Safe Human Robot Navigation in Warehouse Scenario

The integration of autonomous mobile robots (AMRs) in industrial environments, particularly warehouses, has revolutionized logistics and operational efficiency. However, ensuring the safety of human workers in dynamic, shared spaces remains a critical challenge. This work proposes a novel methodology that leverages control barrier functions (CBFs) to enhance safety in warehouse navigation. By integrating learning-based CBFs with the Open Robotics Middleware Framework (OpenRMF), the system achieves adaptive and safety-enhanced controls in multi-robot, multi-agent scenarios. Experiments conducted using various robot platforms demonstrate the efficacy of the proposed approach in avoiding static and dynamic obstacles, including human pedestrians. Our experiments evaluate different scenarios in which the number of robots, robot platforms, speed, and number of obstacles are varied, from which we achieve promising performance.

Controllable Motion Generation via Diffusion Modal Coupling

Diffusion models have recently gained significant attention in robotics due to their ability to generate multi-modal distributions of system states and behaviors. However, a key challenge remains: ensuring precise control over the generated outcomes without compromising realism. This is crucial for applications such as motion planning or trajectory forecasting, where adherence to physical constraints and task-specific objectives is essential. We propose a novel framework that enhances controllability in diffusion models by leveraging multi-modal prior distributions and enforcing strong modal coupling. This allows us to initiate the denoising process directly from distinct prior modes that correspond to different possible system behaviors, ensuring sampling to align with the training distribution. We evaluate our approach on motion prediction using the Waymo dataset and multi-task control in Maze2D environments. Experimental results show that our framework outperforms both guidance-based techniques and conditioned models with unimodal priors, achieving superior fidelity, diversity, and controllability, even in the absence of explicit conditioning. Overall, our approach provides a more reliable and scalable solution for controllable motion generation in robotics.

SEEV: Synthesis with Efficient Exact Verification for ReLU Neural Barrier Functions

Neural Control Barrier Functions (NCBFs) have shown significant promise in enforcing safety constraints on nonlinear autonomous systems. State-of-the-art exact approaches to verifying safety of NCBF-based controllers exploit the piecewise-linear structure of ReLU neural networks, however, such approaches still rely on enumerating all of the activation regions of the network near the safety boundary, thus incurring high computation cost. In this paper, we propose a framework for Synthesis with Efficient Exact Verification (SEEV). Our framework consists of two components, namely (i) an NCBF synthesis algorithm that introduces a novel regularizer to reduce the number of activation regions at the safety boundary, and (ii) a verification algorithm that exploits tight over-approximations of the safety conditions to reduce the cost of verifying each piecewise-linear segment. Our simulations show that SEEV significantly improves verification efficiency while maintaining the CBF quality across various benchmark systems and neural network structures. Our code is available at https://github.com/HongchaoZhang-HZ/SEEV.

Hamilton-Jacobi Reachability in Reinforcement Learning: A Survey

Recent literature has proposed approaches that learn control policies with high performance while maintaining safety guarantees. Synthesizing Hamilton-Jacobi (HJ) reachable sets has become an effective tool for verifying safety and supervising the training of reinforcement learning-based control policies for complex, high-dimensional systems. Previously, HJ reachability was limited to verifying low-dimensional dynamical systems -- this is because the computational complexity of the dynamic programming approach it relied on grows exponentially with the number of system states. To address this limitation, in recent years, there have been methods that compute the reachability value function simultaneously with learning control policies to scale HJ reachability analysis while still maintaining a reliable estimate of the true reachable set. These HJ reachability approximations are used to improve the safety, and even reward performance, of learned control policies and can solve challenging tasks such as those with dynamic obstacles and/or with lidar-based or vision-based observations. In this survey paper, we review the recent developments in the field of HJ reachability estimation in reinforcement learning that would provide a foundational basis for further research into reliability in high-dimensional systems.

Breaking the Barrier: Enhanced Utility and Robustness in Smoothed DRL Agents

Robustness remains a paramount concern in deep reinforcement learning (DRL), with randomized smoothing emerging as a key technique for enhancing this attribute. However, a notable gap exists in the performance of current smoothed DRL agents, often characterized by significantly low clean rewards and weak robustness. In response to this challenge, our study introduces innovative algorithms aimed at training effective smoothed robust DRL agents. We propose S-DQN and S-PPO, novel approaches that demonstrate remarkable improvements in clean rewards, empirical robustness, and robustness guarantee across standard RL benchmarks. Notably, our S-DQN and S-PPO agents not only significantly outperform existing smoothed agents by an average factor of $2.16\times$ under the strongest attack, but also surpass previous robustly-trained agents by an average factor of $2.13\times$. This represents a significant leap forward in the field. Furthermore, we introduce Smoothed Attack, which is $1.89\times$ more effective in decreasing the rewards of smoothed agents than existing adversarial attacks.

