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Zero moment point

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The zero moment point (also referred to as zero-tilting moment point ) is a concept related to the dynamics and control of legged locomotion , e.g. , for humanoid or quadrupedal robots. It specifies the point with respect to which reaction forces at the contacts between the feet and the ground do not produce any moment in the horizontal direction, i.e. , the point where the sum of horizontal inertia and gravity forces is zero. The concept assumes the contact area is planar and has sufficiently high friction to keep the feet from sliding.

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36-508: This concept was introduced to the legged locomotion community in January 1968 by Miomir Vukobratović and Davor Juričić at The Third All-Union Congress of Theoretical and Applied Mechanics in Moscow. The term "zero moment point" itself was coined in works that followed between 1970 and 1972, and was widely and successfully reproduced in works from robotics groups around the world. The zero moment point

72-509: A deal worth US$ 1.7   billion. The deal was subject to federal approval from the U.S. Federal Trade Commission (FTC) and other regulatory agencies. In September 2022, the FTC requested more data from both companies, amid concerns about Amazon's market power and the privacy implications of it gaining information about consumer floorplans. In June 2023, the UK's Competition and Markets Authority cleared

108-465: A docking station to which the robot returns to recharge at the end of its cleaning cycle. They work in conjunction with accessories that use both IR and RF . The company intentionally allows customers to hack the robot because they want people to experiment and improve the product. The API for the serial has been published and the serial port made easily accessible to make modifications easy to perform. In 2015, iRobot released an updated Roomba called

144-578: A full product release in 2006. Early models required either a special non-bleach cleaning solution or white vinegar to wash hard floors. Newer units could use plain water. Several versions were marketed. iRobot discontinued the Scooba line of products in favor of the Braava line of floor moppers in 2016. Dirt Dog was a variant of Roomba designed for workshop use that was released in 2006. The product picks up small objects such as nuts , bolts , dirt, and debris from

180-429: A predefined stability region. The position of the zero moment point is affected by the referred mass and inertia of the robot's torso, since its motion generally requires large angle torques to maintain a satisfactory dynamical postural stability. One approach to solve this problem consists of using small trunk motions to stabilize the posture of the robot. However, some new planning methods are being developed to define

216-648: A range of autonomous home vacuum cleaners ( Roomba ), floor moppers ( Braava ), and other autonomous cleaning devices. A planned takeover deal by Amazon.com for US$ 1.7   billion, announced in August 2022, collapsed in January 2024 amid antitrust scrutiny by the European Commission . iRobot was founded in 1990 by Rodney Brooks , Colin Angle, and Helen Greiner after working in MIT 's Artificial Intelligence Lab . In 1998,

252-427: A remote-controlled robot patterned after a toy tank with an auger mounted on the front. The robot fits inside most gutters to clean out debris stuck inside them, such as leaves and pine needles. It has long treads on its side which allow it to move inside the gutter. The auger dislodges and removes almost all of the debris inside the gutter by flinging it sideways into the air. Looj also has a detachable handle/remote that

288-512: A test person sitting on a toilet, testers were assuming that they did not expect to give up their privacy and such data leakage, while iRobot took the standpoint that such persons are paid and expect their data to be shared. iRobot sent 2 million images to Scale AI, an image annotation service provider, and mentioned it terminated its business relation with Scale AI. iRobot has been criticized for attempting unregulated use of 6240-6740 MHz band, and asking for an FCC exemption to do so. This band

324-564: A theoretical model to explain and control biped locomotion. The fundamental concept of his model is called the Zero Moment Point . He died in 2012 in Belgrade . IRobot iRobot Corporation is an American technology company that designs and builds consumer robots . It was founded in 1990 by three members of MIT 's Artificial Intelligence Lab, who designed robots for space exploration and military defense. The company's products include

360-421: A workshop or similar floor. The unit was able to be used on hard floors, shop carpets and industrial floor surfaces. The Dirt Dog was discontinued in late 2010. My Real Baby was a robotic toy marketed by iRobot from 2000 and produced in partnership with the toy manufacturer Hasbro . It is no longer in production. This product, which was meant to look like a human infant, employed animatronic facial expressions and

396-407: Is an important concept in the motion planning for biped robots. Since they have only two points of contact with the floor and they are supposed to walk , " run " or " jump " (in the motion context), their motion has to be planned concerning the dynamical stability of their whole body. This is not an easy task, especially because the upper body of the robot (torso) has larger mass and inertia than

