Recent strides in nonlinear model predictive control (NMPC) underscore a dependence on numerical advancements to efficiently and accurately solve large-scale problems. Given the substantial number of variables characterizing typical whole-body optimal control (OC) problems - often numbering in the thousands - exploiting the sparse structure of the numerical problem becomes crucial to meet computational demands, typically in the range of a few milliseconds. Addressing the linear-quadratic regulator (LQR) problem is a fundamental building block for computing Newton or Sequential Quadratic Programming (SQP) steps in direct optimal control methods. This paper concentrates on equality-constrained problems featuring implicit system dynamics and dual regularization, a characteristic of advanced interiorpoint or augmented Lagrangian solvers. Here, we introduce a parallel algorithm for solving an LQR problem with dual regularization. Leveraging a rewriting of the LQR recursion through block elimination, we first enhanced the efficiency of the serial algorithm and then subsequently generalized it to handle parametric problems. This extension enables us to split decision variables and solve multiple subproblems concurrently. Our algorithm is implemented in our nonlinear numerical optimal control library ALIGATOR. It showcases improved performance over previous serial formulations and we validate its efficacy by deploying it in the model predictive control of a real quadruped robot.

Learning visuomotor policies in simulation is much safer and cheaper than in the real world. However, due to discrepancies between the simulated and real data, simulator-trained policies often fail when transferred to real robots. One common approach to bridge the visual sim-to-real domain gap is domain randomization (DR). While previous work mainly evaluates DR for disembodied tasks, such as pose estimation and object detection, here we systematically explore visual domain randomization methods and benchmark them on a rich set of challenging robotic manipulation tasks. In particular, we propose an off-line proxy task of cube localization to select DR parameters for texture randomization, lighting randomization, variations of object colors and camera parameters. Notably, we demonstrate that DR parameters have similar impact on our off-line proxy task and on-line policies. We, hence, use off-line optimized DR parameters to train visuomotor policies in simulation and directly apply such policies to a real robot. Our approach achieves 93% success rate on average when tested on a diverse set of challenging manipulation tasks. Moreover, we evaluate the robustness of policies to visual variations in real scenes and show that our simulator-trained policies outperform policies learned using real but limited data. Code, simulation environment, real robot datasets and trained models are available at https://www.di.ens.fr/willow/research/robust_s2r/.

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.