# 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 |

## References

- Suri, S.; Jain, A.; Verma, N.; Prasertpoj, N. SCARA Industrial Automation Robot. In Proceedings of the International Conference on Power Energy, Environment and Intelligent Control (PEEIC), Greater Noida, India, 13–14 April 2018. [Google Scholar]
- Al Khawli, T.; Anwar, M.; Alzaabi, A.; Sunda-Meya, A.; Islam, S. Machine learning for robot-assisted industrial automation of aerospace applications. In Proceedings of the IEEE International Conference on Systems, Man, and Cybernetics (SMC), Miyazaki, Japan, 7–10 October 2018. [Google Scholar]
- Mohammadi Amin, F.; Rezayati, M.; van de Venn, H.W.; Karimpour, H. A Mixed-Perception Approach for Safe Human-Robot Collaboration in Industrial Automation. Sensors
**2020**, 20, 6347. [Google Scholar] [CrossRef] [PubMed] - Freschi, C.; Ferrari, V.; Melfi, F.; Ferrari, M.; Mosca, F.; Cuschieri, A. Technical review of the da Vinci surgical telemanipulator. Int. J. Med. Robot.
**2013**, 9, 396–406. [Google Scholar] [CrossRef] - Yang, C.; Guo, S.; Bao, X. An Isomorphic Interactive Device for the Interventional Surgical Robot after In Vivo Study. Micromachines
**2022**, 13, 111. [Google Scholar] [CrossRef] - Wang, W.; Li, J.; Wang, S.; Su, H.; Jiang, X. System design and animal experiment study of a novel minimally invasive surgical robot. Int. J. Med. Robot.
**2016**, 12, 73–84. [Google Scholar] [CrossRef] [PubMed] - Petereit, J.; Beyerer, J.; Asfour, T.; Gentes, S.; Hein, B.; Hanebeck, U.D.; Kirchner, F.; Dillmann, R.; Götting, H.H.; Weiser, M. ROBDEKON: Robotic systems for decontamination in hazardous environments. In Proceedings of the IEEE International Symposium on Safety, Security, and Rescue Robotics (SSRR), Würzburg, Germany, 2 September 2019. [Google Scholar]
- Lee, C.H.; Kim, S.H.; Kang, S.C.; Kim, M.S.; Kwak, Y.K. Double-track mobile robot for hazardous environment applications. Adv. Robot.
**2003**, 17, 447–459. [Google Scholar] [CrossRef][Green Version] - Luk, B.L.; Cooke, D.S.; Galt, S.; Collie, A.A.; Chen, S. Intelligent legged climbing service robot for remote maintenance applications in hazardous environments. Rob. Auton. Syst.
**2005**, 53, 142–152. [Google Scholar] [CrossRef][Green Version] - Seward, D.; Pace, C.; Agate, R. Safe and effective navigation of autonomous robots in hazardous environments. Auton. Robot.
**2007**, 22, 223–242. [Google Scholar] [CrossRef] - Mondada, F.; Bonani, M.; Raemy, X.; Pugh, J.; Cianci, C.; Klaptocz, A.; Magnenat, S.; Zufferey, J.C.; Floreano, D.; Martinoli, A. The e-puck, a robot designed for education in engineering. In Proceedings of the 9th Conference on Autonomous Robot Systems and Competitions, Castelo Branco, Portugal, 7 May 2009. [Google Scholar]
- Li, S.; Batra, R.; Brown, D.; Chang, H.D.; Ranganathan, N.; Hoberman, C.; Rus, D.; Lipson, H. Particle robotics based on statistical mechanics of loosely coupled components. Nature
**2019**, 567, 361–365. [Google Scholar] [CrossRef] - Erdem, E.Y.; Chen, Y.M.; Mohebbi, M.; Suh, J.W.; Kovacs, G.T.A.; Darling, R.B.; Bohringer, K.F. Thermally Actuated Omnidirectional Walking Microrobot. J. Microelectromech. Syst.
**2010**, 19, 433–442. [Google Scholar] [CrossRef] - Kim, S.; Clark, J.E.; Cutkosky, M.R. iSprawl: Design and Tuning for High-speed Autonomous Open-loop Running. Int. J. Rob. Res.
**2016**, 25, 903–912. [Google Scholar] [CrossRef] - Baisch, A.T.; Ozcan, O.; Goldberg, B.; Ithier, D.; Wood, R.J. High speed locomotion for a quadrupedal microrobot. Int. J. Rob. Res.
**2014**, 33, 1063–1082. [Google Scholar] [CrossRef] - Arvin, F.; Samsudin, K.; Ramli, A.R. Development of a miniature robot for swarm robotic application. Int. J. Electr. Comput. Eng.
**2009**, 1, 436–442. [Google Scholar] [CrossRef] - Goldberg, B.; Zufferey, R.; Doshi, N.; Helbling, E.F.; Whittredge, G.; Kovac, M.; Wood, R.J. Power and Control Autonomy for High-Speed Locomotion With an Insect-Scale Legged Robot. IEEE Rob. Autom. Lett.
**2018**, 3, 987–993. [Google Scholar] [CrossRef] - Nemitz, M.P.; Sayed, M.E.; Mamish, J.; Ferrer, G.; Teng, L.J.; McKenzie, R.M.; Hero, A.O.; Olson, E.; Stokes, A.A. HoverBots: Precise Locomotion Using Robots That Are Designed for Manufacturability. Front. Robot. AI
**2017**, 4, 55. [Google Scholar] [CrossRef][Green Version] - Birkmeyer, P.; Peterson, K.; Fearing, R.S. DASH: A dynamic 16g hexapedal robot. In Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), St. Louis, MO, USA, 11–15 October 2009. [Google Scholar]
- Hoover, A.M.; Steltz, E.; Fearing, R.S. RoACH: An autonomous 2. In 4 g crawling hexapod robot. In Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Nice, France, 26 September 2008. [Google Scholar]
