Robots and robotic systems

SUMMARY: Robots, their motion driven by mathematical algorithms and coordinate or polar geometries, have long been incorporated into society and popular culture.

Robots and robotic systems are increasingly commonplace in many areas of daily life, such as manufacturing, medicine, exploration, security, personal assistance, and entertainment. In general, a robot is a mechanical device that can perform independent tasks guided by some sort of programming. Sometimes, robots are intended to replace humans in tedious or hazardous tasks. In other tasks, such as some surgeries, robots may actually exceed human capabilities. For many, the word “robot” brings to mind both futuristic androids, which are robots that are designed to look human and cyborgs, which contain both mechanical and biological components. Robots used in many industrial applications, such as in medicine, bomb disposal, and repetitive jobs, rarely resemble humans. However, several humanoid robots and robots that realistically mimic the look and behavior of animals have been produced. In 2008, a Japanese play was written and produced for both robots and human actors, and robot animals have sometimes been marketed as replacements for biological pets. The word “robot” can also refer to software-like web crawlers that run automated tasks over the Internet to gather data, though “bot” is a more common name. The field of robotics generates many interesting problems in both theoretical and applied mathematics and benefits from the contributions of mathematicians. For some, the ultimate quest in the twenty-first century and beyond is to develop materials, technology, and algorithms to create robots that meet or perhaps exceed human levels of perception, behavior, and intelligence. Nanorobots, which are ultra-small robots about the size of a nanometer, might one day be developed for tasks like hunting and destroying cancer cells.

Brief History

Playwright Karel Capek is typically credited with introducing the word “robot” from the Czech word for “laborer,” in his 1920 play R.U.R. (Rossum’s Universal Robots). Another writer who popularized robots was Isaac Asimov, who introduced the term “robotics” in his 1941 short story Runaround. However, robotic devices can be found much farther back in history. One early robotic device was a water clock produced by the Babylonians, which used the mathematics of volumes and rates of water flow to calculate time. Greek mathematician Hero of Alexandra described the use of weights and ropes to construct a mobile cart that could be programmed to move along a path. In the thirteenth century, Muslim mathematician and scientist Abu Al-’Iz Ibn Isma’il ibn Al-Razaz Al-Jazari created a set of programmable musicians. The drummer was operated by a rotating shaft that manipulated levers to produce rhythms. Around 1495, Italian painter and mathematician Leonardo da Vinci used his knowledge of the mathematics of anatomy and bodily movement to sketch designs for a warrior robot outfitted in medieval armor.

Interest in robotics accelerated in the nineteenth century as early computer technology with punch cards began to be incorporated into systems such as that used for the Jacquard loom, named for Joseph Jacquard. Others, such as Pafnuty Chebyshev, studied the theoretical mathematics of linkages, inventing the Chebyshev linkage that converts rotating motion to approximate straight-line motion. Charles Babbage’s mathematical engines were some of the first mechanical computers. These engines used finite differences to calculate the values of polynomials. Such inventions were forerunners of computer-controlled robot technology that quickly progressed in the mid-twentieth century to transistors and integrated circuits. Mathematician Norbert Weiner is often known as the “father of cybernetics,” which is the science of self-regulating feedback systems, for his work and 1948 book Cybernetics: Or Control and Communication in the Animal and Machine.

Cybernetics is not synonymous with artificial intelligence or robotics, but this mathematical discipline is essential for environmentally responsive or adaptive robots. Some other areas of mathematics that have contributed to the development and implementation of robots included algebraic and differential geometry, which is used to help solve problems, such as orientation and movement in three dimensions; partial differential equations, which are used to model many aspects of behavior; optimization algorithms to help sequence tasks; combinatorics, which is used to investigate modular components and systems; and Bayesian statistical methods, named for Thomas Bayes, which can be employed in dynamic perception and machine learning.

Robotic Motion

In the twentieth and twenty-first centuries, many robots are complex, electromechanical devices that move and interact with physical objects, often replacing or augmenting human actions by carrying out certain tasks. Some mobile robots use articulated legs or wheels. Somewhat more common are stationary robotic arms with joints that allow for motion similar to the way joints allow human limbs to move. Having more joints increases the possible angles for movement and degrees of freedom, and hence increases fluid motion and accuracy. Articulated robots, used widely in various industries to perform tasks such as welding components or spray-painting parts, look much like human arms and have at least three joints. If the joints are slide-only, called “prismatic joints,” then the robot arm can reach any position in a rectangular workspace by means of translations. If one joint is hinged, which is called a “revolute joint,” then all points within a cylindrical workspace can be reached by a combination of rotation and translation. If two of the joints are hinged, a robot arm with a polar geometry is achieved. Inventor George Devol and engineer Joseph Engelberger developed one of the first modern-day programmable robots, Unimate, which began operation in 1961 at a General Motors plant. In 1969, Stanford University student Victor Scheinman created the predecessor for all robotic arms, the Stanford arm.

