Song, S-M, Waldron, KJ & Kinzel, GL 1985, 'Computer-aided geometric design of legs for a walking vehicle', Mechanism and Machine Theory, vol. 20, no. 6, pp. 587-596.
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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.
Pham, DT & Dissanayake, G 1970, 'Feasibility Study of a Vibratory Sensor for Locating 3-D Objects', Proceedings of the International Machine Tool Design and Research Conference, Macmillan Education UK, pp. 201-211.
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A novel sensor is investigated which is intended to be mounted at the wrist of a robot to enable it to determine the co-ordinates of a part it has picked up from a stack or tray. The device operates by letting the part vibrate about two orthogonal axes and measuring its inertia-dependent instantaneous velocities and angles of vibration. The mathematical procedures for extracting position and orientation data from these measurements are described. The results of computer simulations carried out to determine guidelines for the design of the device are presented and discussed.
Pham, DT & Dissanayake, MWMG 1970, 'INERTIA-BASED SENSORS WITH ONE AND TWO DEGREES OF FREEDOM FOR LOCATING PARTS.', pp. 223-237.
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Two inertia-based sensors for determining the position and orientation of three-dimensional objects are described. One of them involves letting the objects vibrate about two orthogonal axes simultaneously and measuring the angles and velocities of vibration at various instants of time. In the other sensor, the objects are also vibrated about two axes but the vibrations are performed sequentially and the frequencies of vibration are measured. The mathematical procedures for obtaining the position and orientation of the objects from the measurements are outlined for the second sensor. Results of the computer simulations carried out to assess the feasibility of the latter are presented.
Pham, DT & Dissanayake, MWMG 1970, 'THREE-DEGREE-OF-FREEDOM INERTIAL SENSOR FOR LOCATING PARTS.', pp. 613-629.
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A compromise solution to the problem of economically feeding parts to industrial robots is investigated. The parts are neither accurately presented as in the case of traditional feeding equipment nor jumbled up as in the case of bin-picking machines. Instead, they are semi-ordered into stacks or trays and then unloaded by the robots as needed. The robots are to be equipped with a novel sensor fitted to their wrists for determining the exact coordinates of the parts they have picked up. The device operates by letting the parts vibrate about three orthogonal axes and measuring their inertia-dependent natural frequencies of vibration. The mathematical procedures for extracting position and orientation data from those measurements are described. The results of computer simulations carried out to determine guidelines for the design of the device are presented and discussed.
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.
Waldron, K & Nordholt, N 1970, 'Force and motion management in legged locomotion', 1985 24th IEEE Conference on Decision and Control, 1985 24th IEEE Conference on Decision and Control, IEEE, pp. 12-17.
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The control of a legged locomotion system over uneven terrain requires a new approach to coordination. The system has a high degree of static indeterminacy and, because of the stiffness of the structural and actuation systems, has stability problems if position-velocity control is used. The problem has many similarities to that of grasping and manipulating an object in a multifingered hand. The stability problem is removed by controlling actuator force directly, but the necessary computations can be prohibitive. A solution is presented which is moderate in its computational requirements. It is based on an assumption of zero foot interaction forces in the horizontal plane.
