Publications - Augustinos Saravanos

* Equal contribution. See Google Scholar for most up-to-date list.

Preprints / Under Review

Preprint

Scaling Robust Optimization for Multi-Agent Robotic Systems: A Distributed Perspective

A.T. Abdul*, A.D. Saravanos* and E.A. Theodorou

Preprint (Under review), 2025.

Abstract PDF Video

This paper presents a novel distributed robust optimization scheme for steering distributions of multi-agent systems under stochastic and deterministic uncertainty. Robust optimization is a subfield of optimization which aims in discovering an optimal solution that remains robustly feasible for all possible realizations of the problem parameters within a given uncertainty set. Such approaches would naturally constitute an ideal candidate for multi-robot control, where in addition to stochastic noise, there might be exogenous deterministic disturbances. Nevertheless, as these methods are usually associated with significantly high computational demands, their application to multi-agent robotics has remained limited. The scope of this work is to propose a scalable robust optimization framework that effectively addresses both types of uncertainties, while retaining computational efficiency and scalability. In this direction, we provide tractable approximations for robust constraints that relevant in multi-robot settings. Subsequently, we demonstrate how computations can be distributed through an Alternating Direction Method of Multipliers (ADMM) approach towards achieving scalability and communication efficiency. Simulation results highlight the performance of the proposed algorithm in effectively handling both stochastic and deterministic uncertainty in multi-robot systems. The scalability of the method is also emphasized by showcasing tasks with up to 100 agents. The results of this work indicate the promise of blending robust optimization, distribution steering and distributed optimization towards achieving scalable, safe and robust multi-robot control.
Preprint

Second-Order Constrained Dynamic Optimization

Y. Aoyama, O. So, A.D. Saravanos and E.A. Theodorou

Preprint (Under review), 2024.

Abstract PDF

This paper provides an overview, analysis, and comparison of second-order dynamic optimization algorithms, i.e., constrained Differential Dynamic Programming (DDP) and Sequential Quadratic Programming (SQP). Although a variety of these algorithms has been proposed and used successfully, there exists a gap in understanding the key differences and advantages, which we aim to provide in this work. For constrained DDP, we choose methods that incorporate nonlinear programming techniques to handle state and control constraints, including Augmented Lagrangian (AL), Interior Point, Primal Dual Augmented Lagrangian (PDAL), and Alternating Direction Method of Multipliers. Both DDP and SQP are provided in single- and multiple-shooting formulations, where constraints that arise from dynamics are encoded implicitly and explicitly, respectively. As a byproduct of the review, we also propose a single-shooting PDAL DDP which is robust to the growth of penalty parameters and performs better than the normal AL variant. We perform extensive numerical experiments on various systems with increasing complexity to investigate the quality of the solutions, the levels of constraint violation, iterations for convergence, and the sensitivity of final solutions with respect to initialization. The results show that DDP often has the advantage of finding better local minima, while SQP tends to achieve better constraint satisfaction. For multiple-shooting formulation, both DDP and SQP can enjoy informed initial guesses, while the latter appears to be more advantageous in complex systems. It is also worth highlighting that DDP provides favorable computational complexity and feedback gains as a byproduct of optimization.
Preprint

Operator Splitting Covariance Steering for Safe Stochastic Nonlinear Control

A. Ratheesh, V. Pacelli, A.D. Saravanos and E.A. Theodorou

Preprint (Under review), 2024.

Abstract PDF Video

Most robotics applications are typically accompanied with safety restrictions that need to be satisfied with a high degree of confidence even in environments under uncertainty. Controlling the state distribution of a system and enforcing such specifications as distribution constraints is a promising approach for meeting such requirements. In this direction, covariance steering (CS) is an increasingly popular stochastic optimal control (SOC) framework for designing safe controllers via explicit constraints on the system covariance. Nevertheless, a major challenge in applying CS methods to systems with the nonlinear dynamics and chance constraints common in robotics is that the approximations needed are conservative and highly sensitive to the point of approximation. This can cause sequential convex programming methods to converge to poor local minima or incorrectly report problems as infeasible due to shifting constraints. This paper presents a novel algorithm for solving chance-constrained nonlinear CS problems that directly addresses this challenge. Specifically, we propose an operator-splitting approach that temporarily separates the main problem into subproblems that can be solved in parallel. The benefit of this relaxation lies in the fact that it does not require all iterates to satisfy all constraints simultaneously prior to convergence, thus enhancing the exploration capabilities of the algorithm for finding better solutions. Simulation results verify the ability of the proposed method to find higher quality solutions under stricter safety constraints than standard methods on a variety of robotic systems. Finally, the applicability of the algorithm on real systems is confirmed through hardware demonstrations.

