Robot Dynamics AlgorithmsSpringer, 16.10.2007 - 211 Seiten The purpose of this book is to present computationally efficient algorithms for calculating the dynamics of robot mechanisms represented as systems of rigid bodies. The efficiency is achieved by the use of recursive formulations of the equations of motion, i.e. formulations in which the equations of motion are expressed implicitly in terms of recurrence relations between the quantities describing the system. The use of recursive formulations in dynamics is fairly new, 50 the principles of their operation and reasons for their efficiency are explained. Three main algorithms are described: the recursIve Newton-Euler formulation for inverse dynamics (the calculation of the forces given the accelerations), and the composite-rigid-body and articulated-body methods for forward dynamics (the calculation of the accelerations given the forces). These algorithms are initially described in terms of an un-branched, open loop kinematic chain -- a typical serial robot mechanism. This is done to keep the descriptions of the algorithms simple, and is in line with descriptions appearing in the literature. Once the basic algorithms have been introduced, the restrictions on the mechanism are lifted and the algorithms are extended to cope with kinematic trees and loops, and general constraints at the joints. The problem of simulating the effect of contact between a robot and its environment is also considered. Some consideration is given to the details and practical problems of implementing these algori?hms on a computer. |
Inhalt
5 | |
Spatial Kinematics 13 | 12 |
Spatial Dynamics | 37 |
Extending the Dynamics Algorithms | 106 |
Coordinate Systems and Efficiency | 129 |
Contact Impact and Kinematic Loops | 153 |
197 | |
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3-dimensional 6-dimensional vector a₁ absolute coordinates angular velocity applied articulated body articulated-body inertias articulated-body method axes b₁ and b₂ base calculation Chapter components composite-rigid-body method computational requirement contact normals coordinate system coordinate transformation defined degrees of freedom derivative described differentiation dual numbers efficient end effector equations of motion expressed forces acting formulations forward dynamics free vector generalised forces given inverse dynamics inverse inertia joint axis joint forces joint variables joint velocity kinematic chain line vector loop joint magnitude motion constraints motor non-zero positive definite problem recurrence relations representation rigid body rigid-body dynamics rigid-body inertias rigid-body system rigid-body transformation robot dynamics robot mechanism rotation scalar product screw axis screw theory Si+1 solve spatial acceleration spatial force spatial inertia spatial notation spatial quantities spatial rigid-body spatial transpose spatial vector spatial velocity symmetric vector algebra vector space velocity of link velocity-product zero