# Humanitarian Demining Serial-Tracked Robot: Design and Dynamic Modeling

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## Abstract

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## 1. Introduction

- Munitions and explosive devices research—refers to the gathering of information on discovered explosive munitions, namely recognition, which means classifying them into a category (grenade, bomb, projectile, or guided or unguided missile) and identifying that munition, which refers to the type of ammunition (thrown, released, propelled, or placed), its type and condition, for what purpose it was used, how it reached the target, the mechanism of operation and the method of initiation. This step can be performed by specialized EOD personnel or by non-EOD personnel (Explosive Ordnance Reconnaissance Officers who have completed a specialized course);
- Clearing areas of conventional explosive munitions to eliminate any threat produced by them by neutralizing and destroying them according to certain specific procedures tested and applied by EOD personnel;
- The neutralization and destruction of improvised explosive devices, a capability that is most often achieved in military conflict zones by locating, identifying, making safe, and destroying them; neutralization and destruction of chemical, biological, radiological, and nuclear munitions, a capability that requires thorough training in chemical agents and their methods of disposal without causing damage.

## 2. Previous Work

## 3. Design of the Mechanical Structures of the Serial-Tracked Demining Robot

- The tracked base, this type of moving robot is more suitable for rough terrains and ensures the stability of the robot during military operations;
- The robotic system is a TRTTR serial modular robot with 5 degrees of freedom (3 translations and 2 rotation modulus). The robot is equipped with an end-effector to carry out demining tasks, respectively clearing the land of exploded mines;
- The unexploded mine detection device with a translation system mounted on the bottom of the tracked base.

- The robot must autonomously perform the full range of activities necessary for the field cleaning process: survey, field scanning, marking the corridors made in the minefields, and destroying the mines, in different weather conditions and land surfaces, respectively [29];
- The robot should be built on a low budget, to have reduced overall dimensions, increased scanning capability, and a demining speed of at least 1.5 m/s in slightly rugged terrain so that it can be used in humanitarian demining;
- The robot must mark the corridors in the minefields throughout the execution of the demining mission;
- It must have a robust construction to ensure good resistance to explosions and to be easy to repair or replace malfunctioning parts. To protect the exposed mechanical parts of the structure of the horizontal and vertical arm of the serial robot are provided with flexible non-flammable covers;
- The robot should operate based on solar energy using energy-conserving photovoltaic cells to ensure uninterrupted operation at the normal parameters of the robot, both during the day and at night. Selection of drive motors with minimal energy consumption and reduced masses and dimensions, respectively;
- For human operators or EOD safety, it must be handled remotely (wireless).

## 4. Dynamic Model of the TRTTR Serial Structure of Tracked Robot

_{c}represents the kinetic energy of the robot, $R=\frac{1}{2}{C}_{k}\xb7{\dot{q}}_{k}^{2}$ is Rayleigh dissipation function (including the contribution of viscous frictional forces), ${C}_{k},k=1\xf75$ are the viscous friction coefficients in each kinematic joint, and Q

_{k}are the generalized forces.

_{c}, y

_{c}, z

_{c}are the coordinates of the center of gravity, J

_{x}, J

_{y}, J

_{z}are the axial mechanical moments of inertia, and J

_{xy}, J

_{xz}, J

_{zy}are the centrifugal mechanical moments of inertia of the rigid. To simplify the dynamic calculus, it was considered that for each module of the robot, the reference system has the origin in the mass center (x

_{c}= y

_{c}= z

_{c}= 0), and the orientation coincides with the main inertia directions. In this case, the centrifugal mechanical moments of inertia are null (J

_{xy}= J

_{xz}= J

_{zy}= 0), and (2) were written under the following form:

## 5. Numerical Validation of Dynamic Model

#### 5.1. Method Description

#### 5.1.1. Validation of Direct Kinematics Model

#### 5.1.2. Validation of Dynamic Model (Lagrange Equations)

#### 5.2. Numerical Results

- Robot—Physical Model: physical modeling of robot components with elements from the Matlab/Simulink/Simscape/MultiBody libraries;
- Direct Kinematics model: math equations according to [10];
- Dynamic model—Lagrange equations: Simulink implementation of the Lagrange Equations (17).

#### 5.2.1. Validation of Direct Kinematic Model

#### 5.2.2. Validation of Dynamic Model

## 6. Driving Motors Selection of the Translation Modules

_{f}the friction force in the guideway.

_{0}represents the diameter of the cylinder that holds the ball centers, φ is the dwell angle of the helix on the medium cylinder, k is the rolling friction coefficient, d

_{b}represents the ball diameter, $\theta $ is the contact angle between the ball and the runway, M

_{s}represents the torque at the screw-ball axle.

_{s}, n

_{s}the power and the angular speed of the screw-ball, the torque M

_{s}has the following equation:

_{m}is the power developed by the DC motor that drives the movable system at the robotic base into motion. The angular speed of the screw-ball n

_{s}must fulfill the following inequality n

_{s}≤ n

_{m}where with n

_{m}it was noted the angular speed of the driving shaft. Given the (21) and (22) and previous inequality, (20) becomes:

_{f}has the following equation:

^{2}), and µ is the friction coefficient in the guides (standard value, µ = 0.02).

_{3}depending on motor moments, gear ratios, outputs, the geometry of the screw-ball nut transmission, as well as on the used guide-ways type. According to relations (19 ÷ 21), the power P

_{s}can be determined as follows:

_{m,}the necessary power developed by the DC motor that drives the horizontal translation movable system in the robotic arm into motion.

_{s}rotation speed of the screw must fulfill the following inequality:

_{m}stands for the worm gear ratio.

