A phi-model solution for the inverse position problem of calibrated robots using virtual elementary motions
- Authors: Sultan, Ibrahim , Wager, John
- Date: 2001
- Type: Text , Journal article
- Relation: Inverse Problems in Engineering Vol. 9, no. 3 (2001), p. 261-285
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- Description: It is central to the control of manipulators to calculate the set/sets of joint-displacements which correspond to a given spatial pose (position and orientation) of the end-effector. This problem, which is referred to as the inverse position problem, represents one of the most difficult mathematical challenges in the field of robotics, particularly when performed for calibrated robots (or robots with general structures). In such cases, closed form solutions are too impractical to implement and iterative solutions suffer from numerical singularities. In the present work a procedure is introduced to obtain multiple inverse position solutions for serial robotic structures. For calibrated robots, the procedure involves a simple iterative technique designed to ensure fast convergence and eliminate the occurrence of singularity. However, inverse position solutions for spherical-wrist manipulators will be obtained in a straight-forward non-iterative fashion. A published kinematic notation, referred to as the phi -model, was used to develop the system equations.
A technique for the independent-axis calibration of robot manipulators with experimental verification
- Authors: Sultan, Ibrahim , Wager, John
- Date: 2001
- Type: Text , Journal article
- Relation: International Journal of Computer Integrated Manufacturing Vol. 14, no. 5 (2001), p. 501-512
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- Description: Accurate use of robots in an off-line programming mode is only possible through a proper calibration procedure. In this procedure, the end-effector is made to move along a set of known spatial poses where the positional errors are to be measured and employed in mathematical models. The models are subsequently solved for the manipulator dimensions (geometric parameters) using suitable regression techniques. Calibration is usually performed using either aggregate or independent-axis models. While the aggregate models result in all the system parameters being worked out simultaneously, the independent-axis models are meant to work out the geometric particulars of each joint-axis individually. In the present work, the independent-axis technique is used for the analysis with new mathematical models proposed to overcome the drawbacks of the existing methods. Moreover, the techniques employed here result in the prediction of transmission error functions and the modelling of the joint motion dependencies. This is a new concept in the field of robot calibration. Finally, the models proposed have been used to calibrate an ASEA IRB/L6 robot and the results are reported at the end of the paper.
Simplified theodolite calibration for robot metrology
- Authors: Sultan, Ibrahim , Wager, John
- Date: 2002
- Type: Text , Journal article
- Relation: Advanced Robotics Vol. 16, no. 7 (2002), p. 653-671
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- Description: Theodolites represent a well-established three-dimensional-point-measuring technology. However, when used for robot applications they have to be properly calibrated to fulfil the necessary accuracy requirements. The theodolite calibration methods reported in the literature involve the use of costly sophisticated equipment not easily available to most users. Therefore, a new simplified calibration technique is presented based on the use of a graduated precision bar suspended freely to align with the vertical direction. To develop efficient mathematical models, the theodolites will be regarded as 2R open-ended mechanisms with the end-effector axis directed along the line of sight. The proposed models are then coded in a computer program designed to verify the validity of the technique presented. The simulation results will be presented at the end of the paper.
- Description: 2003000163