lifted. <11> Both robots move forward. <12> The operators recognize that the front wheels of *Robot B* have passed over the step edge. The operators manipulate each joystick to adjust the difference between

*A* have reached the upper level of the step, the operators stop each robot.

**3.3 Stage 3**

**86**

**Figure 9.**

*Entire process of step climbing.*

*Industrial Robotics - New Paradigms*

*Industrial Robotics - New Paradigms*

$$\begin{aligned} \,^B T\_4 : \begin{bmatrix} \cos \phi\_{23} & -\sin \phi\_{23} & \varkappa\_4 \\\\ \sin \phi\_{23} & \cos \phi\_{23} & \varkappa\_4 \\\\ 0 & 0 & 1 \end{bmatrix} \end{aligned} \tag{4}$$

Thus, we have:

*DOI: http://dx.doi.org/10.5772/intechopen.90162*

Here

*Bp*6¼ *x*6*y*6 � �*T*

and

where

**89**

Thus, we have:

sin *ϕ*2 ¼ *hLA* cos *ϕ*23 � *lLA* sin *ϕ*23 � *hLB*

*Cooperative Step Climbing Using Connected Wheeled Robots and Evaluation of Remote…*

q

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 � sin 2

cos *ϕ*2356 � sin *ϕ*2356 *x*6 sin *ϕ*2356 cos *ϕ*2356 *y*6 0 01

From (1) and (3), when *p*6 (the tread position of the front wheels of *Robot A*,

*x*6 ¼ *lA* cos *ϕ*23 � �ð Þ *RA* þ *rA* sin *ϕ*23 þ *lLA* cos *ϕ*23

*y*6 ¼ �*rA* þ *lA* sin *ϕ*23 þ �ð Þ *RA* þ *rA* cos *ϕ*23 þ *lLA* sin *ϕ*23

sin *ϕ*23 ¼

� � þ *lA*

, **Figure 10**) is at the bottom of the front wheels, P5

*ϕ*2

cos *ϕ*235 ¼ 0 (12)

sin *ϕ*235 ¼ �1 (13)

þ*hLA* sin *ϕ*23 þ *lB* þ *lLB* þ *d* cos *ϕ*2 (14)

�*hLA* cos *ϕ*23 þ *hLB* þ *RB* þ *d* sin *ϕ*2*:* (15)

*y*6 ¼ *lA* sin *ϕ*23 þ �ð Þ *RA* þ *rA* cos *ϕ*23 þ *RB* � *rA* (16)

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

2 � *e*1 � *y*6 � �2 q

2 (18)

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 � cos 2*ϕ*23 q

> *lA* 2 þ *e*1

*lA* 2 þ *e*1

cos *ϕ*2 ¼

The homogeneous transformation matrix, *BT*6, is given by

*BT*6 :

Here, *ϕ*2356 ¼ *ϕ*2 þ *ϕ*3 þ *ϕ*5 þ *ϕ*6.

*ϕ*2 þ *ϕ*3 þ *ϕ*5 ¼ *ϕ*235 ¼ �90°, where

By substituting (9) for (15), we have:

From (8), (16), and (17), we obtain:

Here, *e*1 ¼ *RA* � *rA*.

cos *ϕ*23 ¼ *e*1 � *e*1 � *y*6

*d* (9)

*:* (10)

*k*¼1*ϕi* ¼

(11)

(17)

Here, *ϕ*23 ¼ *ϕ*2 þ *ϕ*3:

$$\propto\_4 = l\_{LA}\cos\phi\_{23} + h\_{LA}\sin\phi\_{23} + l\_B + l\_{LB} + d\cos\phi\_2 \tag{5}$$

$$\{y\_4 = l\_{LA}\sin\phi\_{23} - h\_{LA}\cos\phi\_{23} + h\_{LB} + R\_B + d\sin\phi\_2\tag{6}$$

Then, *y*4 is equal to *RA* (the radius of the rear wheels of *Robot A*) in *stage 1* (**Figure 10**), and we obtain the following equation from (6):

$$R\_A = l\_{LA} \sin \phi\_{23} - h\_{LA} \cos \phi\_{23} + h\_{LB} + R\_B + d \sin \phi\_2 \tag{7}$$

