In order to make robot manipulators work more compliantly when contacting with the environment, it is necessary to reduce the contact force caused by positioning errors. One effective way to solve this problem is impedance control, which makes the robot manipulator a second-order mass-spring-damping system in principle. In this paper, a position-based fractional-order impedance control design method is proposed for the robot manipulator force control. The end-effector/environment contact model is established, and the closed-loop system is analyzed with the reference force as input. A fractional-order impedance parameters design method is proposed for better force-control performance, which calculates and optimizes parameters through frequency-domain specifications (i.e., phase margin and gain crossover frequency) and time-domain specification (i.e., the minimum JITSE). With the Robotics ToolBox for MATLAB (RTB), the performance comparison between integer-order and fractional-order impedance controls is illustrated in simulation. The fractional-order impedance control system has a faster response, smaller overshoot, and better resistance to external disturbances from the environment.

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