**6. Computer simulations**

*γc <sup>q</sup>* ¼ *a* tan

*Service Robotics*

equations [6, 8]:

formulated below:

**Table 1.**

**72**

2 4

Δ*t* ¼

Δ*z* � *vTz* Δ*t*

<sup>þ</sup> *vTy* <sup>Δ</sup>*<sup>t</sup>* � <sup>Δ</sup>*<sup>y</sup>* � � sin *<sup>η</sup><sup>c</sup>*

*vTx* ¼ *vT* cos *γ<sup>t</sup>* ð Þ (47) *vTy* ¼ *vT* sin *γ<sup>t</sup>* ð Þ (48)

*vTz* ¼ 0 (49)

*q* � �

3

� � (50)

(51)

5 (46)

*q* � �

whose amplitude is vT, i.e., vTx, vTy, and vTz, are defined in the following

In Eqs. (45) and (46), the components of the linear velocity vector of point T

Furthermore, the remaining time till the end of the engagement, i.e., Δt, is

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

*<sup>C</sup>* � *<sup>v</sup>*<sup>2</sup> *T* � �Δ*r*<sup>2</sup>

In the above equation, *<sup>σ</sup>* <sup>¼</sup> *vTx* <sup>Δ</sup>*<sup>x</sup>* <sup>þ</sup> *vTy* <sup>Δ</sup>*<sup>y</sup>* <sup>þ</sup> *vTz* <sup>Δ</sup>*<sup>z</sup>* andΔ*r*<sup>2</sup> <sup>¼</sup> <sup>Δ</sup>*x*<sup>2</sup> <sup>þ</sup> <sup>Δ</sup>*y*<sup>2</sup> <sup>þ</sup> <sup>Δ</sup>*z*2. In this work, it is assumed that the speed and orientation parameters of the moving target are obtained by processing the data acquired by the camera on the system under control. Since the control inputs of the designed control system are linear velocity components, the guidance commands given in Eqs. (45) and (46) should be expressed in terms of the linear velocity parameters for realization. This transformation can be done by writing the velocity vector of point C with amplitude

> cos *η<sup>c</sup> q* � �

sin *η<sup>c</sup> q* � �

**Parameter Numerical value** a1 and a2 1.25 m d1 and d2 0.625 m m1 and m2 10 kg Ic1 and Ic2 1.302 kg�m<sup>2</sup> b1 and b2 0.001 N�m�s/rad ωc1 and ωc2 10 Hz ζc1 and ζc2 0.707 L 2 m ρ 0.5 m d 1.5 m

� sin *<sup>γ</sup><sup>c</sup> q* � �

� �

� *σ*

cos *γ<sup>c</sup> q* � �

cos *γ<sup>c</sup> q* � �

*= v*<sup>2</sup> *<sup>C</sup>* � *<sup>v</sup>*<sup>2</sup> *T*

*<sup>σ</sup>*<sup>2</sup> <sup>þ</sup> *<sup>v</sup>*<sup>2</sup>

q

vC in terms of its components on *F0* as follows [6, 8]:

*Numerical values used in the simulations for the robotic arm [8].*

*xpd* ¼ *vC*

ð Þ *vTx* Δ*t* � Δ*x* cos *η<sup>c</sup>*

where Δ*x* ¼ *xC* � *xT*, Δ*y* ¼ *yC* � *yT*, and Δ*z* ¼ *zC* � *zT*.

The system trajectories acquired from the computer simulations performed in accordance with the numerical values given in **Tables 1**–**3** for the robotic arm, tracked land vehicle, and quadrotor are submitted in **Figures 7**–**10** along with the corresponding target motions. Having constructed the engagement geometry between the mechatronic system under consideration and target, the LHG law is applied for these situations. In the simulations, disturbance effects due to the nonlinear friction characteristic and noise on the sensors on the joints are assumed


### **Table 2.**

*Numerical values used in the simulations for the tracked land vehicle [8].*


**Table 3.**

*Numerical values used in the simulations for the quadrotor [8].*

**Figure 7.** *Engagement geometry of the robotic arm with the mounting line.*

**Figure 8.** *Engagement geometry of the tracked land vehicle with the constant speed target point.*

to randomly change within the intervals of 10 Nm and <sup>1</sup> <sup>10</sup><sup>3</sup> rad for the robotic arm. Also, it is regarded that the angular and linear dynamics of the quadrotor are subjected to random disturbing moment and force with maximum amplitudes of 50 Nm and 100 N, respectively. The simulations of the tracked land vehicle are made on nominal operating conditions [8].

important considerations is the capacity of the actuators of the autonomous systems. Namely, if the maximum force or torque, hence maximum current, level of the actuators (electric motors) does not satisfy the requirements arising due to the planned motion profile, then the relevant system cannot track the target as planned. In general, it can be concluded that the motion planning of mechatronic systems including the service robots can be made against predefined target points by choos-

ing a convenient guidance law.

**Figure 9.**

**Figure 10.**

**75**

*Horizontal engagement geometry of the quadrotor with the platform.*

*Guidance-Based Motion Planning of Autonomous Systems*

*DOI: http://dx.doi.org/10.5772/intechopen.91830*

*Vertical engagement geometry of the quadrotor with the platform.*

#### **7. Conclusion**

As a result of the performed computer simulations, it is shown that the considered autonomous mechatronic systems, i.e., the robotic arm, tracked land vehicle, and quadrotor, can catch the specified target points by regarding the LHG law. Although only one engagement case is presented for each of the systems above, the same result is attained for different situations, too. In this scene, one of the most

*Guidance-Based Motion Planning of Autonomous Systems DOI: http://dx.doi.org/10.5772/intechopen.91830*

#### **Figure 9.**

*Horizontal engagement geometry of the quadrotor with the platform.*

**Figure 10.** *Vertical engagement geometry of the quadrotor with the platform.*

important considerations is the capacity of the actuators of the autonomous systems. Namely, if the maximum force or torque, hence maximum current, level of the actuators (electric motors) does not satisfy the requirements arising due to the planned motion profile, then the relevant system cannot track the target as planned. In general, it can be concluded that the motion planning of mechatronic systems including the service robots can be made against predefined target points by choosing a convenient guidance law.

to randomly change within the intervals of 10 Nm and <sup>1</sup> <sup>10</sup><sup>3</sup> rad for the robotic arm. Also, it is regarded that the angular and linear dynamics of the quadrotor are subjected to random disturbing moment and force with maximum amplitudes of 50 Nm and 100 N, respectively. The simulations of the tracked land

As a result of the performed computer simulations, it is shown that the considered autonomous mechatronic systems, i.e., the robotic arm, tracked land vehicle, and quadrotor, can catch the specified target points by regarding the LHG law. Although only one engagement case is presented for each of the systems above, the same result is attained for different situations, too. In this scene, one of the most

vehicle are made on nominal operating conditions [8].

*Engagement geometry of the tracked land vehicle with the constant speed target point.*

*Engagement geometry of the robotic arm with the mounting line.*

**7. Conclusion**

**74**

**Figure 8.**

**Figure 7.**

*Service Robotics*

*Service Robotics*