In this system

$$R\_A = R\_B.\tag{8}$$

**Figure 10.** *Lifting the front wheels of* Robot A *(stage 1).*

*Cooperative Step Climbing Using Connected Wheeled Robots and Evaluation of Remote… DOI: http://dx.doi.org/10.5772/intechopen.90162*

Thus, we have:

$$\sin \phi\_2 = \frac{h\_{LA} \cos \phi\_{23} - l\_{LA} \sin \phi\_{23} - h\_{LB}}{d} \tag{9}$$

Here

*BT*4 :

(**Figure 10**), and we obtain the following equation from (6):

Here, *ϕ*23 ¼ *ϕ*2 þ *ϕ*3:

*Industrial Robotics - New Paradigms*

In this system

**Figure 10.**

**88**

*Lifting the front wheels of* Robot A *(stage 1).*

cos *ϕ*23 � sin *ϕ*23 *x*4 sin *ϕ*23 cos *ϕ*23 *y*4 0 01

*x*4 ¼ *lLA* cos *ϕ*23 þ *hLA* sin *ϕ*23 þ *lB* þ *lLB* þ *d* cos *ϕ*2 (5)

*y*4 ¼ *lLA* sin *ϕ*23 � *hLA* cos *ϕ*23 þ *hLB* þ *RB* þ *d* sin *ϕ*2 (6)

*RA* ¼ *lLA* sin *ϕ*23 � *hLA* cos *ϕ*23 þ *hLB* þ *RB* þ *d* sin *ϕ*2 (7)

*RA* ¼ *RB:* (8)

Then, *y*4 is equal to *RA* (the radius of the rear wheels of *Robot A*) in *stage 1*

(4)

$$
\cos \phi\_2 = \sqrt{\mathbf{1} - \sin^2 \phi\_2}. \tag{10}
$$

The homogeneous transformation matrix, *BT*6, is given by

$$\begin{aligned} \,^B T\_6 : \begin{bmatrix} \cos \phi\_{2356} & -\sin \phi\_{2356} & \varkappa\_6 \\ \sin \phi\_{2356} & \cos \phi\_{2356} & \varkappa\_6 \\ 0 & 0 & 1 \end{bmatrix} \end{aligned} \tag{11}$$

Here, *ϕ*2356 ¼ *ϕ*2 þ *ϕ*3 þ *ϕ*5 þ *ϕ*6.

From (1) and (3), when *p*6 (the tread position of the front wheels of *Robot A*, *Bp*6¼ *x*6*y*6 � �*T* , **Figure 10**) is at the bottom of the front wheels, P5 *k*¼1*ϕi* ¼ *ϕ*2 þ *ϕ*3 þ *ϕ*5 ¼ *ϕ*235 ¼ �90°, where

$$\cos \phi\_{235} = 0 \tag{12}$$

and

$$
\sin \phi\_{235} = -1 \tag{13}
$$

Thus, we have:

$$\mathbf{x}\_6 = l\_A \cos \phi\_{23} - (-R\_A + r\_A) \sin \phi\_{23} + l\_{LA} \cos \phi\_{23}$$

$$+ h\_{LA} \sin \phi\_{23} + l\_B + l\_{LB} + d \cos \phi\_2 \tag{14}$$

$$y\_{\xi} = -r\_{A} + l\_{A} \sin \phi\_{23} + (-R\_{A} + r\_{A}) \cos \phi\_{23} + l\_{LA} \sin \phi\_{23}$$

$$-h\_{LA} \cos \phi\_{23} + h\_{LB} + R\_{B} + d \sin \phi\_{2}.\tag{15}$$

By substituting (9) for (15), we have:

$$\mathcal{Y}\_6 = l\_A \sin \phi\_{23} + (-R\_A + r\_A) \cos \phi\_{23} + R\_B - r\_A \tag{16}$$

where

$$
\sin \phi\_{23} = \sqrt{\mathbf{1} - \cos^2 \phi\_{23}} \tag{17}
$$

From (8), (16), and (17), we obtain:

$$\cos\phi\_{23} = \frac{e\_1 \cdot \left(e\_1 - y\_6\right) + l\_A\sqrt{l\_A^2 + e\_1^2 - \left(e\_1 - y\_6\right)^2}}{l\_A^2 + e\_1^2} \tag{18}$$

Here, *e*1 ¼ *RA* � *rA*.

