Waldron, KJ, Wang, SL & Bolin, SJ 1985, 'STUDY OF THE JACOBIAN MATRIX OF SERIAL MANIPULATORS.', Journal of mechanisms, transmissions, and automation in design, vol. 107, no. 2, pp. 230-238.
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Inversion of the Jacobian matrix is the critical step in rate decomposition which is used to solve the so-called 'inverse kinematics' problem of robotics. This is the problem of achieving a coordinated motion relative to the fixed reference frame. A general methodology is presented for formulation and manipulation of the Jacobian matrix. The formation is closely tied to the geometry of the system and lends itself to simplification using appropriate coordinate transformations. This is of great importance since it gives a systematic approach to the derivation of efficient, analytical inverses. The method is also applied to the examination of geometrically singular positions. Several important general results relating to the structure of the singularity field are deducible from the structure of the algebraic system.
Waldron, KJ, Wang, S-L & Bolin, SJ 1985, 'A Study of the Jacobian Matrix of Serial Manipulators', Journal of Mechanisms, Transmissions, and Automation in Design, vol. 107, no. 2, pp. 230-237.
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Inversion of the Jacobian matrix is the critical step in rate decomposition which is used to solve the so-called “inverse kinematics” problem of robotics. This is the problem of achieving a coordinated motion relative to the fixed reference frame. In this paper a general methodology is presented for formulation and manipulation of the Jacobian matrix. The formulation is closely tied to the geometry of the system and lends itself to simplification using appropriate coordinate transformations. This is of great importance since it gives a systematic approach to the derivation of efficient, analytical inverses. The method is also applied to the examination of geometrically singular positions. Several important general results relating to the structure of the singularity field are deducible from the structure of the algebraic system.
Vijaykumar, R, Tsai, M & Waldron, K 1970, 'Geometric optimization of manipulator structures for working volume and dexterity', Proceedings. 1985 IEEE International Conference on Robotics and Automation, 1985 IEEE International Conference on Robotics and Automation, Institute of Electrical and Electronics Engineers, pp. 228-236.
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Broadly speaking, the regional structure of a manipulator, which consists of the inboard three joints and the members associated with them, determines the workspace shape and volume. The orientation structure, which, for a six degree of freedom manipulator, consists of the three furthest outboard joints and members, determines the geometric dexterity or orientation potential of the manipulator. It is possible, using straight forward geometric arguments, to determine the optimal dimensions of the regional structure for a given total length. By the use of the spherical counterpart of Grashof's theorem formulated by Freudenstein, it is possible also to show that there is an optimum geometry of the orientation structure.
Waldron, K 1970, 'Mobility and controllability characteristics of mobile robotic platforms', Proceedings. 1985 IEEE International Conference on Robotics and Automation, 1985 IEEE International Conference on Robotics and Automation, Institute of Electrical and Electronics Engineers, pp. 237-243.
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© 1985 IEEE. Mobile platforms available for use in robotic systems vary enormously in their mobility and in their control characteristics. In particular, the characteristics which are desirable in an autonomous vehicle for unstructured terrain are quite different from those which are optimum in a vehicle for partially structured terrain, such as road following, or for a mobile platform for use in a highly structured factory environment. The controlled degrees of freedom of the platform impact the manner in which it can be used. Platforms with articulated steering are severely limited in situations, such as mobile industrial robot service, in which lateral motion may be desirable.
