Risk-sensitive MPC

In this letter, we study dynamic game optimal control with imperfect state observations and introduce an iterative method to find a local Nash equilibrium. The algorithm consists of an iterative procedure combining a backward recursion similar to minimax differential dynamic programming and a forward recursion resembling a risk-sensitive Kalman smoother. A coupling equation renders the resulting control dependent on the estimation. In the end, the algorithm is equivalent to a Newton step but has linear complexity in the time horizon length. Furthermore, a merit function and a line search procedure are introduced to guarantee convergence of the iterative scheme. The resulting controller reasons about uncertainty by planning for the worst case disturbances. Lastly, the low computational cost of the proposed algorithm makes it a promising method to do output-feedback model predictive control on complex systems at high frequency. Numerical simulations on realistic robotic problems illustrate the risk-sensitive behavior of the resulting controller.

Designing robust algorithms in the face of estimation uncertainty is a challenging task. Indeed, controllers seldom consider 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. Leveraging recent results in risk-sensitive optimal control, this paper presents a risk-sensitive Extended Kalman Filter that can adapt its estimation to the control objective, hence allowing safe output-feedback Model Predictive Control (MPC). By taking a pessimistic estimate of 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). The filter has the same computational complexity as an EKF and can be used for real-time control. The paper evaluates the risk-sensitive behavior of the proposed filter when used in a nonlinear MPC 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 ability of the approach to significantly improve performance in face of uncertainties.

We propose an advanced method for controlling the motion of a manipulator robot with strict collision avoidance in dynamic environments, leveraging a velocity damper constraint. Unlike conventional distance-based constraints, which tend to saturate near obstacles to reach optimality, the velocity damper constraint considers both distance and relative velocity, ensuring a safer separation. This constraint is incorporated into a model predictive control framework and enforced as a hard constraint through analytical derivatives supplied to the numerical solver. The approach has been fully implemented on a Franka Emika Panda robot and validated through experimental trials, demonstrating effective collision avoidance during dynamic tasks and robustness to unmodeled disturbances. An efficient open-source implementation along examples are provided here: https://gepettoweb.laas.fr/articles/haffemayer2025.html.