Model Predictive Control
Model Predictive Control (MPC) is a powerful tool to generate complex motions for robots. Its great strength is that it plans online, therefore it can handle any novel situation. However, this comes at the cost of solving complex nonlinear optimization problems at high frequency. To meet this strict time requirement, MPC formulations and computational methods are often simplified to obtain real-time capable controllers, which in turn limits robustness and theoretical guarantees.
To enforce safety, the ability to enforce hard constraints is crucial. With Sébastien Kleff and Avadesh Meduri, we proposed the first demonstration of MPC with hard constraints on a torque-controlled robot at high frequency [1]. To do so, we exploited the sparse structure of optimization problems present in robotics and designed a state-of-the-art solver (available in the mim_solver library).
In addition, I studied how infinite-horizon formulations can help MPC escape local minima. In [2], we combined value function learning with MPC and showed on real hardware how the infinite-horizon formulation could guide MPC out of local minima.
During my PhD, I also collaborated with Arthur Haffemayer on MPC with collision avoidance [3, 4] and with Avadesh Meduri on vision-based MPC [5].
Selected publications
[1] Armand Jordana★, Sébastien Kleff★, Avadesh Meduri★, Justin Carpentier, Nicolas Mansard, and Ludovic Righetti. “Structure-Exploiting Sequential Quadratic Programming for Model-Predictive Control.” IEEE Transactions on Robotics (2025).
Paper Video Abstract
The promise of model-predictive control in robotics has led to extensive development of efficient numerical optimal control solvers in line with differential dynamic programming because it exploits the sparsity induced by time. In this work, we argue that this effervescence has hidden the fact that sparsity can be equally exploited by standard nonlinear optimization. In particular, we show how a tailored implementation of sequential quadratic programming achieves state-of-the-art model-predictive control. Then, we clarify the connections between popular algorithms from the robotics community and well-established optimization techniques. Further, the sequential quadratic program formulation naturally encompasses the constrained case, a notoriously difficult problem in the robotics community. Specifically, we show that it only requires a sparsity-exploiting implementation of a state-of-the-art quadratic programming solver. We illustrate the validity of this approach in a comparative study and experiments on a torque-controlled manipulator. To the best of our knowledge, this is the first demonstration of closed loop nonlinear model-predictive control with constraints on a real robot.
[2] Armand Jordana, Sébastien Kleff, Arthur Haffemayer, Joaquim Ortiz-Haro, Justin Carpentier, Nicolas Mansard, and Ludovic Righetti. “Infinite-Horizon Value Function Approximation for Model Predictive Control.” IEEE Robotics and Automation Letters (2025).
Paper Video Abstract
Model Predictive Control has emerged as a popular tool for robots to generate complex motions. However, the real-time requirement has limited the use of hard constraints and large preview horizons, which are necessary to ensure safety and stability. In practice, practitioners have to carefully design cost functions that can imitate an infinite horizon formulation, which is tedious and often results in local minima. In this work, we study how to approximate the infinite horizon value function of constrained optimal control problems with neural networks using value iteration and trajectory optimization. Furthermore, we experimentally demonstrate how using this value function approximation as a terminal cost provides global stability to the model predictive controller. The approach is validated on two toy problems and a real-world scenario with online obstacle avoidance on an industrial manipulator where the value function is conditioned to the goal and obstacle.
[3] Arthur Haffemayer, Armand Jordana, Ludovic De Matteïs, Krzysztof Wojciechowski, Ludovic Righetti, Florent Lamiraux, and Nicolas Mansard. “Collision avoidance in model predictive control using velocity damper.” In 2025 IEEE International Conference on Robotics and Automation (ICRA).
Paper Video Abstract
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.
[4] Arthur Haffemayer, Armand Jordana, Médéric Fourmy, Krzysztof Wojciechowski, Guilhem Saurel, Vladimír Petrík, Florent Lamiraux, and Nicolas Mansard. “Model predictive control under hard collision avoidance constraints for a robotic arm.” In 2024 21st International Conference on Ubiquitous Robots (UR).
Paper Video Abstract
We design a method to control the motion of a manipulator robot while strictly enforcing collision avoidance in a dynamic obstacle field. We rely on model predictive control while formulating collision avoidance as a hard constraint. We express the constraint as the requirement for a signed distance function to be positive between pairs of strictly convex objects. Among various formulations, we provide a suitable definition for this signed distance and the analytical derivatives the numerical solver needs to enforce the constraint. The method is completely implemented on a manipulator “Panda” robot, and the efficient open-source implementation is provided along with the paper. We experimentally demonstrate the efficiency of our approach by performing dynamic tasks in an obstacle field while reacting to non-modeled perturbations.
[5] Avadesh Meduri, Huaijiang Zhu, Armand Jordana, and Ludovic Righetti. “MPC with sensor-based online cost adaptation.” In 2023 IEEE International Conference on Robotics and Automation (ICRA).
Paper Video Abstract
Model predictive control is a powerful tool to generate complex motions for robots. However, it often requires solving non-convex problems online to produce rich behaviors, which is computationally expensive and not always practical in real time. Additionally, direct integration of high dimensional sensor data (e.g. RGB-D images) in the feedback loop is challenging with current state-space methods. This paper aims to address both issues. It introduces a model predictive control scheme, where a neural network constantly updates the cost function of a quadratic program based on sensory inputs, aiming to minimize a general non-convex task loss without solving a non-convex problem online. By updating the cost, the robot is able to adapt to changes in the environment directly from sensor measurement without requiring a new cost design. Furthermore, since the quadratic program can be solved efficiently with hard constraints, a safe deployment on the robot is ensured. Experiments with a wide variety of reaching tasks on an industrial robot manipulator demonstrate that our method can efficiently solve complex non-convex problems with high-dimensional visual sensory inputs, while still being robust to external disturbances.