Then, *p*4 (the position of the axis of the rear wheels of *Robot A*) moves forward in lifting the front wheels of *Robot A* (**Figure 10**). Time *t* ¼ *tm* is the time for the operators to lift the wheels.

*p*4 ð Þ *t*¼0 ¼ *x*4 ð Þ *t*¼0 *y*4 ð Þ *t*¼0 � �*T* is the first position of *p*4. When the robot manipulation time is *t* ¼ 0, the tilt of *Robot A* is zero (*ϕ*23 ¼ 0). Then, *p*4 ð Þ *t*¼0 moves to *p*4 ð Þ *t*¼*tm* ¼ *x*4 ð Þ *t*¼*tm y*4 ð Þ *t*¼*tm* � �*T* after *Robot A* moves at a constant velocity of *vA* in *t* s, and *Δx* is the distance between *p*4 ð Þ *t*¼0 and *p*4 ð Þ *t*¼*tm* .

When the operator begins to teleoperate the robots ð Þ *t* ¼ 0 , the position of the axis of the rear wheels of *Robot A*, *x*4 ð Þ *t*¼0 , is obtained from (5), as follows:

$$\mathcal{X}\_{\Phi\_{\left(t=0\right)}} = l\_{LA} + l\_B + l\_{LB} + d \cos \phi\_{2\ \left(t=0\right)} \tag{19}$$

Here,

and

*t* ¼ 1 *vA*

**Figure 11.**

**91**

*e*2 ¼ *hLA* cos *ϕ*23 ð Þ *t*¼*tm* � *lLA* sin *ϕ*23 ð Þ *t*¼*tm* � *hLB:* (26)

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 � cos 2*ϕ*23 ð Þ *t*¼*tm* q

> *lA* 2 þ *e*1

> > 2

þ

q

*lA* 2 þ *e*1

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi *d*2 � ð Þ *hLA* � *hLB*

From (26)–(29), the relationships among the velocity of *Robot A* (*vA*), the height of the bottom of the front wheels (*y*6) (**Figure 11(a)**), and the manipulation time

In *stage 1*, the operators lift the bottom of the front wheels of *Robot A* above the

When the horizontal position of the center of gravity is at the contact position between the rear wheels and the road (**Figure 11(b)**), the height of the bottom of the front wheels is *y*6 ¼ 0.1526 m. On the other hand, *Robot B* does not tip over backward during *stage 3* because the link touches its body when the incline of *Robot B* grows large (**Figure 13**), so stopping further inclination. The operators are able to

*Height range of the front wheels of* Robot A *required to climb a step: (a) situation in which the bottom of the front wheels is equal to the step height and (b) situation in which the horizontal position of the center of gravity*

**4.2 Range of front wheel height within which operators must teleoperate**

step height in order to place the wheels on the step (**Figure 11(a)**). Next, the operators maintain a suitable inclination for *Robot A* in order to prevent it from tipping over backward (**Figure 11(b)**). When *Robot B* stops and *Robot A* continues to move forward, *Robot A* tips over backward (**Figure 12**). Hence, the operators must maintain the height of the front wheels within the range between the step

þ *hLA* sin *ϕ*23 ð Þ *t*¼*tm* � �

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi *d*2 � *e*2 2

2 � *e*1 � *y*6 � �2 q

2 (28)

(27)

*:*

(29)

From (17) and (18), we obtain sin *ϕ*2ð Þ *t*¼*tm* and cos *ϕ*2 ð Þ *t*¼*tm* , as follows:

*Cooperative Step Climbing Using Connected Wheeled Robots and Evaluation of Remote…*

� � þ *lA*

sin *ϕ*23 ð Þ *t*¼*tm* ¼

q

cos *ϕ*23 ð Þ *t*¼*tm* ¼ *e*1 � *e*1 � *y*6

Substituting (22) and (23) for (21), we obtain:

for lifting the front wheels (*t* ¼ *tm*) are clarified.

height and the height at which *Robot A* tips over backward.

teleoperate *Robot B* without tipping the robot over backward.

