Anti-Dropping Technology of Four-Wheeled Throwing Robot

Jianzhong Wang, Pengzhan Liu and Jiadong Shi

(State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology， Beijing 100081, China)

Abstract: Within the fields of reconnaissance and surveillance, there is an ongoing need to obtain information from areas that are hard to reach or unsafe to enter. Thus, using robots with high performance in detecting obstacles is advantageous in these situations. The anti-drop impact design is one of the challenges facing the design of the throwing robots. In this present study, the drop model of the four-wheeled mobile robot is established, while the response of the model under shock impact is analyzed. Using the response of the model, we can obtain relationships between the maximum compression displacements of the wheels and the maximum acceleration of the robot, the drop height of the robot, the natural frequency of the impact response. Using the relationship between the maximum stress, the maximum deformation of the shell and the thickness of the shell, we can obtain the maximum acceleration of the robot. According to the relationships between the parameters, the optimal design parameters for the anti-dropping capability of the robot are chosen. A finite element model was established with Abaqus and a free fall from a height of 6 m to the solid ground was tested. The results show that the optimized structure can survive from the impact with solid ground from a free fall at a height of 6 m．

Key words: robotics; investigation; anti-dropping impact; stress analysis

The future battlefield will soon become urban areas due to external influencing factors, which will be the center for future combat operations. Unbalanced confrontations in urban areas are a major challenge for military planners as this confined battlefield limits the advantages of maneuver warfare, degrades the effective ranges of direct fire weapons and limits the use of indirect fire weapons. Timely reconnaissance, surveillance and target capture (RSTA) capabilities are the most important issues that will be faced in urban combat environments[1-3]. Quick and covert access to the target area is critical for robots to be able to perform tasks, such as investigations and target monitoring. Robots need a specific size and weight for throwing, while they also require strong anti-drop capability. As they lack the sensing or processing capabilities required to do anything meaningful, micro-robots is rarely used in practical applications. For autonomous mobile robots, it is necessary to have enough space to fit the resources required for handing demanding tasks[4]. However, the effectiveness of current robot designs in these environments is limited by the inherent fragility of the current robots, which makes these robots susceptible to failure due to rough handling or high-impact forces, which frequently occur during these missions[5]. There is a need to improve the ability of robots to withstand high-impact forces and general rough handling.

The National Robotics Engineering Consortium at Carnegie Mellon University have developed a robot named Dragon Runner, which weighs about 16 pounds and is able to survive high-impact forces at full speed or due to a drop from the third story[5]. A coaxial sliding clutch is used to keep the motor and the drive system from overloading. The internal electronic components are protected by the thermoplastic injection molding to increase their impact resistance.

Beihang University presents aminiature robot that utilizes a flexible structure for reconnaissance, with a total weight of 2.05 kg and with the size of 21.7 cm×20.5 cm×8.5 cm[6]. It can survive more than 10 drops from a height of 6 m without apparent damage. They embedded the sensitive components of the robot in a rubber shell to reduce the impact. The main body and the tire of the robot are connected with a rubber support block suspension system.

With the support of U.S. Department of Defense, the iRobot company developed the First Looke which uses a crawler structure[7]. They installed a swing arm in the front of the track of the robot, which only has one degree of freedom. The robot weighs 2.45 kg and has a dimensions of 22.9 cm×25.4 cm×10.2 cm. It can survive a drop from 4.8 m.

The ODF Optronics Ltd. of Israel has developed a four-wheeled throwing robot named EyeDrive, which has a total weight of 2.3 kg and can carry an additional load of up to 3 kg[8]. The robot may be thrown in through windows at height of up to 3 m. It has dimensions of 26 cm×16 cm×10 cm.

The biggest challenged faced by the throwing robot is climbing stairs, as those that can climb stairs can only move slowly. The Beijing Institute of Technology developed a four-wheeled mobile robot named MFRobot, which can climb stairs though flipping[9]. Therefore, this paper proposes an anti-drop design so that the MFRobot can achieve the goal of throwing.

This paper is organized as follows: Section 1 presents the damping spring quality model with single freedom. Furthermore, by using the model we obtained the relationships between the maximum compression displacements of the wheels, the maximum acceleration of the robot and the height of the robot, the natural frequency of the falling shock. The deformation and internal stress of the shell of the robot is analyzed in Section 2. The 3D model of the robot is shown in Section 3. Section 4 presents the simulation results of the drop impact, which is based on Abaqus. Finally, the conclusions are provided in Section 5.

1 Analysis of Drop Model

The collision of the robot occurs under the conditions of acceleration changes. The maximum acceleration of the robot during impact is very complex and is affected by the elasticity, density and damping of its wheels and the characteristics of the ground. The acceleration of the internal components should be the same as the shell when they are fully fastened to the shell[10]. For the design of throwing robots, the essential problem involves the optimization of the structural and stiffness of wheels based on collision analysis, thus reducing the impact on the robot by lowering the peak of acceleration in order to prevent the robot from breaking.

