  Stochastic Optimal Control (SOC) typically considers noise only in the
process model, i.e. unknown disturbances. However, in many robotic applications
involving interaction with the environment, such as locomotion and
manipulation, uncertainty also comes from lack of precise knowledge of the
world, which is not an actual disturbance. We analyze the effects of also
considering noise in the measurement model, by developing a SOC algorithm based
on risk-sensitive control, that includes the dynamics of an observer in such a
way that the control law explicitly depends on the current measurement
uncertainty. In simulation results on a simple 2D manipulator, we have observed
that measurement uncertainty leads to low impedance behaviors, a result in
contrast with the effects of process noise that creates stiff behaviors. This
suggests that taking into account measurement uncertainty could be a
potentially very interesting way to approach problems involving uncertain
contact interactions.