Journal Papers

IEEE Transactions
on Robotics

Distributed Differential Dynamic Programming Architectures for Large-Scale Multi-Agent Control

A.D. Saravanos, Y. Aoyama, H. Zhu, and E. A. Theodorou

IEEE Transactions on Robotics , 2023.

Abstract PDF Video

In this paper, we propose two novel decentralized optimization frameworks for multi-agent nonlinear optimal control problems in robotics. The aim of this work is to suggest architectures that inherit the computational efficiency and scalability of Differential Dynamic Programming (DDP) and the distributed nature of the Alternating Direction Method of Multipliers (ADMM). In this direction, two frameworks are introduced. The first one called Nested Distributed DDP (ND-DDP), is a three-level architecture which employs ADMM for enforcing a consensus between all agents, an Augmented Lagrangian layer for satisfying local constraints and DDP as each agent’s optimizer. In the second approach, both consensus and local constraints are handled with ADMM, yielding a two-level architecture called Merged Distributed DDP (MD-DDP), which further reduces computational complexity. Both frameworks are fully decentralized since all computations are parallelizable among the agents and only local communication is necessary. Simulation results that scale up to thousands of vehicles and hundreds of drones verify the effectiveness of the methods. Superior scalability to large-scale systems against centralized DDP and centralized/decentralized sequential quadratic programming is also illustrated. Finally, hardware experiments on a multi-robot platform demonstrate the applicability of the proposed algorithms, while highlighting the importance of optimizing for feedback policies to increase robustness against uncertainty. A video with all results is available here.

Conference Papers

Preprint

Deep Distributed Optimization for Large-Scale Quadratic Programming

A.D. Saravanos, H. Kuperman, A. Oshin, A.T. Abdul, V. Pacelli and E.A. Theodorou

International Conference on Learning Representations (ICLR), 2025.

Abstract PDF

Quadratic programming (QP) forms a crucial foundation in optimization, encompassing a broad spectrum of domains and serving as the basis for more advanced algorithms. Consequently, as the scale and complexity of modern applications continue to grow, the development of efficient and reliable QP algorithms is becoming increasingly vital. In this context, this paper introduces a novel deep learning-aided distributed optimization architecture designed for tackling large-scale QP problems. First, we combine the state-of-the-art Operator Splitting QP (OSQP) method with a consensus approach to derive DistributedQP, a new method tailored for network-structured problems, with convergence guarantees to optimality. Subsequently, we unfold this optimizer into a deep learning framework, leading to DeepDistributedQP, which leverages learned policies to accelerate reaching to desired accuracy within a restricted amount of iterations. Our approach is also theoretically grounded through Probably Approximately Correct (PAC)-Bayes theory, providing generalization bounds on the expected optimality gap for unseen problems. The proposed framework, as well as its centralized version DeepQP, significantly outperform their standard optimization counterparts on a variety of tasks such as randomly generated problems, optimal control, linear regression, transportation networks and others. Notably, DeepDistributedQP demonstrates strong generalization by training on small problems and scaling to solve much larger ones (up to 50K variables and 150K constraints) using the same policy. Moreover, it achieves orders-of-magnitude improvements in wall-clock time compared to OSQP. The certifiable performance guarantees of our approach are also demonstrated, ensuring higher-quality solutions over traditional optimizers.
Preprint

Scalable Robust Optimization for Safe Multi-Agent Control Under Deterministic Uncertainty

A.T. Abdul*, A.D. Saravanos* and E.A. Theodorou

American Control Conference (ACC), 2025.

