A computer-implemented method (500) executed by data processing hardware (36) of a robot (10) causes the data processing hardware to perform operations. The robot includes an articulated arm (20) having an end effector (24) engaged with a constrained object (4). The operations include receiving a measured task parameter set (322) for the end effector, including position parameters (P322) defining a position of the end effector. The operations include determining, using the measured task parameter set, at least one axis of freedom and at least one constrained axis for the end effector. The operations include assigning a first impedance value (238) to the end effector along the at least one axis of freedom and a second impedance value (238) to the end effector along the at least one constrained axis. The operations include instructing the articulated arm to move the end effector along the at least one axis of freedom.