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This article presents two simple on-line schemes for force tracking within the impedance-control framework. The force- tracking capability of impedance control is particularly important for providing robustness in the presence of large uncertainties or variations in environmental parameters. The two proposed schemes generate the reference position trajec tory required to produce a desired contact force despite lack of knowledge of the environmental stiffness and location. The first scheme uses direct adaptive control to generate the refer ence position on-line as a function of the force-tracking error. Alternatively, the second scheme utilizes an indirect adaptive strategy in which the environmental parameters are estimated on-line, and the required reference position is computed based on these estimates. In both schemes, adaptation allows au tomatic gain adjustment to provide a uniform performance despite variations in the environmental parameters. Simula tion studies are presented for a 7-DOF Robotics Research arm using full arm dynamics, demonstrating that the adaptive schemes are able to compensate for uncertainties in both the environmental stiffness and location. The simulation studies also highlight the limitations of pure impedance control without the force-tracking capability for robust execution of realistic contact tasks. Experimental results are also presented for the Robotics Research arm to demonstrate that the end effector applies the desired contact force while exhibiting the specified impedance dynamics.
Seraji et al. (Sat,) studied this question.