Titlebook: Geometric Algebra Applications Vol. II; Robot Modelling and Eduardo Bayro-Corrochano Book 2020 Springer Nature Switzerland AG 2020 Cogniti

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Geometric Algebra for Modeling in Robotic Physics,n the fields of artificial intelligence, robotics, and intelligent machines acting within the perception and action cycle. We begin with a short tour of the history of mathematics to find the roots of the fundamental concepts of geometry and algebra.

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Control of Robot Manipulatorsd using the recursive Newton–Euler algorithm. We compute the local Hamiltonians at each joint and derive their localized controllers as well. In the experimental part, we compare the performance of PD, Bang–Bang, and sliding mode controllers.

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Rigid Motion Estimation Using Line Observationsthe first uses a batch approach for the estimation of the unknown 3D transformation between the coordinate reference systems of a robot neck, or arm, and of a digital camera. This problem is called the hand–eye problem and it is solved using a motion-of-lines model.

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Springer Nature Switzerland AG 2020

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Alex Tyrrell,Patricia Hill,Diane KirkbyThis chapter gives a detailed outline of geometric algebra and explains the related traditional algebras in common use by mathematicians, physicists, computer scientists, and engineers.

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Uncertainties and ApproximationsThe geometric algebra of a 3D Euclidean space . has a point basis and the motor algebra . a line basis. In the latter, the lines expressed are expressed in terms of Plücker coordinates and the points and planes in terms of bivectors.

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