Mathematical programming and calibration for proper movement of robots depends on kinematics, which is the study of motion; and dynamics, which is the study of how force affects motion. With articulated or jointed robots, for example, the mathematics of kinematics is at the heart of positioning, collision avoidance, and redundancy. Direct kinematics makes use of given joint values to determine the end position that a robot arm may achieve. The mathematics of inverse kinematics is used to determine the required values for the joints when the end position of the robotic arm motion is known. Getting the robot arm to the right position is only half of the mathematical problem. The other half involves calculating forces using dynamics. For example, a robot designed to fight fires would need motors to move the robot and its arms. Calculations incorporated in determining which motors to use would involve dynamics. Inverse dynamics would help determine the required values of forces to generate the desired acceleration of the robot or its components. The movement involved in robotics most often occurs in three-dimensional space, so geometry plays a role in the positioning and movement of robots. Matrices can be used to represent the points through which robots navigate. These algebraic representations are then reviewed and coordinated using sophisticated applications of basic calculus principles, like differentiation, to ensure maximum efficiency when designing and operating robots.

Movement and action in robots are driven by algorithms. Some robots respond to direct human input from keyboard commands or from haptic devices that respond to tactile or body motion. Others autonomously perform programmed tasks. Some robots are “smart” or “intelligent,” meaning that they are able to sense and adapt to their surroundings while completing their tasks. Even then, these robots are able to accomplish tasks only because they have been programmed to do so. For example, “smart” mobile robots, like lunar rovers, make use of a variety of sensors with terrain-identification and obstacle-detection programs using input data and probabilistic models to guide trajectory and avoid collisions. Probabilistic robotics is increasingly of interest, with the goal of developing algorithms that facilitate accurate autonomous decision making in the face of real-work complexity and uncertainty, which would increase the reliability of automated behavior and more closely replicate the type of processing that occurs in the human brain.

Robots: Fiction and Fact

Robots are widely used in entertainment, especially science fiction. Mary Shelley’s 1818 novel Frankenstein is cited by some as showing that scientific creations able to perform human tasks long preceded television and movies. Some well-known examples include C-3PO from the Star Wars series and Wall-E from the 2008 Pixar movie of the same name. Data, from the 1987–1994 television series Star Trek: The Next Generation, is an example of a fictional android. The science fiction show Humans (2015–18) and the science fiction Western Westworld (2016–) both also heavily feature androids. The Borg species from the Star Trek series, the Terminator robot from The Terminator movie series, and the DC comic book superhero Cyborg are examples of cyborg characters, usually hybrid humans whose biological capabilities are sustained or enhanced through robotic elements—though the Terminator may be thought of by some as a robot enhanced by biology. Enhancing human capabilities through robotic elements, like pacemakers and prosthetic devices, is common in the twenty-first century. However, the medical applications of robotics have not focused on humans achieving superhuman powers (as is done in fiction) but rather on helping those with medical conditions and disabilities.

Robots in Education

Robots are often used in schools to motivate learning of mathematics concepts, such as two- and three-dimensional coordinate geometry. The roBlocks construction system was developed by computational design scientists Mark Gross and Eric Schweikardt. Users can build robots using modular sensor, logic, and actuator blocks to study concepts like kinematics, feedback, and control. They can also create their own control programs to further explore robot mathematics and dynamics. The Lego Group produces a robotic construction and programming system called Mindstorms NXT that has been marketed for both education and entertainment. Robots can also be used to help with social and emotional skills, language learning, and programming.

Bibliography

Craig, John J. Introduction to Robotics: Mechanics and Control. 3rd ed. Prentice Hall, 2004.

Gottsegen, Gordon, and Matthew Urwin. "7 Examples of Robotics in Education to Know." Built In, 8 July 2024, builtin.com/robotics/robotics-in-the-classroom. Accessed 1 Oct. 2024.

Murray, Richard M., Zexiang Li, and S. Shankar Sastry. A Mathematical Introduction to Robotic Manipulation. CRC Press, 1994.

Thrun, Sebastian, Wolfram Burgard, and Dieter Fox. Probabilistic Robotics. MIT Press, 2005.

"Types of Robots: How Robotics Technologies Are Shaping Today’s World." Intel, www.intel.com/content/www/us/en/robotics/types-and-applications.html. Accessed 1 Oct. 2024.