Abstract PDF

This paper introduces a novel framework for addressing multi-agent trajectory optimization under unknown deterministic uncertainty. Many systems are affected by deterministic disturbances, such as environmental effects, system degradation, etc., which cannot be accurately modeled using stochastic signals. Therefore, it is crucial to develop trajectory optimization frameworks that ensure safety despite these disturbances. To this end, we focus on solving a multi-agent trajectory optimization problem involving \textit{robust} constraints, such as collision avoidance, that must be satisfied for all possible realizations of uncertainty lying in an ellipsoidal set. Conventional robust optimization techniques that are used to address such problems are computationally expensive and struggle when dealing with numerous constraints. To overcome this, we propose tighter approximations of robust constraints that significantly reduce computational complexity without compromising safety. Furthermore, leveraging these constraint approximations, we introduce a distributed robust optimization framework for decentralized multi-agent robust trajectory optimization based on Alternating Direction Method of Multipliers (ADMM). This framework allows agents to optimize their trajectories without sharing control parameters or system information (e.g., dynamics), thereby preserving data security. The effectiveness of the proposed robust constraint approximations and the scalability of the proposed distributed framework are demonstrated through simulation data.
IROS 2024

Distributed Model Predictive Covariance Steering

A.D. Saravanos, I.M. Balci, E. Bakolas, and E.A. Theodorou

IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), 2024.

Abstract PDF Video

This paper proposes Distributed Model Predictive Covariance Steering (DiMPCS) for multi-agent control under stochastic uncertainty. The scope of our approach is to blend covariance steering theory, distributed optimization and model predictive control (MPC) into a single framework that is safe, scalable and decentralized. Initially, we pose a problem formulation that uses the Wasserstein distance to steer the state distributions of a multi-agent system to desired targets, and probabilistic constraints to ensure safety. We then transform this problem into a finite-dimensional optimization one by utilizing a disturbance feedback policy parametrization for covariance steering and a tractable approximation of the safety constraints. To solve the latter problem, we derive a decentralized consensus-based algorithm using the Alternating Direction Method of Multipliers. This method is then extended to a receding horizon form, which yields the proposed DiMPCS algorithm. Simulation experiments on a variety of multi-robot tasks with up to hundreds of robots demonstrate the effectiveness of DiMPCS. The superior scalability and performance of the proposed method is also highlighted through a comparison against related stochastic MPC approaches. Finally, hardware results on a multi-robot platform also verify the applicability of DiMPCS on real systems.
IROS 2024

A Robust Differential Neural ODE Optimizer

P. Theodoropoulos, G.H. Liu, T. Chen, A.D. Saravanos and E.A. Theodorou

International Conference on Learning Representations (ICLR), 2024.

Abstract PDF

Neural networks and neural ODEs tend to be vulnerable to adversarial attacks, rendering robust optimizers critical to curb the success of such attacks. In this regard, the key insight of this work is to interpret Neural ODE optimization as a min-max optimal control problem. More particularly, we present Game Theoretic Second-Order Neural Optimizer (GTSONO), a robust game theoretic optimizer based on the principles of min-max Differential Dynamic Programming. The proposed method exhibits significant computational benefits due to efficient matrix decompositions and provides convergence guarantees to local saddle points. Empirically, the robustness of the proposed optimizer is demonstrated through greater robust accuracy compared to benchmark optimizers when trained on clean images. Additionally, its ability to provide a performance increase when adapted to an already existing adversarial defense technique is also illustrated. Finally, the superiority of the proposed update law over its gradient based counterpart highlights the potential benefits of incorporating robust optimal control paradigms into adversarial training methods.
RSS 2023

Distributed Hierarchical Distribution Control for Very-Large-Scale Clustered Multi-Agent Systems

A.D. Saravanos, Y. Li and E.A. Theodorou

Robotics: Science and Systems (RSS), 2023.

Abstract PDF Video

As the scale and complexity of multi-agent robotic systems are subject to a continuous increase, this paper considers a class of systems labeled as Very-Large-Scale Multi-Agent Systems (VLMAS) with dimensionality that can scale up to the order of millions of agents. In particular, we consider the problem of steering the state distributions of all agents of a VLMAS to prescribed target distributions while satisfying probabilistic safety guarantees. Based on the key assumption that such systems often admit a multi-level hierarchical clustered structure - where the agents are organized into cliques of different levels - we associate the control of such cliques with the control of distributions, and introduce the Distributed Hierarchical Distribution Control (DHDC) framework. The proposed approach consists of two sub-frameworks. The first one, Distributed Hierarchical Distribution Estimation (DHDE), is a bottom-up hierarchical decentralized algorithm which links the initial and target configurations of the cliques of all levels with suitable Gaussian distributions. The second part, Distributed Hierarchical Distribution Steering (DHDS), is a top-down hierarchical distributed method that steers the distributions of all cliques and agents from the initial to the targets ones assigned by DHDE. Simulation results that scale up to two million agents demonstrate the effectiveness and scalability of the proposed framework. The increased computational efficiency and safety performance of DHDC against related methods is also illustrated. The results of this work indicate the importance of hierarchical distribution control approaches towards achieving safe and scalable solutions for the control of VLMAS.
IROS 2024

