Editing Microbotics (section)

== Locomotion of microrobots ==
Microrobots employ various locomotion methods to navigate through different environments, from solid surfaces to fluids. These methods are often inspired by biological systems and are designed to be effective at the micro-scale.<ref name=":0">{{Cite journal |last1=Abbott |first1=Jake J. |last2=Peyer |first2=Kathrin E. |last3=Lagomarsino |first3=Marco Cosentino |last4=Zhang |first4=Li |last5=Dong |first5=Lixin |last6=Kaliakatsos |first6=Ioannis K. |last7=Nelson |first7=Bradley J. |date=November 2009 |title=How Should Microrobots Swim? |url=http://journals.sagepub.com/doi/10.1177/0278364909341658 |journal=The International Journal of Robotics Research |language=en |publication-date=July 21, 2009 |volume=28 |issue=11–12 |pages=1434–1447 |doi=10.1177/0278364909341658 |issn=0278-3649|url-access=subscription }}</ref> Several factors need to be maximized (precision, speed, stability), and others have to be minimized (energy consumption, energy loss) in the design and operation of microrobot locomotion in order to guarantee accurate, effective, and efficient movement.<ref name=":1">{{Cite book |last=Sitti |first=Metin |title=Mobile microrobotics |date=2017 |publisher=MIT Press |isbn=978-0-262-03643-6 |series=Intelligent robotics and autonomous agents |location=Cambridge, MA}}</ref>

When describing the locomotion of microrobots, several key parameters are used to characterize and evaluate their movement, including stride length and transportation costs. A stride refers to a complete cycle of movement that includes all the steps or phases necessary for an organism or robot to move forward by repeating a specific sequence of actions. Stride length (𝞴<sub>s</sub>) is the distance covered by a microrobot in one complete cycle of its locomotion mechanism. Cost of transport (CoT) defines the work required to move a unit of mass of a microrobot a unit of distance <ref name=":1" />

=== Surface locomotion ===
Microrobots that use surface locomotion can move in a variety of ways, including walking, crawling, rolling, or jumping. These microrobots meet different challenges, such as gravity and friction. One of the parameters describing surface locomotion is the Frounde number, defined as:

<math>Fr=\frac{v^2}{g*\lambda_s}</math>

Where ''v'' is motion speed, g is the gravitational field, and 𝞴s is a stride length. A microrobot demonstrating a low [[Froude number]] moves slower and more stable as gravitational forces dominate, while a high Froude number indicates that inertial forces are more significant, allowing faster and potentially less stable movement.<ref name=":1" />

Crawling is one of the most typical surface locomotion types. The mechanisms employed by microrobots for crawling can differ but usually include the synchronized movement of multiple legs or appendages. The mechanism of the microrobots' movements is often inspired by animals such as insects, reptiles, and small mammals. An example of a crawling microrobot is RoBeetle. The autonomous microrobot weighs 88 milligrams (approximately the weight of three rice grains). The robot is powered by the catalytic combustion of methanol. The design relies on controllable NiTi-Pt–based catalytic artificial micromuscles with a mechanical control mechanism.<ref>{{Cite journal |last1=Yang |first1=Xiufeng |last2=Chang |first2=Longlong |last3=Pérez-Arancibia |first3=Néstor O. |date=2020-08-26 |title=An 88-milligram insect-scale autonomous crawling robot driven by a catalytic artificial muscle |url=https://www.science.org/doi/10.1126/scirobotics.aba0015 |journal=Science Robotics |language=en |volume=5 |issue=45 |doi=10.1126/scirobotics.aba0015 |pmid=33022629 |issn=2470-9476|url-access=subscription }}</ref>

Other options for actuating microrobots' surface locomotion include magnetic, electromagnetic, piezoelectric, electrostatic, and optical actuation.

=== Swimming locomotion ===
Swimming microrobots are designed to operate in 3D through fluid environments, like biological fluids or water. To achieve effective movements, locomotion strategies are adopted from small aquatic animals or microorganisms, such as flagellar propulsion, pulling, chemical propulsion, jet propulsion, and tail undulation. Swimming microrobots, in order to move forward, must drive water backward.<ref name=":1" />

Microrobots move in the low Reynolds number regime due to their small sizes and low operating speeds, as well as high viscosity of the fluids they navigate. At this level, viscous forces dominate over inertial forces. This requires a different approach in the design compared to swimming at the macroscale in order to achieve effective movements. The low Reynolds number also allows for accurate movements, which makes it good application in medicine, micro-manipulation tasks, and environmental monitoring.<ref name=":0" /><ref name=":1" />

Dominating viscous ([[Stokes' law|Stokes]]) drag forces T<sub>drag</sub> on the robot balances the propulsive force F<sub>p</sub> generated by a swimming mechanism.

