Active Disruption Avoidance and Trajectory Design for Tokamak Ramp-downs with Neural Differential Equations and Reinforcement Learning

The tokamak offers a promising path to fusion energy, but plasma disruptions pose a major economic risk, motivating considerable advances in disruption avoidance. This work develops a reinforcement learning approach to this problem by training a policy to safely ramp-down the plasma current while avoiding limits on a number of quantities correlated with disruptions. The policy training environment is a hybrid physics and machine learning model trained on simulations of the SPARC primary reference discharge (PRD) ramp-down, an upcoming burning plasma scenario which we use as a testbed. To address physics uncertainty and model inaccuracies, the simulation environment is massively parallelized on GPU with randomized physics parameters during policy training. The trained policy is then successfully transferred to a higher fidelity simulator where it successfully ramps down the plasma while avoiding user-specified disruptive limits. We also address the crucial issue of safety criticality by demonstrating that a constraint-conditioned policy can be used as a trajectory design assistant to design a library of feed-forward trajectories to handle different physics conditions and user settings. As a library of trajectories is more interpretable and verifiable offline, we argue such an approach is a promising path for leveraging the capabilities of reinforcement learning in the safety-critical context of burning plasma tokamaks. Finally, we demonstrate how the training environment can be a useful platform for other feed-forward optimization approaches by using an evolutionary algorithm to perform optimization of feed-forward trajectories that are robust to physics uncertainty

GCBF+: A Neural Graph Control Barrier Function Framework for Distributed Safe Multi-Agent Control

Distributed, scalable, and safe control of large-scale multi-agent systems (MAS) is a challenging problem. In this paper, we design a distributed framework for safe multi-agent control in large-scale environments with obstacles, where a large number of agents are required to maintain safety using only local information and reach their goal locations. We introduce a new class of certificates, termed graph control barrier function (GCBF), which are based on the well-established control barrier function (CBF) theory for safety guarantees and utilize a graph structure for scalable and generalizable distributed control of MAS. We develop a novel theoretical framework to prove the safety of an arbitrary-sized MAS with a single GCBF. We propose a new training framework GCBF+ that uses graph neural networks (GNNs) to parameterize a candidate GCBF and a distributed control policy. The proposed framework is distributed and is capable of directly taking point clouds from LiDAR, instead of actual state information, for real-world robotic applications. We illustrate the efficacy of the proposed method through various hardware experiments on a swarm of drones with objectives ranging from exchanging positions to docking on a moving target without collision. Additionally, we perform extensive numerical experiments, where the number and density of agents, as well as the number of obstacles, increase. Empirical results show that in complex environments with nonlinear agents (e.g., Crazyflie drones) GCBF+ outperforms the handcrafted CBF-based method with the best performance by up to 20% for relatively small-scale MAS for up to 256 agents, and leading reinforcement learning (RL) methods by up to 40% for MAS with 1024 agents. Furthermore, the proposed method does not compromise on the performance, in terms of goal reaching, for achieving high safety rates, which is a common trade-off in RL-based methods.

Almost-Sure Safety Guarantees of Stochastic Zero-Control Barrier Functions Do Not Hold

The 2021 paper "Control barrier functions for stochastic systems" provides theorems that give almost sure safety guarantees given stochastic zero control barrier function (ZCBF). Unfortunately, both the theorem and its proof is invalid. In this letter, we illustrate on a toy example that the almost sure safety guarantees for stochastic ZCBF do not hold and explain why the proof is flawed. Although stochastic reciprocal barrier functions (RCBF) also uses the same proof technique, we provide a different proof technique that verifies that stochastic RCBFs are indeed safe with probability one. Using the RCBF, we derive a modified ZCBF condition that guarantees safety with probability one. Finally, we provide some discussion on the role of unbounded controls in the almost-sure safety guarantees of RCBFs, and show that the rate of divergence of the ratio of the drift and diffusion is the key for whether a system has almost sure safety guarantees.