*is at the contact position between the rear wheels and the road.*

*lLA* cos *ϕ*23 ð Þ *t*¼*tm* � 1 � � �

*DOI: http://dx.doi.org/10.5772/intechopen.90162*

**for step climbing**

Here, cos *ϕ*2 ð Þ *t*¼0 is the value of cos *ϕ*2 at *t* ¼ 0 s.

After manipulating the robots for *t* ¼ *tm*, the position of the axis of the rear wheels of *Robot A* (*x*4 ð Þ *t*¼*tm* ) is given by

$$\mathbf{x}\_{4\ (t=tm)} = l\_{LA}\cos\phi\_{23\ (t=tm)} + h\_{LA}\sin\phi\_{23\ (t=tm)} + l\_B + l\_{LB} + d\cos\phi\_{2\ (t=tm)}\tag{20}$$

Here, cos *ϕ*23 ð Þ *t*¼*tm* is the value of cos *ϕ*23 at *t* ¼ *tm*.

Based on (19) and (20), the movement distance of *Robot A* while lifting the front wheels, *Δx* (**Figure 10**), is given as

$$\begin{split} \Delta \mathbf{x} &= \nu\_{A} \mathbf{t} = \mathbf{x}\_{4 \ (t=tm)} - \boldsymbol{\mathcal{X}}\_{4 \ (t=0)} \\ &= l\_{LA} \left\{ \cos \phi\_{23(t=tm)} - \mathbf{1} \right\} + h\_{LA} \sin \phi\_{23(t=tm)} + d \left\{ \cos \phi\_{2 \ (t=tm)} - \cos \phi\_{2(t=0)} \right\} \end{split} \tag{21}$$

Here, *vA* is the constant velocity of *Robot A*. When the front wheels begin to be lifted (*t* ¼ 0, **Figure 10**), the incline of *Robot A* is zero (*ϕ*2 þ *ϕ*3 ¼ 0). In this case, from (9) and (10), we obtain:

$$\sin \phi\_{2\ (t=0)} = \frac{h\_{LA} - h\_{LB}}{d} \tag{22}$$

and

$$\cos\phi\_{2\ (t=0)} = \sqrt{\frac{d^2 - (h\_{LA} - h\_{LB})^2}{d}}\tag{23}$$

After manipulating the robots for a time *tm*, the front wheels start to lift. Then, from (9) and (10), we obtain the following:

$$\sin\phi\_{2(t=tm)} = \frac{h\_{LA}\cos\phi\_{23\ (t=tm)} - l\_{LA}\sin\phi\_{23\ (t=tm)} - h\_{LB}}{d} \tag{24}$$

and

$$\cos \phi\_{2\ (t=tm)} = \sqrt{\frac{d^2 - \mathbf{e}\_2^2}{d}}\tag{25}$$

*Cooperative Step Climbing Using Connected Wheeled Robots and Evaluation of Remote… DOI: http://dx.doi.org/10.5772/intechopen.90162*

Here,

Then, *p*4 (the position of the axis of the rear wheels of *Robot A*) moves forward in lifting the front wheels of *Robot A* (**Figure 10**). Time *t* ¼ *tm* is the time for the

ulation time is *t* ¼ 0, the tilt of *Robot A* is zero (*ϕ*23 ¼ 0). Then, *p*4 ð Þ *t*¼0 moves to

axis of the rear wheels of *Robot A*, *x*4 ð Þ *t*¼0 , is obtained from (5), as follows:

When the operator begins to teleoperate the robots ð Þ *t* ¼ 0 , the position of the

After manipulating the robots for *t* ¼ *tm*, the position of the axis of the rear

*x*4 ð Þ *t*¼*tm* ¼ *lLA* cos *ϕ*23 ð Þ *t*¼*tm* þ *hLA* sin *ϕ*23 ð Þ *t*¼*tm* þ *lB* þ *lLB* þ *d* cos *ϕ*2 ð Þ *t*¼*tm* (20)

Based on (19) and (20), the movement distance of *Robot A* while lifting the front