 <math>T=T_(drag)=\frac{bv}{m}</math>

Where b is the viscous drag coefficient, v is motion speed, and m is the body mass.<ref name=":1" />

One of the examples of a swimming microrobot is a helical magnetic microrobot consisting of a spiral tail and a magnetic head body. This design is inspired by the flagellar motion of bacteria. By applying a magnetic torque to a helical microrobot within a low-intensity rotating magnetic field, the rotation can be transformed into linear motion. This conversion is highly effective in low Reynolds number environments due to the unique helical structure of the microrobot. By altering the external magnetic field, the direction of the spiral microrobot's motion can be easily reversed.<ref>{{Cite journal |last1=Liu |first1=Huibin |last2=Guo |first2=Qinghao |last3=Wang |first3=Wenhao |last4=Yu |first4=Tao |last5=Yuan |first5=Zheng |last6=Ge |first6=Zhixing |last7=Yang |first7=Wenguang |date=2023-01-01 |title=A review of magnetically driven swimming microrobots: Material selection, structure design, control method, and applications |journal=Reviews on Advanced Materials Science |language=en |volume=62 |issue=1 |page=119 |doi=10.1515/rams-2023-0119 |bibcode=2023RvAMS..62..119L |issn=1605-8127|doi-access=free }}</ref>

=== At Air-Fluid Interface locomotion ===
In the specific instance when microrobots are at the air-fluid interface, they can take advantage of surface tension and forces provided by capillary motion. At the point where air and a liquid, most often water, come together, it is possible to establish an interface capable of supporting the weight of the microrobots through the work of surface tension. Cohesion between molecules of a liquid creates surface tension, which otherwise creates ‘skin’ over the water’s surface, letting the microrobots float instead of sinking. Through such concepts, microrobots could perform specific locomotion functions, including climbing, walking, levitating, floating, and or even jumping, by exploring the characteristics of the air-fluid interface.<ref name=":1" /><ref>{{Cite journal |last1=Koh |first1=Je-Sung |last2=Yang |first2=Eunjin |last3=Jung |first3=Gwang-Pil |last4=Jung |first4=Sun-Pill |last5=Son |first5=Jae Hak |last6=Lee |first6=Sang-Im |last7=Jablonski |first7=Piotr G. |last8=Wood |first8=Robert J. |last9=Kim |first9=Ho-Young |last10=Cho |first10=Kyu-Jin |date=2015-07-31 |title=Jumping on water: Surface tension–dominated jumping of water striders and robotic insects |url=https://www.science.org/doi/10.1126/science.aab1637 |journal=Science |language=en |volume=349 |issue=6247 |pages=517–521 |doi=10.1126/science.aab1637 |bibcode=2015Sci...349..517K |issn=0036-8075|url-access=subscription }}</ref>

Due to the surface tension ,σ, the buoyancy force, F<sub>b</sub>, and the curvature force, F<sub>c</sub>, play the most important roles, particularly in deciding whether the microrobot will float or sink on the surface of the liquid. This can be expressed as

<math>\sigma=F_b+F_c</math>

F<sub>b</sub> is obtained by integrating the hydrostatic pressure over the area of the body in contact with the water. In contrast, F<sub>c</sub> is obtained by integrating the curvature pressure over this area or, alternatively, the vertical component of the surface tension, <math>\sigma\sin\theta</math>, along the contact perimeter.<ref>{{Cite journal |last1=Hu |first1=David L. |last2=Chan |first2=Brian |last3=Bush |first3=John W. M. |date=August 2003 |title=The hydrodynamics of water strider locomotion |url=https://www.nature.com/articles/nature01793 |journal=Nature |language=en |volume=424 |issue=6949 |pages=663–666 |doi=10.1038/nature01793 |pmid=12904790 |bibcode=2003Natur.424..663H |issn=0028-0836|url-access=subscription }}</ref>

One example of a climbing, walking microrobot that utilizes air-fluid locomotion is the Harvard Ambulatory MicroRobot with Electroadhesion (HAMR-E).<ref name=":2">{{Cite journal |last1=de Rivaz |first1=Sébastien D. |last2=Goldberg |first2=Benjamin |last3=Doshi |first3=Neel |last4=Jayaram |first4=Kaushik |last5=Zhou |first5=Jack |last6=Wood |first6=Robert J. |date=2018-12-19 |title=Inverted and vertical climbing of a quadrupedal microrobot using electroadhesion |url=https://www.science.org/doi/10.1126/scirobotics.aau3038 |journal=Science Robotics |language=en |volume=3 |issue=25 |doi=10.1126/scirobotics.aau3038 |pmid=33141691 |issn=2470-9476|url-access=subscription }}</ref> The control system of HAMR-E is developed to allow the robot to function in a flexible and maneuverable manner in a challenging environment. Its features include its ability to move on horizontal, vertical, and inverted planes, which is facilitated by the electro-adhesion system. This uses electric fields to create electrostatic attraction, causing the robot to stick and move on different surfaces.<ref>{{Cite journal |last1=Rajagopalan |first1=Pandey |last2=Muthu |first2=Manikandan |last3=Liu |first3=Yulu |last4=Luo |first4=Jikui |last5=Wang |first5=Xiaozhi |last6=Wan |first6=Chaoying |date=July 2022 |title=Advancement of Electroadhesion Technology for Intelligent and Self-Reliant Robotic Applications |url=https://onlinelibrary.wiley.com/doi/10.1002/aisy.202200064 |journal=Advanced Intelligent Systems |language=en |volume=4 |issue=7 |doi=10.1002/aisy.202200064 |issn=2640-4567}}</ref> With four compliant and electro-adhesion footpads, HAMR-E can safely grasp and slide over various substrate types, including glass, wood, and metal.<ref name=":2" /> The robot has a slim body and is fully posable, making it easy to perform complex movements and balance on any surface.