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432-623: Is an inflatable arm robot developed by iRobot. The inflatable arm uses pumps to inflate the arm. Since the arm uses strings and actuators, no motors were used at the joints. FirstLook is a small reconnaissance robot weighing 5.2 lb (2.4 kg) with a top speed of 3.8 mph (6.1 km/h) and line-of-sight control range of 200 m (219 yd). It has visible and thermal cameras and infrared sensors to gather and transmit images of buildings, caves, or other locations. It can participate in explosive ordnance disposal by carrying 2.5 lb (1.1 kg) of C4 explosive to an IED. The robot has

468-463: Is defined, where the moment is parallel to the normal vector n {\displaystyle n} from the surface about every point of the axis, then the zero moment point (ZMP) necessarily belongs to this axis, since it is by definition directed along the vector n {\displaystyle n} . The ZMP will then be the intersection between the axis Δ g i {\displaystyle \Delta ^{gi}} and

504-429: Is programmed through a tablet or smartphone. iRobot acquired Root Robotics in 2019. In 2019, iRobot received FCC approval to move forward with their plans to commercialize a robotic lawn mower capable of using wireless localization technology, which they announced would be branded as "Terra". Terra uses mapping to navigate and mow the lawn in a straight-line pattern. It uses smart beacon stakes to localize itself in

540-508: Is the resultant of the contact forces at X and M X c {\displaystyle M_{X}^{c}} is the moment related with contact forces about any point X. The Newton–Euler equations can be rewritten as: so it's easier to see that we have: These equations show that the biped robot is dynamically balanced if the contact forces and the inertia and gravity forces are strictly opposite. If an axis Δ g i {\displaystyle \Delta ^{gi}}

576-419: Is used to carry and operate the robot. It was discontinued in 2017. Mirra was a swimming-pool cleaning robot, the successor of Verro. Mirra cleaned a pool's floor and walls of large and small debris. It was discontinued in 2014. In April 2016, iRobot sold off its Defense & Security unit, with a new company being formed called Endeavor Robotics. This unit became part of Teledyne FLIR in 2019. AIRarm

612-532: The Roomba 980, with a camera that uses VSLAM technology to map out a room and the objects in the room to clean the entire floor of a home. The Roomba 980 also includes carpet boost, increasing suction when the Roomba detects itself on carpets or rugs. This was also one of the first Roombas to include Wi-Fi connectivity with app control. In May 2022, iRobot announced the new operating system and software platform for its Roomba vacuum cleaners, iRobot OS. The company stated

648-609: The US military in Iraq and Afghanistan, PackBots have been used to gather data in dangerous conditions at the Fukushima Daiichi nuclear disaster site, and an iRobot Seaglider detected underwater pools of oil after the Deepwater Horizon oil spill . In February 2016, iRobot announced that it would sell its military robotics business to Arlington Capital Partners , in order to focus more on

684-583: The ability to mesh together a network of feeds from other robots to extend the range of its sensors. The FirstLook has CBRN detectors and is semi-autonomous, meaning it can perform tasks like course correction and flipping itself over without direct intervention. 100 were bought by JIEDDO in March 2012 and the Pentagon has ordered hundreds more. When training data for the Roomba J7 vacuum robot ended up on Facebook, like

720-640: The acquisition, saying it wouldn't lead to competition concerns in the country. The European Commission launched a formal investigation into the proposed purchase in July 2023, citing that it would "allow Amazon to restrict competition in the market for robot vacuum cleaners ('RVCs') and to strengthen its position as online marketplace provider." In July 2023, Amazon reduced the offer price to $ 1.42   billion after iRobot raised $ 200   million in new debt to fund its daily operations. In January 2024, Amazon and iRobot announced they would end their plans to merge in

756-428: The center of mass. The moment in any point X {\displaystyle X} can be defined as: where H ˙ G {\displaystyle {\dot {H}}_{G}} is the rate of angular momentum at the center of mass. The Newton–Euler equations of the global motion of the biped robot can be written as: where F c {\displaystyle F_{}^{c}}

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792-448: The center of mass. Zero moment point has been proposed as a metric that can be used to assess stability against tipping over of robots like the iRobot PackBot when navigating ramps and obstacles. Miomir Vukobratovi%C4%87 Miomir Vukobratović ( Serbian Cyrillic : Миомир Вукобратовић ) (December 24, 1931 – March 11, 2012) was a Serbian mechanical engineer and pioneer in humanoid robots . His major interest laid in

828-688: The company received a DARPA research contract which led to the development of the PackBot . In September 2002, iRobot unveiled its flagship home robot, the Roomba , which went on to sell a million units by 2004. iRobot began being traded on the NASDAQ in November 2005, under ticker symbol IRBT. On September 17, 2012, iRobot announced that it had acquired Evolution Robotics , manufacturer of automated floor mopper Mint. In addition to deployment as bomb-disposal units with

