# Miniature Mobile Robot Using Only One Tilted Vibration Motor

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## Abstract

**:**

## 1. Introduction

## 2. Robot Design

#### 2.1. Mechanical Design

#### 2.2. Locomotion

#### 2.3. Communication and Sensing

#### 2.4. Electrical Circuit

^{2}C serial communication protocol for communication with the controller. Furthermore, the controller has an additional four output pins available for accessory sensors and actuators, which may be useful for complex tasks.

#### 2.5. Cost

## 3. Modeling

#### 3.1. Kinematics and Dynamics Analysis

#### 3.2. Trajectory Modeling

## 4. Motion Strategy

## 5. Experiments

#### 5.1. Performance of the Motor

#### 5.2. Following Circular Trajectories

#### 5.3. Following Arbitrary Trajectories

#### 5.4. Commuication and Sensing

**Step 1:**Record the maximum light intensity during the entire rotation.

**Step 2:**Determine the moving direction.

**Step 3:**Approaching Transmitter.

## 6. Conclusions and Discussion

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Appendix A

Symbols | Description |
---|---|

$x,y,z$ | Coordinate system 1 (on the vibration motor) |

$X,Y,Z$ | Coordinate system 2 (on the robot body) |

${X}_{G},{Y}_{G},{Z}_{G}$ | Coordinate system 3 (the global coordinate system) |

${m}_{r}$ | The mass of the rotor and eccentric mass |

${\omega}_{r}$ | The angular speed of the vibration motor |

${d}_{r}$ | $\mathrm{The}\mathrm{distance}\mathrm{between}\mathrm{the}\mathrm{rotor}\u2019\mathrm{s}\mathrm{center}\mathrm{of}\mathrm{gravity}\mathrm{and}\mathrm{the}z$ axis |

$F$ | The centrifugal force generated by the rotor |

$\theta $ | The tilt angle of the motor |

${F}_{x}$$,{F}_{y}$$,{F}_{z}$ | $\mathrm{The}\mathrm{components}\mathrm{of}\mathrm{the}\mathrm{centrifugal}\mathrm{force}F$$\mathrm{in}\mathrm{the}x$$,y$$,\mathrm{and}z$ directions |

${F}_{X}$$,{F}_{Y}$$,{F}_{Z}$ | $\mathrm{The}\mathrm{components}\mathrm{of}\mathrm{the}\mathrm{centrifugal}\mathrm{force}F$$\mathrm{in}\mathrm{the}X$$,Y$$,\mathrm{and}Z$ directions |

${F}_{XY}$ | $\mathrm{The}\mathrm{components}\mathrm{of}\mathrm{the}\mathrm{centrifugal}\mathrm{force}F$$\mathrm{in}\mathrm{the}XY$ plane |

${f}_{XY}$ | $\mathrm{The}\mathrm{friction}\mathrm{force}\mathrm{in}\mathrm{the}XY$ plane |

${\gamma}_{XY}$ | $\mathrm{The}\mathrm{angle}\mathrm{between}{F}_{XY}$$\mathrm{and}\mathrm{the}Y$ axis |

$\mu $ | The coefficient of friction between the robot legs and the ground |

$m$ | The mass of the robot |

$g$ | Gravitational acceleration |

$d$ | The distance between the origins of coordinate system 1 and 2 |

$h$ | The distance between the robot gravity center and the origin of coordinate system 2 |

${f}_{X}$$,{f}_{Y}$ | $\mathrm{The}\mathrm{components}\mathrm{of}\mathrm{the}\mathrm{friction}\mathrm{force}{f}_{XY}$$\mathrm{in}\mathrm{the}X$$\mathrm{and}Y$ directions |

${a}_{X}$$,{a}_{Y}$ | $\mathrm{The}\mathrm{acceleration}\mathrm{of}\mathrm{the}\mathrm{robot}\mathrm{in}X$$\mathrm{and}Y$ directions |

${\alpha}_{Z}$ | $\mathrm{The}\mathrm{angular}\mathrm{acceleration}\mathrm{of}\mathrm{the}\mathrm{robot}\mathrm{around}\mathrm{the}Z$ axis |

${J}_{Z}$ | $\mathrm{The}\mathrm{moment}\mathrm{of}\mathrm{inertia}\mathrm{of}\mathrm{the}\mathrm{robot}\mathrm{around}\mathrm{the}Z$ axis |

${r}_{leg}$ | $\mathrm{The}\mathrm{distance}\mathrm{between}\mathrm{the}\mathrm{robot}\u2019\mathrm{s}\mathrm{leg}\mathrm{and}\mathrm{the}Z$ axis at the initial status |

