Danil Kulminskiy

The paper experimentally investigates the problem of the influence of periodic vibrations of the pivot point of a physical pendulum on its nonlinear oscillations in the vicinity of a stable equilibrium position on the vertical. The vibrations are assumed to be periodic and occur in the plane of the pendulum’s motion along an elliptical trajectory. In the experimental plane of parameters: the amplitude of pendulum oscillations and the parameter characterizing the difference in the vibration intensity of the pivot point in the horizontal and vertical directions, the values at which the pendulum clock gains and delays are selected. The experiment showed that with a vibration of $7.0$ Hz, which is more intense in the horizontal direction, the oscillation period of the pendulum angle increases by $0.017$ seconds compared to the pendulum’s natural period. In contrast, with vibration more intense in the vertical direction, the period decreases by $0.0164$ seconds. The experiments were carried out on an ABB IRB $1600$ industrial robot manipulator with a developed pendulum and a reflector with a lens system for a laser tracker installed at the end effector of the robot. Tracking of the trajectory of the pendulum pivot point was carried out using an API Radian Pro laser tracker, the amplitude and frequency of pendulum oscillations were recorded using a machine vision camera and image processing methods.

This paper presents a practical approach to fully automated kinematic calibration of an industrial manipulator. The approach is based on the principle of plane constraint. The electrical signal is used to fix the moment of contact between the conductive tool and the flat surface. The measurement data are manipulator configurations (joint angles) at the moment of contact. A modification of the algorithm to deal with the scaling problem is also proposed. This approach provides both high calibration accuracy and lower cost of the experimental setup compared to coordinate measuring machines (CMMs), laser trackers, and vision systems. The article examines the impact of various methods of kinematic parameterization of manipulators: the Denavit – Hartenberg agreement (DH), product of exponentials (POE), as well as the complete and parametrically continuous model (CPC) on the calibration accuracy. A comparison is made of the open-loop and the proposed closed-loop calibration methods on the Puma 560 model known in the literature. POE parameters were converted to DH and CPC to compare accuracy after calibration based on these parameterizations. The method of computing POE-CPC transformation as a solution to a certain optimization problem is proposed. The problem of identifying geometric parameters in the presence of restrictions is solved by gradient optimization methods. Experiments have been carried out on an ABB IRB 1600 industrial manipulator with an installed conductive probe and an ABB IRBP A-500 robotic positioner with a conductive metal flat surface. A technique for indirectly checking the accuracy of calibration of kinematic parameters is proposed based on a study of the accuracy of manipulation when using these parameters. A comparison is made of the manipulation accuracy when using four sets of parameters: nominal parameters obtained during factory calibration with the Leica AT901B laser tracker and two sets of parameters obtained by applying the proposed calibration method. The kinematic parameters obtained from the experiment determine more accurately the position of the manipulator TCP for part of the configuration working space, even for areas that were not used for calibration.