Here, *vA* is the constant velocity of *Robot A*. When the front wheels begin to be lifted (*t* ¼ 0, **Figure 10**), the incline of *Robot A* is zero (*ϕ*2 þ *ϕ*3 ¼ 0). In this case,

sin *ϕ*2 ð Þ *t*¼0 ¼ *hLA* � *hLB*

s

After manipulating the robots for a time *tm*, the front wheels start to lift. Then,

sin *ϕ*2ð Þ *t*¼*tm* ¼ *hLA* cos *ϕ*23 ð Þ *t*¼*tm* � *lLA* sin *ϕ*23 ð Þ *t*¼*tm* � *hLB*

cos *ϕ*2 ð Þ *t*¼*tm* ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi *d*2 � ð Þ *hLA* � *hLB*

*d*

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi *d*2 � *e*2 2

s

*d*

2

cos *ϕ*2 ð Þ *t*¼0 ¼

from (9) and (10), we obtain the following:

� �*T* is the first position of *p*4. When the robot manip-

� �*T* after *Robot A* moves at a constant velocity of *vA* in

*x*4 ð Þ *t*¼0 ¼ *lLA* þ *lB* þ *lLB* þ *d* cos *ϕ*2 ð Þ *t*¼0 (19)

þ *hLA* sin *ϕ*23ð Þ *t*¼*tm* þ *d* cos *ϕ*2 ð Þ *t*¼*tm* � cos *ϕ*2ð Þ *t*¼0

n o

*d* (22)

*d* (24)

(21)

(23)

(25)

operators to lift the wheels.

*p*4 ð Þ *t*¼*tm* ¼ *x*4 ð Þ *t*¼*tm y*4 ð Þ *t*¼*tm*

*p*4 ð Þ *t*¼0 ¼ *x*4 ð Þ *t*¼0 *y*4 ð Þ *t*¼0

*Industrial Robotics - New Paradigms*

*t* s, and *Δx* is the distance between *p*4 ð Þ *t*¼0 and *p*4 ð Þ *t*¼*tm* .

Here, cos *ϕ*2 ð Þ *t*¼0 is the value of cos *ϕ*2 at *t* ¼ 0 s.

Here, cos *ϕ*23 ð Þ *t*¼*tm* is the value of cos *ϕ*23 at *t* ¼ *tm*.

wheels of *Robot A* (*x*4 ð Þ *t*¼*tm* ) is given by

wheels, *Δx* (**Figure 10**), is given as

*Δx* ¼ *vA t* ¼ *x*4 ð Þ *t*¼*tm* � *x*4 ð Þ *t*¼0 ¼ *lLA* cos *ϕ*23ð Þ *t*¼*tm* � 1 n o

from (9) and (10), we obtain:

and

and

**90**

$$\mathcal{C}\_2 = h\_{LA} \cos \phi\_{23 \ (t=tm)} - l\_{LA} \sin \phi\_{23 \ (t=tm)} - h\_{LB}. \tag{26}$$

From (17) and (18), we obtain sin *ϕ*2ð Þ *t*¼*tm* and cos *ϕ*2 ð Þ *t*¼*tm* , as follows:

$$
\sin \phi\_{23 \ (t=tm)} = \sqrt{1 - \cos^2 \phi\_{23 \ (t=tm)}} \tag{27}
$$

and

$$\cos\phi\_{23\ (t=tm)} = \frac{e\_1 \cdot \left(e\_1 - \chi\_6\right) + l\_A\sqrt{l\_A^2 + e\_1^2 - \left(e\_1 - \chi\_6\right)^2}}{l\_A^2 + e\_1^2} \tag{28}$$

Substituting (22) and (23) for (21), we obtain:

$$t = \frac{1}{v\_A} \left[ l\_{LA} \left( \cos \phi\_{23 \ (t = m)} - 1 \right) - \sqrt{d^2 - \left( h\_{LA} - h\_{LB} \right)^2} + \sqrt{d^2 - e\_2^2} + h\_{LA} \sin \phi\_{23 \ (t = m)} \right]. \tag{29}$$

From (26)–(29), the relationships among the velocity of *Robot A* (*vA*), the height of the bottom of the front wheels (*y*6) (**Figure 11(a)**), and the manipulation time for lifting the front wheels (*t* ¼ *tm*) are clarified.

