  In robotics, designing robust algorithms in the face of estimation
uncertainty is a challenging task. Indeed, controllers often do not consider
the estimation uncertainty and only rely on the most likely estimated state.
Consequently, sudden changes in the environment or the robot's dynamics can
lead to catastrophic behaviors. In this work, we present a risk-sensitive
Extended Kalman Filter that allows doing output-feedback Model Predictive
Control (MPC) safely. This filter adapts its estimation to the control
objective. By taking a pessimistic estimate concerning the value function
resulting from the MPC controller, the filter provides increased robustness to
the controller in phases of uncertainty as compared to a standard Extended
Kalman Filter (EKF). Moreover, the filter has the same complexity as an EKF, so
that it can be used for real-time model-predictive control. The paper evaluates
the risk-sensitive behavior of the proposed filter when used in a nonlinear
model-predictive control loop on a planar drone and industrial manipulator in
simulation, as well as on an external force estimation task on a real quadruped
robot. These experiments demonstrate the abilities of the approach to improve
performance in the face of uncertainties significantly.
