Model-Predictive Control (MPC) is an appealing framework to control robots due to its ability to reason over the future and to update decisions online based on sensory information. Part of my research focuses on developing new tools to achieve this potential and push the limits of nonlinear MPC in practice on torque-controlled robots.
In particular during the early years of my PhD, I proposed the first implementation of high-frequency nonlinear MPC on a torque-controlled manipulator, thereby demonstrating experimentally those benefits and opening up new possibilities for the real-time motion generation and control of robots [3].
Adding inequality constraints in the MPC problem has long been considered a challenging problem in robotics. With my colleagues (with Armand Jordana and Avadesh Meduri), we showed that it was possible to tackle this issue by tailoring standard numerical optimization algorithms to the MPC problem by exploiting its structure (a.k.a. sparsity). We developed a state-of-the-art Sequential Quadratic Programming (SQP) solver for nonlinear MPC [1], showing the first implementation of inequality constraints in MPC on torque-controlled robots. The solver is open-sourced in the mim_solvers library and is actively maintained.
I also contributed to pushing the limits of MPC, by investigating how the Value Function (VF) can serve as a terminal cost. I collaborated with Amit Parag to develop and validate a Sobolev learning framework that exploits derivatives of the value function to accelerate reinforcement learning[4]. I also collaborated with Armand Jordana to extend this idea to constrained problems by learning the infinite-horizon value functionm which enabled MPC to escape from local minima[2].