- Zhu, P.; Peng, H.; Lu, X.; Guo, M.; Zhao, G.; Liu, W. A steerable miniature legged robot based on piezoelectric bending actuators. Smart Mater. Struct.
**2020**, 29, 045009. [Google Scholar] [CrossRef] - Ng, C.S.X.; Tan, M.W.M.; Xu, C.; Yang, Z.; Lee, P.S.; Lum, G.Z. Locomotion of Miniature Soft Robots. Adv. Mater.
**2021**, 33, e2003558. [Google Scholar] [CrossRef] - Fan, X.; Dong, X.; Karacakol, A.C.; Xie, H.; Sitti, M. Reconfigurable multifunctional ferrofluid droplet robots. Proc. Natl. Acad. Sci. USA
**2020**, 117, 27916–27926. [Google Scholar] [CrossRef] [PubMed] - Xiao, J.; Xiao, J.; Xi, N. Minimal power control of a miniature climbing robot. In Proceedings of the IEEE/ASME International Conference on Advanced Intelligent Mechatronics (AIM), Kobe, Japan, 20–24 July 2003. [Google Scholar]
- Kossett, A.; D’Sa, R.; Purvey, J.; Papanikolopoulos, N. Design of an improved land/air miniature robot. In Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), Anchorage, AK, USA, 3–8 May 2010. [Google Scholar]
- Seok, S.; Onal, C.D.; Cho, K.-J.; Wood, R.J.; Rus, D.; Kim, S. Meshworm: A peristaltic soft robot with antagonistic nickel titanium coil actuators. IEEE/ASME Trans. Mechatron.
**2012**, 18, 1485–1497. [Google Scholar] [CrossRef] - Kohut, N.J.; Hoover, A.M.; Ma, K.Y.; Baek, S.S.; Fearing, R.S. MEDIC: A legged millirobot utilizing novel obstacle traversal. In Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), Shanghai, China, 9–13 May 2011. [Google Scholar]
- Pickem, D.; Lee, M.; Egerstedt, M. The GRITSBot in its natural habitat-a multi-robot testbed. In Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), Seattle, WA, USA, 26–30 May 2015. [Google Scholar]
- Pullin, A.O.; Kohut, N.J.; Zarrouk, D.; Fearing, R.S. Dynamic turning of 13 cm robot comparing tail and differential drive. In Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), Saint Paul, MN, USA, 14–18 May 2012. [Google Scholar]
- Rios, S.A.; Fleming, A.J.; Yong, Y.K. Miniature resonant ambulatory robot. IEEE Rob. Autom. Lett.
**2016**, 2, 337–343. [Google Scholar] [CrossRef] - Rubenstein, M.; Ahler, C.; Nagpal, R. Kilobot: A Low Cost Scalable Robot System for Collective Behaviors. In Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), Saint Paul, MN, USA, 14–18 May 2012. [Google Scholar]
- Klingner, J.; Kanakia, A.; Farrow, N.; Reishus, D.; Correll, N. A stick-slip omnidirectional powertrain for low-cost swarm robotics: Mechanism, calibration, and control. In Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Chicago, IL, USA, 14–18 September 2014. [Google Scholar]
- Zarrouk, D.; Fearing, R.S. Controlled In-Plane Locomotion of a Hexapod Using a Single Actuator. IEEE Trans. Rob.
**2015**, 31, 157–167. [Google Scholar] [CrossRef] - Zarrouk, D.; Fearing, R.S. Compliance-based dynamic steering for hexapods. In Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Algarve, Portugal, 7–12 October 2012. [Google Scholar]
- Dharmawan, A.G.; Hariri, H.H.; Foong, S.; Soh, G.S.; Wood, K.L. Steerable miniature legged robot driven by a single piezoelectric bending unimorph actuator. In Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), Singapore, 29 May–3 June 2017. [Google Scholar]
- Wang, G.; Li, C.; Yuan, T. Design and experiment of a small-scale walking robot employing stick-slip motion principle. Rev. Sci. Instrum.
**2017**, 88, 115001. [Google Scholar] [CrossRef] [PubMed] - Zhang, Y.; Zhu, R.; Wu, J.; Wang, H. SimoBot: An Underactuated Miniature Robot Driven by a Single Motor. IEEE/ASME Trans. Mechatron.
**2022**, 26, 2616–2628. [Google Scholar] [CrossRef]

**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