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In this paper, we proposed and compared two control schemes of exploring tumors/vessels under soft tissue. The constant contact depth scheme and constant contact force scheme were tested in differentiating hard objects from soft rubber foam. The experimental results showed that these two exploration schemes can both successfully detect the existence and location of the underlying object under a soft foam in our test rig. We found that the distinguishing ability of the former scheme is superior to the latter scheme in terms of the stiffness differentiation. An analytic explanation was given based on the concept of palpation sensitivity and the soft tissue biomechanics and the criterion proposed in this paper can be useful in developing advanced exploration method for breast cancer palpation.