=== Flying locomotion ===
Flying microrobots are miniature robotic systems meticulously engineered to operate in the air by emulating the flight mechanisms of insects and birds. These microrobots have to overcome the issues related to lift, thrust, and movement that are challenging to accomplish at such a small scale where most aerodynamic theories must be modified. Active flight is the most energy-intensive mode of locomotion, as the microrobot must lift its body weight while propelling itself forward.<ref name=":1" /> To achieve this function, these microrobots mimic the movement of insect wings and generate the necessary airflow for producing lift and thrust. Miniaturized wings of the robots are actuated with [[Piezoelectric material|Piezoelectric]] materials, which offer better control of wing kinematics and flight dynamics.<ref>{{Cite journal |last1=Jafferis |first1=Noah T. |last2=Helbling |first2=E. Farrell |last3=Karpelson |first3=Michael |last4=Wood |first4=Robert J. |date=June 2019 |title=Untethered flight of an insect-sized flapping-wing microscale aerial vehicle |url=https://www.nature.com/articles/s41586-019-1322-0 |journal=Nature |language=en |volume=570 |issue=7762 |pages=491–495 |doi=10.1038/s41586-019-1322-0 |pmid=31243384 |bibcode=2019Natur.570..491J |issn=1476-4687|url-access=subscription }}</ref>

To calculate the necessary aerodynamic power for maintaining a hover with flapping wings, the primary physical equation is expressed as

<math>mg=2*\rho*l^2*\phi*\upsilon_i^2</math>

where m is the body mass, L is the wing length, Φ represents the wing flapping amplitude in radians, ρ indicates the air density, and V<sub>i</sub> corresponds to the induced air speed surrounding the body, a consequence of the wings' flapping and rotation movements. This equation illustrates that a small insect or robotic device must impart sufficient momentum to the surrounding air to counterbalance its own weight.<ref>{{Cite book |last1=Shyy |first1=Wei |url=https://www.cambridge.org/core/books/aerodynamics-of-low-reynolds-number-flyers/B73F3DB3BF37F6D6A76E8194CFC2F692 |title=Aerodynamics of Low Reynolds Number Flyers |last2=Lian |first2=Yongsheng |last3=Tang |first3=Jian |last4=Viieru |first4=Dragos |last5=Liu |first5=Hao |date=2007 |publisher=Cambridge University Press |isbn=978-0-521-88278-1 |series=Cambridge Aerospace Series |location=Cambridge |doi=10.1017/cbo9780511551154}}</ref>

One example of a flying microrobot that utilizes flying locomotion is the RoboBee and DelFly Nimble,<ref name=":3">{{Cite journal |last1=Wang |first1=S. |last2=den Hoed |first2=M. |last3=Hamaza |first3=S. |date=2024 |title=A Low-cost Fabrication Approach to Embody Flexible and Lightweight Strain Sensing on Flapping Wings: 2024 IEEE International Conference onRobotics and Automation |url=https://research.tudelft.nl/en/publications/a-low-cost-fabrication-approach-to-embody-flexible-and-lightweigh |journal=IEEE ICRA 2024 - Workshop on Bioinspired, Soft, and Other Novel Design Paradigms for Aerial Robotics}}</ref><ref name=":4">{{Cite journal |last1=Chen |first1=Yufeng |last2=Wang |first2=Hongqiang |last3=Helbling |first3=E. Farrell |last4=Jafferis |first4=Noah T. |last5=Zufferey |first5=Raphael |last6=Ong |first6=Aaron |last7=Ma |first7=Kevin |last8=Gravish |first8=Nicholas |last9=Chirarattananon |first9=Pakpong |last10=Kovac |first10=Mirko |last11=Wood |first11=Robert J. |date=2017-10-25 |title=A biologically inspired, flapping-wing, hybrid aerial-aquatic microrobot |url=https://www.science.org/doi/10.1126/scirobotics.aao5619 |journal=Science Robotics |language=en |volume=2 |issue=11 |doi=10.1126/scirobotics.aao5619 |pmid=33157886 |issn=2470-9476}}</ref> which, regarding flight dynamics, emulate bees and fruit flies, respectively. Harvard University invented the RoboBee, a miniature robot that mimics a bee fly, takes off and lands like one, and moves around confined spaces. It can be used in self-driving pollination and search operations for missing people and things. The DelFly Nimble, developed by the Delft University of Technology, is one of the most agile micro aerial vehicles that can mimic the maneuverability of a fruit fly by doing different tricks due to its minimal weight and advanced control mechanisms.<ref name=":3" /><ref name=":4" />