The paper defines impedance control based control laws for interaction tasks with environments of unknown geometrical and mechanical properties, both considering manipulators mounted on A) rigid and B) compliant bases. In A) a deformation-tracking strategy allows the control of a desired deformation of the target environment. In B) a force-tracking strategy allows the control of a desired interaction force. In both A) and B) the on-line estimation of the environment stiffness is required. Therefore, an Extended Kalman Filter is defined. In B) the on-line estimation of the robot base position is used as a feedback in the control loop. The compliant base is modelled as a second-order physical system with known parameters (offline identification) and the base position is estimated from the measure of interaction forces. The Extended Kalman Filter, the grounding position estimation and the defined control laws are validated in simulation and with experiments, especially dedicated to an insertion-assembly task with A) time-varing stiffness environment and B) constant stiffness environment.

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