In order to simplify the analysis, it is assumed that only the wheels are in contact with the ground during the collision and the ground is solid. First, the robot drops as a free-faller from a height ofH, and the collision occurs when the wheels touches the ground. The deformation of the wheels reaches their maximum value when the falling speed of the robot is reduced to zero. The energy stored in the wheels is released to recover itself from deformation and allow the robot to rebound from ground. After this, the robot falls and rises again until the energy is consumed. In order to encompass the concrete structural characteristics of the four-wheeled throwing robot, a simplified mathematical model is proposed as follows.

1.1 Model of mass spring system with damp

For four-wheeled robots, the collision response can be described by one connected mass-spring system. In order to describe the acceleration of the robot more accurately, a damped single freedom mass spring system model is used to describe the impact process, which is shown in Fig.1. The nature of the mass spring system is determined by the material and shape of the wheels and the characteristics of the ground. The quality of the wheel has a relatively small impact compared to the overall robot and thus, we ignored the effect of its quality on the model.

Fig.1 Mass-spring system model

The acceleration of the electronic components is as same as the main body of the robot as they are fixed in the main body. The acceleration passes on to the electronic components though the suspended system of the wheels and the main body. We assumed that the stiffness coefficient for each wheel isKand the wheels touch the ground at the same time. It is known that the collision time of the wheels and ground does not exceed 0.1 s.

The mass of the robot ism, the stiffness coefficient for the wheels isk, and the damping coefficient of the wheels isc. The compression displacement of the wheels when the robot is standing still on the ground isδand thus, the differential equation is

(1)

Using a soft material can improve the buffer capacity of the wheels, but there are restricted choices for the stiffness and damping of the wheels cannot be chosen unlimited. Less stiff wheels have greater buffering ability, which results in a larger corresponding impact deformation. A larger damping coefficient of the wheels can contribute to the attenuation of its vibration, but this would also increase the contact force between the wheels and ground at the beginning of the impact. The damping coefficient of common materials is not enough to contribute a large impact force so a bigger damping coefficient can reduce the maximum impact force.

The relationship of the natural frequency and relative damping coefficient of the impact of the robot can be described as:

ξωn=c/(2m)

(2)

whereεis the relative damping coefficient of the robot andωnis the natural frequency of the robot. It can be seen that a smaller weight of the robot results in a larger relative damping coefficient. The deformation of the wheels should not exceed its elastic deformation range during the process of dropping.

Nature rubber is often used as the material for wheels because of its excellent performance. The damping coefficient of nature rubber is in the range of 0.1-0.3, with 0.3 being used in this paper. The total weight of the robot is about 4 kg. It can be seen thatεωnis 4.8 if the natural rubber is used as the material of wheels. Without a loss of generality, the range ofωnis chosen as 100-316 Hz. Therefore, the range of the stiffness coefficient of a single wheel is 10-100 N/mm, the range of the relative damping coefficient of the robot is 0.015-0.048, and the range of relative damping coefficient of a single wheel is 0.003 75-0.012.

1.2 Compression deformation of the wheels

The relationship between the compression deformation of the wheels and time can be expressed as

x(t)=e-ξωntAsin (ωdt+φ)

(3)

(4)

whereωdis the natural frequency of the system;Ais the amplitude of the impact displacement; andφis the phase angle of the displacement of the vibration system. The relationship between the compression displacement of the wheels, the natural frequency and drop height is shown in Fig.2.

Fig.2 Relationship between the compression displacement of wheels, natural frequency and drop height

As shown in Fig.2, a higher drop height results in a larger compression displacement of the wheels, while a bigger natural frequency of the robot results in a smaller compression displacement of the wheels.

1.3 Acceleration of the robot

The relationship between the acceleration of the robot and time is shown as

(5)

(6)

whereA1is the amplitude of the impact acceleration andφ1is the phase angle of the acceleration of the vibration system. The relationship between the acceleration of the robot, the natural frequency and drop height is shown in Fig.3.

As shown in Fig.3, larger natural frequency and drop height of the robot results in faster acceleration of the robot. The relationship between the acceleration of the robot and the compression displacement of the wheels at a drop height of 6 m is shown in Fig.4.

As seen in Fig.4, there is a non-linear inverse ratio relationship between the compression displacement and acceleration of the robot. The maximum compression displacement of the wheels is proportional to the radius of wheels. The radius of wheels can be selected according to the size of the robot.