Improved Exploration for Safety-Embedded Differential Dynamic Programming Using Tolerant Barrier States

J.E. Kuperman, H. Almubarak, A.D. Saravanos and E.A. Theodorou

International Conference on Advanced Robotics (ICAR), 2023.

Abstract PDF Video

In this paper, we introduce Tolerant Discrete Barrier States (T-DBaS), a novel safety-embedding technique for trajectory optimization with enhanced exploratory capabilities. The proposed approach generalizes the standard discrete barrier state (DBaS) method by accommodating temporary constraint violation during the optimization process while still approximating its safety guarantees. Consequently, the proposed approach eliminates the DBaS's safe nominal trajectories assumption, while enhancing its exploration effectiveness for escaping local minima. Towards applying T-DBaS to safety-critical autonomous robotics, we combine it with Differential Dynamic Programming (DDP), leading to the proposed safe trajectory optimization method T-DBaS-DDP, which inherits the convergence and scalability properties of the solver. The effectiveness of the T-DBaS algorithm is verified on differential drive robot and quadrotor simulations. In addition, we compare against the classical DBaS-DDP as well as Augmented-Lagrangian DDP (AL-DDP) in extensive numerical comparisons that demonstrate the proposed method's competitive advantages. Finally, the applicability of the proposed approach is verified through hardware experiments on the Georgia Tech Robotarium platform.
RSS 2022

Decentralized Safe Multi-agent Stochastic Optimal Control using Deep FBSDEs and ADMM

M.A. Pereira*, A.D. Saravanos*, O. So, and E.A. Theodorou

Robotics: Science and Systems (RSS), 2022.

Abstract PDF Video

In this work, we propose a novel safe and scalable decentralized solution for multi-agent control in the presence of stochastic. Safety is mathematically encoded using stochastic control barrier functions and safe controls are computed by solving quadratic programs. Decentralization is achieved by augmenting to each agent’s optimization variables, copy variables, for its neighboring agents. This allows us to decouple the centralized multi-agent optimization problem. However, to ensure safety, neighboring agents must agree on what is safe for both of us and this creates a need for consensus. To enable safe consensus solutions, we incorporate an ADMM-based approach. Specifically, we propose a Merged CADMM-OSQP implicit neural network layer, that solves a mini-batch of both, local quadratic programs as well as the overall consensus problem, as a single optimization problem. This layer is embedded within a Deep FBSDEs network architecture at every time step, to facilitate end-to-end differentiable, safe and decentralized stochastic optimal control. The efficacy of the proposed approach is demonstrated on several challenging multi-robot tasks in simulation. By imposing requirements on safety specified by collision avoidance constraints, the safe operation of all agents is ensured during the entire training process. We also demonstrate superior scalability in terms of computational and memory savings as compared to a centralized approach.
CDC 2021

Receding Horizon Differential Dynamic Programming Under Parametric Uncertainty

Y. Aoyama, A.D. Saravanos, and E.A. Theodorou

IEEE Conference on Decision and Control (CDC), 2021.