Learning Safe Control for Multi-Robot Systems: Methods, Verification, and Open Challenges

In this survey, we review the recent advances in control design methods for robotic multi-agent systems (MAS), focussing on learning-based methods with safety considerations. We start by reviewing various notions of safety and liveness properties, and modeling frameworks used for problem formulation of MAS. Then we provide a comprehensive review of learning-based methods for safe control design for multi-robot systems. We start with various types of shielding-based methods, such as safety certificates, predictive filters, and reachability tools. Then, we review the current state of control barrier certificate learning in both a centralized and distributed manner, followed by a comprehensive review of multi-agent reinforcement learning with a particular focus on safety. Next, we discuss the state-of-the-art verification tools for the correctness of learning-based methods. Based on the capabilities and the limitations of the state of the art methods in learning and verification for MAS, we identify various broad themes for open challenges: how to design methods that can achieve good performance along with safety guarantees; how to decompose single-agent based centralized methods for MAS; how to account for communication-related practical issues; and how to assess transfer of theoretical guarantees to practice.

How to Train Your Neural Control Barrier Function: Learning Safety Filters for Complex Input-Constrained Systems

Control barrier functions (CBF) have become popular as a safety filter to guarantee the safety of nonlinear dynamical systems for arbitrary inputs. However, it is difficult to construct functions that satisfy the CBF constraints for high relative degree systems with input constraints. To address these challenges, recent work has explored learning CBFs using neural networks via neural CBF (NCBF). However, such methods face difficulties when scaling to higher dimensional systems under input constraints. In this work, we first identify challenges that NCBFs face during training. Next, to address these challenges, we propose policy neural CBF (PNCBF), a method of constructing CBFs by learning the value function of a nominal policy, and show that the value function of the maximum-over-time cost is a CBF. We demonstrate the effectiveness of our method in simulation on a variety of systems ranging from toy linear systems to an F-16 jet with a 16-dimensional state space. Finally, we validate our approach on a two-agent quadcopter system on hardware under tight input constraints.

GAME-UP: Game-Aware Mode Enumeration and Understanding for Trajectory Prediction

Interactions between road agents present a significant challenge in trajectory prediction, especially in cases involving multiple agents. Because existing diversity-aware predictors do not account for the interactive nature of multi-agent predictions, they may miss these important interaction outcomes. In this paper, we propose GAME-UP, a framework for trajectory prediction that leverages game-theoretic inverse reinforcement learning to improve coverage of multi-modal predictions. We use a training-time game-theoretic numerical analysis as an auxiliary loss resulting in improved coverage and accuracy without presuming a taxonomy of actions for the agents. We demonstrate our approach on the interactive subset of Waymo Open Motion Dataset, including three subsets involving scenarios with high interaction complexity. Experiment results show that our predictor produces accurate predictions while covering twice as many possible interactions versus a baseline model.

Solving Stabilize-Avoid Optimal Control via Epigraph Form and Deep Reinforcement Learning

Tasks for autonomous robotic systems commonly require stabilization to a desired region while maintaining safety specifications. However, solving this multi-objective problem is challenging when the dynamics are nonlinear and high-dimensional, as traditional methods do not scale well and are often limited to specific problem structures. To address this issue, we propose a novel approach to solve the stabilize-avoid problem via the solution of an infinite-horizon constrained optimal control problem (OCP). We transform the constrained OCP into epigraph form and obtain a two-stage optimization problem that optimizes over the policy in the inner problem and over an auxiliary variable in the outer problem. We then propose a new method for this formulation that combines an on-policy deep reinforcement learning algorithm with neural network regression. Our method yields better stability during training, avoids instabilities caused by saddle-point finding, and is not restricted to specific requirements on the problem structure compared to more traditional methods. We validate our approach on different benchmark tasks, ranging from low-dimensional toy examples to an F16 fighter jet with a 17-dimensional state space. Simulation results show that our approach consistently yields controllers that match or exceed the safety of existing methods while providing ten-fold increases in stability performance from larger regions of attraction.

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.