$\u2206t$ | The time step for each iteration |

${v}_{X}$$,{v}_{Y}$ | $\mathrm{The}\mathrm{linear}\mathrm{speed}\mathrm{of}\mathrm{the}\mathrm{robot}\mathrm{in}\mathrm{the}X$$\mathrm{and}Y$ directions |

${\omega}_{Z}$ | $\mathrm{The}\mathrm{angular}\mathrm{speed}\mathrm{of}\mathrm{the}\mathrm{robot}\mathrm{around}Z$ axis |

$\u2206X$$,\u2206Y$ | $\mathrm{The}\mathrm{displacement}\mathrm{of}\mathrm{the}\mathrm{robot}\mathrm{during}\mathrm{each}\mathrm{iteration}\mathrm{in}\mathrm{the}X$$\mathrm{and}Y$ directions |

$\u2206{\phi}_{Z}$ | $\mathrm{The}\mathrm{angular}\mathrm{angle}\mathrm{of}\mathrm{the}\mathrm{robot}\mathrm{around}\mathrm{the}Z$ axis during each iteration |

${X}_{G}$$,{Y}_{G}$ | The position of the robot in the global coordinate system |

Parameters | Value |

${m}_{r}$ | $2.5\times {10}^{-4}$ kg |

${d}_{r}$ | $1.54\times {10}^{-3}$ m |

${\omega}_{r}$ | 3600 rpm |

$\theta $ | 30° |

$\mu $ | 0.3 |

$m$. | $11.15\times {10}^{-3}$ kg |

$h$ | $2.5\times {10}^{-3}$ m |

${J}_{Z}$ | $4.09\times {10}^{-7}$$\mathrm{kg}\cdot {\mathrm{m}}^{2}$ |

${r}_{leg}$ | 0.01 m |

$\u2206t$ | ${10}^{-4}$ s |

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**Figure 1.**Miniature mobile robots. (

**a**) The prototype compared with a pencil as a reference. (

**b**) The components of the robot, including some RGB LEDs, a visible light sensor, the robot’s body, a vibration motor, a battery, a controller, and magnets.

**Figure 3.**Definition of parameters and load distribution. In the coordinate system $XYZ$, the line from leg B to D is the $X$ axis, the center of the legs is the origin, and the $XY$ plane is horizontal. (

**a**) Cartesian coordinate systems in robot modeling. The forces on the robot resulting in rotating around the $Z$-axis in (

**b**) and translation on the $XY$ plane in (

**c**).

**Figure 4.**The movement of the robot on the ${X}_{G}{Y}_{G}$ plane. (

**a**) The trajectory circle generated by the robot while the rotor continuously spins at a constant speed. The orange spiral line is the trajectory during one revolution of the rotor. There is some parameter variance including the acceleration, velocity, and displacement on both $X$-axis and $Y$-axis, and the angular acceleration, angular velocity, and rotational angle along the $Z$-axis. (

**b**) The corresponding trajectories of the robot under different motor speed. (

**c**) The blue and red arcs represent that the robot’s motor is driven by positive and negative voltage and the robot rotates in counterclockwise and clockwise directions, respectively.

**Figure 5.**Effects of different parameters on robot motion performance, including (

**a**) the motor speed, (

**b**) the initial inclination angle, (

**c**) the horizontal distance between the legs, (

**d**) the coefficient of friction, and (

**e**) robot mass.

**Figure 6.**The path of the robot while fitting a large circle, a straight line, and an arbitrary curve, respectively.

**Figure 7.**The motor speeds and centrifugal force on different voltages. The centrifugal force of the motor while the motor is powered on 1.1 V.

**Figure 9.**(

**a**–

**d**) The trajectories of the robot fitting all the letters of WOOD (in honor of Professor Robert J. Wood).

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**MDPI and ACS Style**

Zhu, R.; Zhang, Y.; Wang, H.
Miniature Mobile Robot Using Only One Tilted Vibration Motor. *Micromachines* **2022**, *13*, 1184.
https://doi.org/10.3390/mi13081184

**AMA Style**

Zhu R, Zhang Y, Wang H.
Miniature Mobile Robot Using Only One Tilted Vibration Motor. *Micromachines*. 2022; 13(8):1184.
https://doi.org/10.3390/mi13081184

**Chicago/Turabian Style**

Zhu, Renjie, Yifan Zhang, and Hongqiang Wang.
2022. "Miniature Mobile Robot Using Only One Tilted Vibration Motor" *Micromachines* 13, no. 8: 1184.
https://doi.org/10.3390/mi13081184