Activation-Descent Regularization for Input Optimization of ReLU Networks

We present a new approach for input optimization of ReLU networks that explicitly takes into account the effect of changes in activation patterns. We analyze local optimization steps in both the input space and the space of activation patterns to propose methods with superior local descent properties. To accomplish this, we convert the discrete space of activation patterns into differentiable representations and propose regularization terms that improve each descent step. Our experiments demonstrate the effectiveness of the proposed input-optimization methods for improving the state-of-the-art in various areas, such as adversarial learning, generative modeling, and reinforcement learning.

Mollification Effects of Policy Gradient Methods

Policy gradient methods have enabled deep reinforcement learning (RL) to approach challenging continuous control problems, even when the underlying systems involve highly nonlinear dynamics that generate complex non-smooth optimization landscapes. We develop a rigorous framework for understanding how policy gradient methods mollify non-smooth optimization landscapes to enable effective policy search, as well as the downside of it: while making the objective function smoother and easier to optimize, the stochastic objective deviates further from the original problem. We demonstrate the equivalence between policy gradient methods and solving backward heat equations. Following the ill-posedness of backward heat equations from PDE theory, we present a fundamental challenge to the use of policy gradient under stochasticity. Moreover, we make the connection between this limitation and the uncertainty principle in harmonic analysis to understand the effects of exploration with stochastic policies in RL. We also provide experimental results to illustrate both the positive and negative aspects of mollification effects in practice.

Understanding the Difficulty of Solving Cauchy Problems with PINNs

Physics-Informed Neural Networks (PINNs) have gained popularity in scientific computing in recent years. However, they often fail to achieve the same level of accuracy as classical methods in solving differential equations. In this paper, we identify two sources of this issue in the case of Cauchy problems: the use of $L^2$ residuals as objective functions and the approximation gap of neural networks. We show that minimizing the sum of $L^2$ residual and initial condition error is not sufficient to guarantee the true solution, as this loss function does not capture the underlying dynamics. Additionally, neural networks are not capable of capturing singularities in the solutions due to the non-compactness of their image sets. This, in turn, influences the existence of global minima and the regularity of the network. We demonstrate that when the global minimum does not exist, machine precision becomes the predominant source of achievable error in practice. We also present numerical experiments in support of our theoretical claims.

Extremum-Seeking Action Selection for Accelerating Policy Optimization

Reinforcement learning for control over continuous spaces typically uses high-entropy stochastic policies, such as Gaussian distributions, for local exploration and estimating policy gradient to optimize performance. Many robotic control problems deal with complex unstable dynamics, where applying actions that are off the feasible control manifolds can quickly lead to undesirable divergence. In such cases, most samples taken from the ambient action space generate low-value trajectories that hardly contribute to policy improvement, resulting in slow or failed learning. We propose to improve action selection in this model-free RL setting by introducing additional adaptive control steps based on Extremum-Seeking Control (ESC). On each action sampled from stochastic policies, we apply sinusoidal perturbations and query for estimated Q-values as the response signal. Based on ESC, we then dynamically improve the sampled actions to be closer to nearby optima before applying them to the environment. Our methods can be easily added in standard policy optimization to improve learning efficiency, which we demonstrate in various control learning environments.

Efficient Motion Planning for Manipulators with Control Barrier Function-Induced Neural Controller

Sampling-based motion planning methods for manipulators in crowded environments often suffer from expensive collision checking and high sampling complexity, which make them difficult to use in real time. To address this issue, we propose a new generalizable control barrier function (CBF)-based steering controller to reduce the number of samples needed in a sampling-based motion planner RRT. Our method combines the strength of CBF for real-time collision-avoidance control and RRT for long-horizon motion planning, by using CBF-induced neural controller (CBF-INC) to generate control signals that steer the system towards sampled configurations by RRT. CBF-INC is learned as Neural Networks and has two variants handling different inputs, respectively: state (signed distance) input and point-cloud input from LiDAR. In the latter case, we also study two different settings: fully and partially observed environmental information. Compared to manually crafted CBF which suffers from over-approximating robot geometry, CBF-INC can balance safety and goal-reaching better without being over-conservative. Given state-based input, our neural CBF-induced neural controller-enhanced RRT (CBF-INC-RRT) can increase the success rate by 14% while reducing the number of nodes explored by 30%, compared with vanilla RRT on hard test cases. Given LiDAR input where vanilla RRT is not directly applicable, we demonstrate that our CBF-INC-RRT can improve the success rate by 10%, compared with planning with other steering controllers. Our project page with supplementary material is at https://mit-realm.github.io/CBF-INC-RRT-website/.