Fig.3 Relationship between the acceleration, natural frequency and drop height

Fig.4 Relationship between the compression displacement and acceleration of the robot

After comprehensive consideration, the stiffness coefficient of the wheel can be selected as 45.369 N/mm, while the compression displacement of the wheels at a stationary state is 0.22 mm. The natural frequency of the robot is 213 Hz, the compressive displacement of the wheels is 3.5 cm and the maximum acceleration of the robot is 1 580 m/s2at a drop height of 6 m.

2 Analysis of Stress of the Shell

The maximum stress placed on the robot component should be less than its ultimate stress in the process of collision. Plastic deformation would occur when the stress of the robot component is greater than its yield stress. After repeated shocks, the plastic deformation of the robot gradually accumulates which finally causes stress damage.

There are two commonly used methods for the anti-impact design of the four-wheeled robot; One method involves reducing the impact though increasing the flexibility of the wheels, while the other method involves increasing the thickness (or using a material with higher strength) of the parts that are placed under a higher concentration of stress. However, the two improvements cannot be implemented blindly.

In order to simplify the model, a beam was adopted to study the major phenomena of the robot under shock impact. The wheelbase of the front and rear wheels is used as the length (L) direction of the beam, which is shown in Fig.5a. The weight of the shell of the robot isM, while the weight of inner parts ism. The model is simplified as a freely supported beam, and the cross-sectional shape of the beam is shown in Fig.5b. The force provided by the shell of the robot is replaced by a uniform load size ofM(a+g)/L, while the force provided by the internal parts is replaced by a concentrated size ofm(a+g).

Fig.5 Simplified model of shell

The maximum normal stress, maximum bending stress and the radius of the curvature of the beam bending can be calculated as

(7)

(8)

(9)

whereEis the elastic modulus of the beam;ρis the density of the shell; andδis the thickness of the side of the shell. As the process of collision was complex, 2 000 m/s2was used as the value of acceleration, while the range of 0.001-0.005 m was used as the values of the thickness of shell, according to the actual measurements. The value of the design parameters were chosen according to the actual situation:H=0.04,b=0.2 andL=0.26. There were two types of materials (steel Q235 and aluminum alloy 7075T6) that were used to calculate the force of the robot.

2.1 Steel

The density of steel (Q235) was 7 900 kg/m3, the ultimate stress of steel was 375 MPa and the elastic modulus of steel was 206 GPa. The relationship between the maximum stress of shell, the thickness of shell and the weight of load is shown in Fig.6, at a drop height of 6 m.

Fig.6 Relationship between maximum normal stress, thickness of shell and weight of the inner part

The maximum normal stress of shell decreases as the thickness of the shell increases and weight of inner part decreases. The maximum normal stress of shell is over the ultimate stress of steel under the given thickness range of the shell, after the weight of inner part exceed 3 kg.

We found that the maximum bending stress of the shell is much smaller compared to the normal stress so the effect of the bending stress was not calculated. The deformation of the shell occured at the center of the shell in the process of collision which can be calculated using

(10)

The relationship between the maximum deformation of the shell, the thickness of shell and the weight of the inner part is shown in Fig.7.

Fig.7 Relationship between deformation of shell and thickness of shell, the weight of inner part

As shown in Fig.7, the maximum deformation of the shell is 1.8 mm when the weight of inner part is 5 kg and the thickness of the shell is 1 mm.

2.2 Aluminum alloy

The density of the aluminum alloy (7075T6) was 2 820 kg/m3, the ultimate stress of the steel was 540 MPa and the elastic modulus of the steel was 69 GPa. The relationship between the maximum stress of shell, the thickness of shell and the weight of load is shown in Fig.8, at a drop height of 6 m.

Fig.8 Relationship between the normal stress, the thickness of shell and weight of the load

Fig.8 shows that the maximum normal stress decreases as the thickness of the shell increases and the weight of the inner part increases. The maximum normal stress did not reach the ultimate stress of aluminum alloy (7075T6) even when the weight of inner part reached 5 kg and after the thickness of the shell was over 3.3 mm.

The relationship between the maximum deformation of the shell, the thickness of shell and the weight of inner part is shown in Fig.9. This figure shows that the maximum deformation of the shell is 5.2 mm when the weight of inner part is 5 kg and the thickness of the shell is 1 mm.

Compared to the steel, the aluminum alloy (7075T6) improved the ultimate stress of the shell obviously and increased the deformation of the shell.

Fig.9 Relationship between the deformation of shell, the thickness of shell and weight of the inner part

3 Design of the Robot

3.1 Design of the wheel and axle

The density of rubber is 1 000 kg/m3and the elastic modulus is 540 MPa. As the stiffness coefficient of the wheel was selected as 45.369 N/mm (refer to Section 1 for more details), the effective cross-sectional area of a single wheel should be 290 mm2. The shape of the wheel should be round, and thus the diameter of wheel is chosen as 95 mm and the thickness of wheel is chosen as 35 mm. Drillings on the wheel are used to adjust the effective longitudinal cross-sectional area of the tire. The design of wheel is shown in Fig.10.