864-407: The consumer market. In November 2021, iRobot announced that it had acquired Aeris Cleantec AG, a Swiss air purifier manufacturer. iRobot began selling Aeris-designed air purifiers through its own brand in 2022. By 2020, iRobot had sold more than 30 million home robots, and deployed more than 5,000 defense & security robots. On August 5, 2022, Amazon announced its intent to acquire iRobot in

900-650: The development of efficient modeling and control of robot dynamics . He was born in Botoš , near Zrenjanin , Kingdom of Yugoslavia . Vukobratović received the B.Sc. and Ph.D. degrees in Mechanical Engineering from the University of Belgrade in 1957 and 1964, respectively, and the D.Sc. degree from the Institute Mashinovedeniya, Soviet (now Russian ) Academy of Sciences, Moscow , 1972. 1968 onwards, he

936-545: The face of opposition from EU antitrust regulators. This resulted in Amazon paying iRobot a $ 94   million reverse breakup fee , iRobot laying off 31   percent of its employees, and CEO Colin Angle departing. Gary Cohen was appointed as the company’s new chief executive in May 2024. Roomba is an automated vacuum cleaning robot first released in 2002. Roomba is powered by a rechargeable battery, and many models are available with

972-462: The ground surface such that: with where Z {\displaystyle Z} represents the ZMP. Because of the opposition between the gravity and inertia forces and the contact forces mentioned before, the Z {\displaystyle Z} point (ZMP) can be defined by: where P {\displaystyle P} is a point on the contact plane, e.g. the normal projection of

1008-409: The inertia and gravity forces acting on a biped robot is expressed by the formula: where m {\displaystyle m} is the total mass of the robot, g {\displaystyle g} is the acceleration of the gravity, G {\displaystyle G} is the center of mass and a G {\displaystyle a_{G}} is the acceleration of

1044-415: The legs which are supposed to support and move the robot. This can be compared to the problem of balancing an inverted pendulum . The trajectory of a walking robot is planned using the angular momentum equation to ensure that the generated joint trajectories guarantee the dynamical postural stability of the robot, which usually is quantified by the distance of the zero moment point in the boundaries of

1080-462: The move from iRobot genius to iRobot OS will aid in giving their products a deeper understanding of the user’s households and the users habits, in addition to voice commands and greater objected identification. In October 2022, iRobot released the Roomba Combo, which includes mopping capabilities. The robot is able to differentiate between hardwood floor and carpet, and it lifts its mop to the top of

1116-448: The robot when transitioning to carpet. Braava is iRobot's floor mopping robot, designed to work on hard-surface floors. Braava uses disposable or microfiber cleaning cloths for damp and/or dry cleaning. The 380t model comes with a Channel 4 NorthStar Navigation Cube, which is set on a high surface and directs the robot around the area it cleans. The design was known as the Mint until 2013. It

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1152-412: The trajectories of the legs' links in such a way that the torso of the robot is naturally steered in order to reduce the ankle torque needed to compensate its motion. If the trajectory planning for the leg links is well-formed, then the zero moment point won't move out of the predefined stability region and the motion of the robot will become smoother, mimicking a natural trajectory. The resultant force of

1188-546: The yard, and is taught a boundary by the user (where the robot should avoid going, such as a garden). Terra includes Wi-Fi capabilities and a docking station for recharging. Terra was available as a beta program in 2019 in Germany and the United States. The program was indefinitely postponed in March 2020. Scooba was iRobot's floor-washing robot . The product became commercially available in limited quantities in late 2005 before

1224-443: Was developed by Evolution Robotics , which was acquired by iRobot in 2012. Create is a hobby robot, released in 2007. Create offers users the possibility of changing or adapting the robot's functions through experimentation with the basic elements of robotics as well as by adding sensors, grippers, wireless connections, computers, or other hardware. Root is an educational robot designed for use by children learning how to code. It

1260-519: Was developed from an emotionally expressive and responsive robot developed by iRobot corporation called "IT." ConnectR was a videoconferencing robot which was prototyped in 2010. It did not pass pilot tests and was not sold commercially. Verro was a swimming-pool cleaning robot released in April 2007. Looj was a gutter-cleaning robot released in September 2007. Looj is not an autonomous robot , but rather

1296-651: Was head of the Biodynamics Department, director of the Laboratory for Robotics and Flexible Automation and director of Robotics Laboratory at the Mihailo Pupin Institute in Belgrade . Most of Vukobratović’s research work was related with robot dynamics. He contributed to manipulators’ dynamics in adaptive and non-adaptive control for contact and non-contact tasks. He also studied dynamic modeling and control in locomotion robots. In 1970 Vukobratović proposed

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