### **4.2 Range of front wheel height within which operators must teleoperate for step climbing**

In *stage 1*, the operators lift the bottom of the front wheels of *Robot A* above the step height in order to place the wheels on the step (**Figure 11(a)**). Next, the operators maintain a suitable inclination for *Robot A* in order to prevent it from tipping over backward (**Figure 11(b)**). When *Robot B* stops and *Robot A* continues to move forward, *Robot A* tips over backward (**Figure 12**). Hence, the operators must maintain the height of the front wheels within the range between the step height and the height at which *Robot A* tips over backward.

When the horizontal position of the center of gravity is at the contact position between the rear wheels and the road (**Figure 11(b)**), the height of the bottom of the front wheels is *y*6 ¼ 0.1526 m. On the other hand, *Robot B* does not tip over backward during *stage 3* because the link touches its body when the incline of *Robot B* grows large (**Figure 13**), so stopping further inclination. The operators are able to teleoperate *Robot B* without tipping the robot over backward.

**Figure 11.**

*Height range of the front wheels of* Robot A *required to climb a step: (a) situation in which the bottom of the front wheels is equal to the step height and (b) situation in which the horizontal position of the center of gravity is at the contact position between the rear wheels and the road.*

**Figure 12.** *Tipping over backward of* Robot A*.*

**Figure 13.** *Link touching the front part of* Robot B*, which acts to prevent incline of* Robot A*.*


**New Antimicrobial Phenyl Alkenoic Acids Isolated from an Oil Palm Rhizosphere-Associated Actinomycete,** *Streptomyces palmae* **CMU-AB204T**

**Kanaporn Sujarit 1,2, Mihoko Mori 2,3,\*, Kazuyuki Dobashi 2, Kazuro Shiomi 2,3, Wasu Pathom-aree 1,4 and Saisamorn Lumyong 1,4,5,\***

Received: 15 January 2020; Accepted: 28 February 2020; Published: 1 March 2020

**Abstract:** Basal stem rot (BSR), or *Ganoderma* rot disease, is the most serious disease associated with the oil palm plant of Southeast Asian countries. A basidiomycetous fungus, *Ganoderma boninense*, is the causative microbe of this disease. To control BSR in oil palm plantations, biological control agents are gaining attention as a major alternative to chemical fungicides. In the course of searching for effective actinomycetes as potential biological control agents for BSR, *Streptomyces palmae* CMU-AB204T was isolated from oil palm rhizosphere soil collected on the campus of Chiang Mai University. The culture broth of this strain showed significant antimicrobial activities against several bacteria and phytopathogenic fungi including *G. boninense*. Antifungal and antibacterial compounds were isolated by antimicrobial activity-guided purification using chromatographic methods. Their structures were elucidated by spectroscopic techniques, including Nuclear Magnetic Resonance (NMR), Mass Spectrometry (MS), Ultraviolet (UV), and Infrared (IR) analyses. The current study isolated new phenyl alkenoic acids **1**–**6** and three known compounds, anguinomycin A (**7**), leptomycin A (**8**), and actinopyrone A (**9**) as antimicrobial agents. Compounds **1** and **2** displayed broad antifungal activity, though they did not show antibacterial activity. Compounds **3** and **4** revealed a strong antibacterial activity against both Gram-positive and Gram-negative bacteria including the phytopathogenic strain *Xanthomonas campestris* pv. *oryzae*. Compounds **7**–**9** displayed antifungal activity against *Ganoderma*. Thus, the antifungal compounds obtained in this study may play a role in protecting oil palm plants from *Ganoderma* infection with the strain *S. palmae* CMU-AB204T.

**Keywords:** actinomycetes; antimicrobial; phenyl alkenoic acid; rhizosphere; *Streptomyces palmae*


2.2.3. Metal Ion Chelation Activity Assay

Fe2+ chelation activities were determined according to the methods described by Zhang [15] with some modifications. First, 0.05 mL of 2 mM FeCl2 was mixed with 0.1 mL of 5 mM ferrozine. After the addition of samples solutions, the final volume was increased up to 3 mL with ultrapure water. The absorbance change was measured at 562 nm after being incubated for 10 min at room temperature. The metal ion chelation activity was calculated by Equation (3).

$$\text{Metal ion calculation activity} \%= (1 - A\_{\text{sample}}/A\_{\text{blank}}) \times 100\tag{3}$$

where A means absorbance value of samples (Asample) and blank (Ablank) at 562 nm.