Session: Optimization for Robotics I
Chair: Panos Patrinos
Cluster: Optimization Applications (Communication, Energy, Health, ML, ...)
Talk 1: Robotics Applications of the Direct Optimal Control of Nonsmooth Systems
Speaker: Anton Pozharskiy
Abstract: When developing control algorithms for robotic systems, practitioners must contend with modeling complex environmental interactions, including contact and friction, which are often modeled as nonsmooth dynamical systems. We discuss several alternate models of varying fidelity that can be applied to robotic manipulation problems, particularly comparing those coming from complementarity-lagrangian models and those coming from simpler projected dynamical systems. In order to efficiently be used in an optimal control context, these systems must be accurately discretized, as naive discretizations result in low accuracy and incorrect sensitivities. To this end, the Finite Elements with Switch Detection (FESD) discretization can be applied, which results in nonsmooth optimization problems called Mathematical Programs with Complementarity Constraints (MPCCs). The theoretical and practical difficulties of solving MPCCs coming from optimal control and several solution methods are then described. Finally, we present the open source package nosnoc, in which both the discretization and MPCC solution methods are implemented.
Talk 2: Real-time constrained nonlinear MPC in robotics: augmented Lagrangians and fast block-sparse matrix factorizations
Speaker: Wilson Jallet
Abstract: In high-dimensional robotic platforms, such as legged robots and humanoids, achieving real-time control is a critical challenge, particularly when managing complex dynamics and constraints in nonlinear model predictive control (MPC). This talk presents recent advances in constrained nonlinear MPC, focusing on augmented Lagrangian methods and fast block-sparse matrix factorizations. By exploiting the block-banded structure arising from the time dependency in MPC, we extend the Riccati recursion to efficiently handle constraints. Additionally, a Schur complement-like approach enables parallelization, significantly accelerating computation. We also discuss ongoing developments in a flexible C++ library, open-sourced last year, designed for real-time robotic applications. Current work emphasizes performance optimization, including updating OCPs and warm-starting MPC, improvements to cache-friendliness and future work on a computation graph. Flexibility remains a key focus, enabling users to define dynamics from their own ODE or DAE models (such as those provided by the Pinocchio rigid-body dynamics library), with support for a variety of time integrators, such as Euler and Runge-Kutta (with potential support for more advanced, energy-conserving integrators in the future). Additionally, we explore the use of generalized augmented Lagrangian methods, which allow geometric handling of more complex constraint sets, further enhancing the library's capabilities for constrained optimization. These advancements aim to make real-time control in complex robotic systems, particularly humanoids, more efficient and adaptable.
Talk 3: High-performance linear algebra in quadratic programming solvers for real-time optimal control
Speaker: Pieter Pas
Abstract: Model predictive control (MPC) is a powerful control strategy that is widely used in robotics due to its excellent performance and the ability to handle constraints. However, the real-time implementation of MPC presents significant computational challenges, especially in high-speed or large-scale control applications. Efficient numerical optimization solvers are therefore essential, and remain an active area of research. Solvers based on quadratic programming and interior point methods both rely on the fast solution of linear systems with a particular KKT structure. In this talk, we explore how the specific block-wise structure of KKT systems that arise in optimal control problems can be exploited in specialized batched linear algebra routines. By employing tailored storage schemes and highly optimized micro-kernels, combined with advanced vectorization and parallelization techniques, these routines leverage the full power of modern hardware, even for small to moderately sized models. We conclude by demonstrating that the practical performance of the quadratic programming solver QPALM can be substantially improved by replacing its general-purpose linear solver with optimal-control-specific variants based on the aforementioned batched linear algebra routines. The resulting QPALM-OCP solver is released as an open-source software library.