Abstract PDF

Generalized Polynomial Chaos (gPC) theory has been widely used for representing parametric uncertainty in a system, thanks to its ability to propagate uncertainty evolution. In an optimal control context, gPC can be combined with several optimization techniques to achieve a control policy that handles effectively this type of uncertainty. Such a suitable method is Differential Dynamic Programming (DDP), leading to an algorithm that inherits the scalability to high-dimensional systems and fast convergence nature of the latter. In this paper, we expand this combination aiming to acquire probabilistic guarantees on the satisfaction of nonlinear constraints. In particular, we exploit the ability of gPC to express higher order moments of the uncertainty distribution - without any Gaussianity assumption - and we incorporate chance constraints that lead to expressions involving the state covariance. Furthermore, we demonstrate that by implementing our algorithm in a receding horizon fashion, we are able to compute control policies that effectively reduce the accumulation of uncertainty on the trajectory. The applicability of our method is verified through simulation results on a differential wheeled robot and a quadrotor that perform obstacle avoidance tasks.
RSS 2021

Distributed Covariance Steering with Consensus ADMM for Stochastic Multi-Agent Systems

A.D. Saravanos, A. Tsolovikos, E. Bakolas, and E.A. Theodorou

Robotics: Science and Systems (RSS), 2021.

Abstract PDF Video

In this paper, we address the problem of steering a team of agents under stochastic linear dynamics to prescribed final state means and covariances. The agents operate in a common environment where inter-agent constraints may also be present. In order for our method to be scalable to large-scale systems and computationally efficient, we approach the problem in a distributed control framework using the Alternating Direction Method of Multipliers (ADMM). Each agent solves its own covariance steering problem in parallel, while additional copy variables for its closest neighbors are introduced to ensure that the inter-agent constraints will be satisfied. The inclusion of these additional variables creates a requirement for consensus between original and copy variables that involve the same agent. For this reason, we employ a variation of ADMM for consensus optimization. Simulation results on multi-vehicle systems under uncertainty with collision avoidance constraints illustrate the effectiveness of our algorithm. The substantially improved scalability of our distributed approach with respect to the number of agents is also demonstrated, in comparison with an equivalent centralized scheme.

Workshop Papers & Technical Reports

Preprint

Sim2Real on the Robotarium Platform Using Decentralized Multi-Agent Safe Deep FBSDEs

M.A. Pereira*, A.D. Saravanos* and E.A. Theodorou

Robotics: Science and Systems (RSS), Workshop on Scaling Robot Learning, 2022.

Abstract PDF Video 1 Video 2

In this work, we propose a novel sim2real framework for multi-robot control that relies on stochastic optimal control theory. Specifically, we use a recently proposed Deep Forward-Backward Stochastic Differential Equations (FBSDEs) algorithm to train LSTM-network-based feedback policies in simulation that are subsequently deployed directly on real hardware. This particular Deep FBSDE variant is tailored for multi-agent systems and ensures safety during the entire training process. Safety is facilitated by employing stochastic control barrier functions and decentralization is achieved by an ADMM-based consensus optimization approach. By randomizing the initial conditions and inducing noise into the robot's dynamics, the policy is trained to control a mini-batch of trajectories to their respective targets on average, while ensuring safety for each trajectory with probability 1. We hypothesize that the ability to control an ensemble of trajectories empowers the feedback policy to compensate for uncertainty when transferred from simulation to real robots. We test this hypothesis on the Robotarium swarm-robotics testbed and successfully demonstrate the completion of tasks as well as safe operation when a policy trained in simulation is deployed without any prior real-world experience.
Preprint

Sampling-Based Optimization for Multi-Agent Model Predictive Control

Z. Wang, A.D. Saravanos, H. Almubarak, O. So and E.A. Theodorou

Technical Report, 2022.

Abstract PDF Video

We systematically review the Variational Optimization, Variational Inference and Stochastic Search perspectives on sampling-based dynamic optimization and discuss their connections to state-of-the-art optimizers and Stochastic Optimal Control (SOC) theory. A general convergence and sample complexity analysis on the three perspectives is provided through the unifying Stochastic Search perspective. We then extend these frameworks to their distributed versions for multi-agent control by combining them with consensus Alternating Direction Method of Multipliers (ADMM) to decouple the full problem into local neighborhood-level ones that can be solved in parallel. Model Predictive Control (MPC) algorithms are then developed based on these frameworks, leading to fully decentralized sampling-based dynamic optimizers. The capabilities of the proposed algorithms framework are demonstrated on multiple complex multi-agent tasks for vehicle and quadcopter systems in simulation. The results compare different distributed sampling-based optimizers and their centralized counterparts using unimodal Gaussian, mixture of Gaussians, and stein variational policies. The scalability of the proposed distributed algorithms is demonstrated on a 196-vehicle scenario where a direct application of centralized sampling-based methods is shown to be prohibitive.