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The paper focuses on vibration damping control of a new anthropomorphic robot arm enabling the torque measurement in each joint and tactile area recognition to ensure safety while performing tasks of physical interaction with environment or human beings. The vibrations in heavily loaded joints have risen due to compliances introduced into each joint of the robot arm by means of torque sensors. Such oscillations deteriorate the performance of the manipulator and present undesirable disturbance during interaction with human beings. In order to overcome this disadvantage we have proposed robust technique allowing considerable reduction of the oscillation amplitude through acceleration signal feedback. The detailed design procedure of the lead controller enabling improvement of transient response is presented in the paper. The experimental results of vibration damping control show the feasibility of proposed approach to suppress the oscillations of compliant robot joint.