ICCOPT2025USC

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.

Session: Optimization for Robotics II
Chair: Panos Patrinos
Cluster: Optimization Applications (Communication, Energy, Health, ML, ...)

Talk 1: Graphs of Convex Sets with Applications to Robot Motion Planning
Speaker: Tobia Marcucci
Abstract: In this talk we introduce a novel modeling and computational framework for joint discrete and continuous decision making. We consider graphs where each vertex is associated with a convex optimization problem, and each edge couples two problems through additional convex costs and constraints. We call these Graphs of Convex Sets (GCS). Many classical problems in graph theory are naturally generalized to GCS, yielding a new class of problems at the interface of combinatorial and convex optimization with a wide variety of applications. For the solution of these problems, we present a unified technique that leverages perspective operators to formulate tight convex relaxations and strong mixed-integer formulations. In the second part of the presentation, we focus on the shortest-path problem in GCS and its application to robot motion planning. We present early experiments from Amazon Robotics, where our framework enables warehouse robots to move packages between bins nearly twice as fast as the current motion-planning solution.

Talk 2: Deep-Learning Aided Optimization for Decision-Making
Speaker: Evangelos Theodorou
Abstract: Optimization problems in robotics are typically nonlinear and nonconvex, while their scalability can range from few to millions of states and controls variables depending on the use case, the robotic system and the task in consideration. In this talk I will present a new class of algorithms for distributed optimization of multi-agent systems with emphasis on robotics applications. The primary goal is to out-perform existing algorithms in terms of convergence speed, optimality and scaling. To do so we will draw connections between iterative optimization algorithms and model-based deep learning approaches. These connections will allow us to develop neural networks architectures for learning to optimize that are interpretable, scalable and come with generalization guarantees. The interpretability arises from treating each iteration of an optimization method as layer with the corresponding tuning parameters treated as learnable parameters. Training of such architectures takes place in a supervised as well as semi-supervised learning fashion. We will show a range of applications of such neural network architectures including large-scale distributed optimal control, model predictive control, and network flow problems. The proposed architectures do not only improve performance, they also address a long-standing problem in industry and academia related to interpretability of neural network architectures when deployed to the real world.

Talk 3: Safe treatment of infeasible convex optimization problems via the augmented Lagrangian
Speaker: Roland Andrews
Abstract: This work focuses on constrained convex optimization problems. The augmented Lagrangian method is a popular algorithm designed to tackle such problems by solving sequences of unconstrained optimization problems. It is practically efficient and offers strong theoretical guarantees under minimal assumptions, provided that the feasible set associated with the constraints is non-empty. However, the infeasible setting for constrained optimization problems has only recently started to attract attention. This issue is particularly relevant in areas such as optimal control (e.g., Model Predictive Control) and machine learning (e.g., neural networks using convex optimization layers), where infeasibility frequently arises. Recent studies have approached this problem under various assumptions. In this work, we analyze the general case, relying solely on convexity as the key assumption. Our approach leverages the classical relationship between the augmented Lagrangian algorithm and the dual proximal point algorithm.