Fig.10 Design of the wheel

The design of the axle and bearing seat is shown in Fig.11. A common method for improving the anti-drop ability of the axle is to increase the diameter of it. In this paper, the impact of the collision is transmitted from the wheels to the axle and bearing seat, before being transmitted to the shell of the robot. The total stress acting on the shell is ((M+m)(a(t)+g)) /4.

3.2 Design of the shell

The aluminum alloy (7075T6) is selected as the material of the shell in this paper, with a thickness of 2.5 mm. A prototype is processed and the weight of the inner part is 2.5 kg. As mentioned in Section 2, the maximum normal stress of the shell is 385 MPa and the maximum deformation of the shell is 1.23 mm. The maximum normal stress and maximum deformation is reduced by thickening the middle part of the shell, which is shown in Fig.12.

Fig.11 Wheel mounting diagram

Fig.12 Design of the shell

4 Simulation and Revision of the Robot

The finite element simulation technique provides an effective solution for the dropping problem, with the Abaqus software having rich libraries of units and materials. Thus, the Abaqus is used as the simulation and solution tool in this paper. The third-order Odgen model is used to simulate the performance of the wheels, while the Johnson-Cook model is used to simulate the performance of the shell and axles. The specific parameters of the materials are given in Sections 2 and 3.

We assumed that the ground is solid and the drop height of robot is 6 m. The meshing parts and results are shown in Fig.13. The state of the robot in the process of the finite element simulation is shown in Fig.13a.

Fig.13 Stress contours of dropping postures

As seen in Fig.13, the wheels begin to compress after it comes into contact with the ground. The compression displacement of the wheels is too long when the shell is in contact with the ground, which is shown in Fig.13c.

The kinetic energy of the robot is shown in Fig.14. As shown in Fig.14, the kinetic energy of the robot has an abrupt change and has a peak value that is significantly higher than expected. The abrupt change of the kinetic energy is caused by the collision of the shell of the robot with the ground. The collision between the shell and the ground dramatically enlarges the acceleration of the robot. The key to reducing the acceleration of the robot is to avoid the contact between the shell and ground.

Fig.14 Kinetic energy curve

Therefore, it is important to increase the diameter of the wheels in order to increase the compression displacement of the wheels. According to the simulation results, the diameter of the wheels was increased to 120 mm, and the weight of the robot was decreased to 2.8 kg. The kinetic energy curve of the robot during the impact process is shown in Fig.15.

Fig.15 Kinetic energy curve after improvement

As seen in Fig.15, the improved energy curve has a smoother changing curve compared to Fig.14, with the buffer time increased from 2 ms to 5 ms. The displacement curve of the robot in the dropping process is shown in Fig.16. As shown in Fig.16, the compression displacement of the wheels can be up to 33.42 mm. The maximum value appears in 0.004 5 s, which represents the point where the robot begins to bounce back.

Fig.16 Displacement curve of the robot

Fig.17 Acceleration of the robot

The acceleration curve of the robot in the dropping process is shown in Fig.17. As shown in Fig.17, the maximum acceleration of the robot is up to 4 600 m/s2. The maximum acceleration of the robot is about 2 times larger than the calculated value, which may be caused by the nonlinear stiffness of the wheels. Furthermore, reinforcing ribs were required to reduce the deformation of the shell of the robot, as the deformation of the shell was too large under these circumstances.

5 Conclusions

Simple theoretical models were adopted to study the structural dynamic response of the drop of robot, while a finite element simulation based on Abaqus was conducted. Through the discussion of the above models, the following conclusions can be drawn.

①The range of the natural frequency (ωn) of the dropping impact is 100-316 Hz, the stiffness of wheel (k) is 10-100 N/mm and the relative damping coefficient of the robot (ε) 0.015-0.048 under normal circumstances.

②There is a nonlinear inverse relationship between the maximum acceleration of robot and the maximum compression displacement of the wheels. The compression displacement of the wheels should be no less than 35 mm. The maximum acceleration of robot is 2 000 m/s2when rubber is used as the material of the wheel and the non-linearity of the wheel stiffness is ignored.

③The maximum acceleration of the robot is 4 600 m/s2when the compression displacement of the wheels is 33.42 mm due to the non-linearity of the wheel stiffness.

④The diameter of the wheels should not be less than 120 mm; in order to avoid the collision of the shell of the robot with the ground (as the material of the wheel is selected as rubber and the ground is solid).

⑤Reinforcing ribs are required to reduce the deformation of the shell of the robot, when the aluminum alloy (7075T6) is used as the material of the shell and the thickness of the shell is 2.5 mm. This will help the robot to survive from the impact with solid ground from a free fall of 6 m.