_{f}, is calculated using the following relation:

_{4}depending on motor moments, gear ratios, outputs, the geometry of the screw-ball nut transmission, as well as on the type of guideways used, can be determined. According to relations (19), (20), and (21), the power P

_{s}is determined as follows:

_{r}the output of a pair of bearings, η

_{c}the output of the spur-gear drive and P

_{m}the power developed by the DC motor that drives the translation movable system in the robotic arm vertical structure into motion.

_{m_theoretical}) was determined. After performing the calculations, the following results were obtained (Table 1). With the theoretical value of the driving moment (M

_{m_theoretical}), for each translation modulus, the real driving motor (M

_{m_selected}) and servomotor from the QMot QBL4208 family catalog [39] (Table 2) were easily selected. The driving motors were chosen to fulfill the condition of reduced dimensions and minimal energy consumption imposed by the design criteria.

_{b}= 0.0055 m; θ = 45°; η

_{r}= 0.995; ${q}_{1}=\pi /4\mathrm{r}\mathrm{a}\mathrm{d};{v}_{2}=0.25\mathrm{m};{\ddot{v}}_{2}=1.5\mathrm{m}/{\mathrm{s}}^{2}$; ${\dot{q}}_{1}=0.75\mathrm{r}\mathrm{a}\mathrm{d}/\mathrm{s};{\ddot{q}}_{1}=0.25\mathrm{m}/{\mathrm{s}}^{2};{\dot{v}}_{1}=0.30\mathrm{m}/\mathrm{s};{\ddot{v}}_{1}=1\mathrm{m}/{\mathrm{s}}^{2};{\dot{v}}_{2}=0.4\mathrm{m}/\mathrm{s};$ P

_{4}= 421.47 N; P

_{5}= 438.5 N. It is specified that the mass values of the robot modules include the mass of the end-effector.

## 7. Conclusions

_{m}/n

_{m}ratio resulting from the design calculations. This approach has the advantage of properly sizing and selecting electric motors to minimize electricity consumption. The theoretical values of the driving motors moments of each translation module of the serial-tracked robot are given. Technical specifications of the selected driving motors for each translation module are also presented.

## 8. Patents

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**The kinematic diagram of the TRTTR modular serial tracked robot [9]. The movements in the kinematic joints are highlighted.

**Figure 5.**Validation of direct kinematics model. Numerical results: (

**a**) Robot—Physical Model; (

**b**) 3D end-effector displacements in operational space; (

**c**) P

_{x}, end-effector displacement in operational space (X axis); (

**d**) P

_{y}, end-effector displacement in operational space (Y axis); (

**e**) P

_{z}, end-effector displacement in operational space (Z axis); (

**f**) end-effector absolute errors about X, Y, and Z axis.

**Figure 6.**Validation of dynamic model. Numerical results: (

**a**) P

_{x}, end-effector displacement in operational space (X axis); (

**b**) P

_{y}, end-effector displacement in operational space (Y axis); (

**c**) P

_{z}, end-effector displacement in operational space (Z axis); (

**d**) end-effector relative errors about X, Y, and Z axis.

**Figure 7.**Validation of dynamic model. Numerical results: (

**a**) v

_{1}, joint J

_{1}displacement; (

**b**) q

_{1}, joint J

_{2}displacement; (

**c**) v

_{2}, joint J

_{3}displacement; (

**d**) v

_{3}, joint J

_{4}displacement; (

**e**) q

_{2}, joint J

_{5}displacement; (

**f**) Joint displacements relative errors.

Module | Frictional Force | Dwell Angle | Power Driving Motor and | Theoretical Driving |
---|---|---|---|---|

Type | F_{f} | φ | Angular Speed | Moment |

Ratio | M_{m_theoretical} | |||

P_{m}/n_{m} | ||||

[N] | [°] | [kW·min/rot] | [N·m] | |

MTB SIL | 33.367 | 4.852 | 1.65421·10^{−3} | 1.93 |

MTV SIL | 16.226 | 4.852 | 0.1253·10^{−3} | 0.10 |

MT SIL | 7.626 | 4.852 | 0.02385·10^{−3} | 0.35 |

Module | Selected | Servo- | Rotation Speed | Driving Power | Mass |
---|---|---|---|---|---|

Type | Driving Motor | Motor Type | n_{m} | P | m |

Moment | |||||

M_{m_selected} | |||||

[N·m] | [rpm] | [kW] | [kg] | ||

MTB SIL | 2.15 | QBL17E40-01D-05RO | 5000 | 1.2 | 3.3 |

MTV SIL | 0.18 | QBL4208-81-04-019 | 4000 | 0.07 | 1.5 |

MT SIL | 0.56 | QBL4208-81-04-019 | 4000 | 0.08 | 1.8 |

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**MDPI and ACS Style**

Petrişor, S.M.; Simion, M.; Bârsan, G.; Hancu, O.
Humanitarian Demining Serial-Tracked Robot: Design and Dynamic Modeling. *Machines* **2023**, *11*, 548.
https://doi.org/10.3390/machines11050548

**AMA Style**

Petrişor SM, Simion M, Bârsan G, Hancu O.
Humanitarian Demining Serial-Tracked Robot: Design and Dynamic Modeling. *Machines*. 2023; 11(5):548.
https://doi.org/10.3390/machines11050548

**Chicago/Turabian Style**

Petrişor, Silviu Mihai, Mihaela Simion, Ghiţã Bârsan, and Olimpiu Hancu.
2023. "Humanitarian Demining Serial-Tracked Robot: Design and Dynamic Modeling" *Machines* 11, no. 5: 548.
https://doi.org/10.3390/machines11050548