Differentiable Robust Model Predictive Control

Deterministic model predictive control (MPC), while powerful, is often insufficient for effectively controlling autonomous systems in the real-world. Factors such as environmental noise and model error can cause deviations from the expected nominal performance. Robust MPC algorithms aim to bridge this gap between deterministic and uncertain control. However, these methods are often excessively difficult to tune for robustness due to the nonlinear and non-intuitive effects that controller parameters have on performance. To address this challenge, a unifying perspective on differentiable optimization for control is presented, which enables derivation of a general, differentiable tube-based MPC algorithm. The proposed approach facilitates the automatic and real-time tuning of robust controllers in the presence of large uncertainties and disturbances.

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

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. A video with all results is available in https://youtu.be/0QPyR4bD2q0 .

A Multi-step Dynamics Modeling Framework For Autonomous Driving In Multiple Environments

Modeling dynamics is often the first step to making a vehicle autonomous. While on-road autonomous vehicles have been extensively studied, off-road vehicles pose many challenging modeling problems. An off-road vehicle encounters highly complex and difficult-to-model terrain/vehicle interactions, as well as having complex vehicle dynamics of its own. These complexities can create challenges for effective high-speed control and planning. In this paper, we introduce a framework for multistep dynamics prediction that explicitly handles the accumulation of modeling error and remains scalable for sampling-based controllers. Our method uses a specially-initialized Long Short-Term Memory (LSTM) over a limited time horizon as the learned component in a hybrid model to predict the dynamics of a 4-person seating all-terrain vehicle (Polaris S4 1000 RZR) in two distinct environments. By only having the LSTM predict over a fixed time horizon, we negate the need for long term stability that is often a challenge when training recurrent neural networks. Our framework is flexible as it only requires odometry information for labels. Through extensive experimentation, we show that our method is able to predict millions of possible trajectories in real-time, with a time horizon of five seconds in challenging off road driving scenarios.

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

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.

Deep Momentum Multi-Marginal Schrödinger Bridge

Reconstructing population dynamics using only samples from distributions at coarse time intervals is a crucial challenge. Recent data-driven approaches such as flow-based models or Schr\"odinger Bridge models have demonstrated appealing performance, yet the inferred sample trajectories either fail to account for the underlying stochasticity or are unnecessarily rigid. In this article, we propose $\underline{D}$eep $\underline{M}$omentum Multi-Marginal $\underline{S}$chr\"odinger $\underline{B}$ridge(DMSB), a novel computational framework that learns the smooth measure-valued spline for stochastic systems without violating the position marginal constraints across time. We first extend the scalable mean matching objective used in the state space SB algorithm into the phase space. We next carefully craft a multi-constraint optimization training method based on Bregman Iteration that enables effective phase space means matching training for the high-dimensional dataset. We demonstrate that the resulting training algorithm significantly outperforms baselines on both synthetic datasets and a real-world single-cell RNA sequence dataset.

I$^2$SB: Image-to-Image Schrödinger Bridge

We propose Image-to-Image Schr\"odinger Bridge (I$^2$SB), a new class of conditional diffusion models that directly learn the nonlinear diffusion processes between two given distributions. These diffusion bridges are particularly useful for image restoration, as the degraded images are structurally informative priors for reconstructing the clean images. I$^2$SB belongs to a tractable class of Schr\"odinger bridge, the nonlinear extension to score-based models, whose marginal distributions can be computed analytically given boundary pairs. This results in a simulation-free framework for nonlinear diffusions, where the I$^2$SB training becomes scalable by adopting practical techniques used in standard diffusion models. We validate I$^2$SB in solving various image restoration tasks, including inpainting, super-resolution, deblurring, and JPEG restoration on ImageNet 256x256 and show that I$^2$SB surpasses standard conditional diffusion models with more interpretable generative processes. Moreover, I$^2$SB matches the performance of inverse methods that additionally require the knowledge of the corruption operators. Our work opens up new algorithmic opportunities for developing efficient nonlinear diffusion models on a large scale. scale. Project page: https://i2sb.github.io/

Distributed Model Predictive Covariance Steering

This paper proposes Distributed Model Predictive Covariance Steering (DMPCS), a novel method for safe multi-robot control under uncertainty. The scope of our approach is to blend covariance steering theory, distributed optimization and model predictive control (MPC) into a single methodology 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-robot team 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 (ADMM). This method is then extended to a receding horizon form, which yields the proposed DMPCS algorithm. Simulation experiments on large-scale problems with up to hundreds of robots successfully demonstrate the effectiveness and scalability of DMPCS. Its superior capability in achieving safety is also highlighted through a comparison against a standard stochastic MPC approach. A video with all simulation experiments is available in https://youtu.be/Hks-0BRozxA.

Gaussian Process Barrier States for Safe Trajectory Optimization and Control

This paper proposes embedded Gaussian Process Barrier States (GP-BaS), a methodology to safely control unmodeled dynamics of nonlinear system using Bayesian learning. Gaussian Processes (GPs) are used to model the dynamics of the safety-critical system, which is subsequently used in the GP-BaS model. We derive the barrier state dynamics utilizing the GP posterior, which is used to construct a safety embedded Gaussian process dynamical model (GPDM). We show that the safety-critical system can be controlled to remain inside the safe region as long as we can design a controller that renders the BaS-GPDM's trajectories bounded (or asymptotically stable). The proposed approach overcomes various limitations in early attempts at combining GPs with barrier functions due to the abstention of restrictive assumptions such as linearity of the system with respect to control, relative degree of the constraints and number or nature of constraints. This work is implemented on various examples for trajectory optimization and control including optimal stabilization of unstable linear system and safe trajectory optimization of a Dubins vehicle navigating through an obstacle course and on a quadrotor in an obstacle avoidance task using GP differentiable dynamic programming (GP-DDP). The proposed framework is capable of maintaining safe optimization and control of unmodeled dynamics and is purely data driven.

MPOGames: Efficient Multimodal Partially Observable Dynamic Games

Game theoretic methods have become popular for planning and prediction in situations involving rich multi-agent interactions. However, these methods often assume the existence of a single local Nash equilibria and are hence unable to handle uncertainty in the intentions of different agents. While maximum entropy (MaxEnt) dynamic games try to address this issue, practical approaches solve for MaxEnt Nash equilibria using linear-quadratic approximations which are restricted to unimodal responses and unsuitable for scenarios with multiple local Nash equilibria. By reformulating the problem as a POMDP, we propose MPOGames, a method for efficiently solving MaxEnt dynamic games that captures the interactions between local Nash equilibria. We show the importance of uncertainty-aware game theoretic methods via a two-agent merge case study. Finally, we prove the real-time capabilities of our approach with hardware experiments on a 1/10th scale car platform.

Data-driven discovery of non-Newtonian astronomy via learning non-Euclidean Hamiltonian

Incorporating the Hamiltonian structure of physical dynamics into deep learning models provides a powerful way to improve the interpretability and prediction accuracy. While previous works are mostly limited to the Euclidean spaces, their extension to the Lie group manifold is needed when rotations form a key component of the dynamics, such as the higher-order physics beyond simple point-mass dynamics for N-body celestial interactions. Moreover, the multiscale nature of these processes presents a challenge to existing methods as a long time horizon is required. By leveraging a symplectic Lie-group manifold preserving integrator, we present a method for data-driven discovery of non-Newtonian astronomy. Preliminary results show the importance of both these properties in training stability and prediction accuracy.