Solving Minimum-Cost Reach Avoid using Reinforcement Learning

Current reinforcement-learning methods are unable to directly learn policies that solve the minimum cost reach-avoid problem to minimize cumulative costs subject to the constraints of reaching the goal and avoiding unsafe states, as the structure of this new optimization problem is incompatible with current methods. Instead, a surrogate problem is solved where all objectives are combined with a weighted sum. However, this surrogate objective results in suboptimal policies that do not directly minimize the cumulative cost. In this work, we propose RC-PPO, a reinforcement-learning-based method for solving the minimum-cost reach-avoid problem by using connections to Hamilton-Jacobi reachability. Empirical results demonstrate that RC-PPO learns policies with comparable goal-reaching rates to while achieving up to 57% lower cumulative costs compared to existing methods on a suite of minimum-cost reach-avoid benchmarks on the Mujoco simulator. The project page can be found at https://oswinso.xyz/rcppo.

Planning Anything with Rigor: General-Purpose Zero-Shot Planning with LLM-based Formalized Programming

While large language models (LLMs) have recently demonstrated strong potential in solving planning problems, there is a trade-off between flexibility and complexity. LLMs, as zero-shot planners themselves, are still not capable of directly generating valid plans for complex planning problems such as multi-constraint or long-horizon tasks. On the other hand, many frameworks aiming to solve complex planning problems often rely on task-specific preparatory efforts, such as task-specific in-context examples and pre-defined critics/verifiers, which limits their cross-task generalization capability. In this paper, we tackle these challenges by observing that the core of many planning problems lies in optimization problems: searching for the optimal solution (best plan) with goals subject to constraints (preconditions and effects of decisions). With LLMs' commonsense, reasoning, and programming capabilities, this opens up the possibilities of a universal LLM-based approach to planning problems. Inspired by this observation, we propose LLMFP, a general-purpose framework that leverages LLMs to capture key information from planning problems and formally formulate and solve them as optimization problems from scratch, with no task-specific examples needed. We apply LLMFP to 9 planning problems, ranging from multi-constraint decision making to multi-step planning problems, and demonstrate that LLMFP achieves on average 83.7% and 86.8% optimal rate across 9 tasks for GPT-4o and Claude 3.5 Sonnet, significantly outperforming the best baseline (direct planning with OpenAI o1-preview) with 37.6% and 40.7% improvements. We also validate components of LLMFP with ablation experiments and analyzed the underlying success and failure reasons.

RPCBF: Constructing Safety Filters Robust to Model Error and Disturbances via Policy Control Barrier Functions

Control Barrier Functions (CBFs) have proven to be an effective tool for performing safe control synthesis for nonlinear systems. However, guaranteeing safety in the presence of disturbances and input constraints for high relative degree systems is a difficult problem. In this work, we propose the Robust Policy CBF (RPCBF), a practical method of constructing CBF approximations that is easy to implement and robust to disturbances via the estimation of a value function. We demonstrate the effectiveness of our method in simulation on a variety of high relative degree input-constrained systems. Finally, we demonstrate the benefits of RPCBF in compensating for model errors on a hardware quadcopter platform by treating the model errors as disturbances. The project page can be found at https://oswinso.xyz/rpcbf.

Failure Prediction from Limited Hardware Demonstrations

Prediction of failures in real-world robotic systems either requires accurate model information or extensive testing. Partial knowledge of the system model makes simulation-based failure prediction unreliable. Moreover, obtaining such demonstrations is expensive, and could potentially be risky for the robotic system to repeatedly fail during data collection. This work presents a novel three-step methodology for discovering failures that occur in the true system by using a combination of a limited number of demonstrations from the true system and the failure information processed through sampling-based testing of a model dynamical system. Given a limited budget $N$ of demonstrations from true system and a model dynamics (with potentially large modeling errors), the proposed methodology comprises of a) exhaustive simulations for discovering algorithmic failures using the model dynamics; b) design of initial $N_1$ demonstrations of the true system using Bayesian inference to learn a Gaussian process regression (GPR)-based failure predictor; and c) iterative $N - N_1$ demonstrations of the true system for updating the failure predictor. To illustrate the efficacy of the proposed methodology, we consider: a) the failure discovery for the task of pushing a T block to a fixed target region with UR3E collaborative robot arm using a diffusion policy; and b) the failure discovery for an F1-Tenth racing car tracking a given raceline under an LQR control policy.

Steering Large Language Models between Code Execution and Textual Reasoning

While a lot of recent research focuses on enhancing the textual reasoning capabilities of Large Language Models (LLMs) by optimizing the multi-agent framework or reasoning chains, several benchmark tasks can be solved with 100% success through direct coding, which is more scalable and avoids the computational overhead associated with textual iterating and searching. Textual reasoning has inherent limitations in solving tasks with challenges in math, logics, optimization, and searching, which is unlikely to be solved by simply scaling up the model and data size. The recently released OpenAI GPT Code Interpreter and multi-agent frameworks such as AutoGen have demonstrated remarkable proficiency of integrating code generation and execution to solve complex tasks using LLMs. However, based on our experiments on 7 existing popular methods for steering code/text generation in both single- and multi-turn settings with 14 tasks and 6 types of LLMs (including the new O1-preview), currently there is no optimal method to correctly steer LLMs to write code when needed. We discover some interesting patterns on when models use code vs. textual reasoning with the evolution to task complexity and model sizes, which even result in an astonishingly inverse scaling law. We also discover that results from LLM written code are not always better than using textual reasoning, even if the task could be solved through code. To mitigate the above issues, we propose three methods to better steer LLM code/text generation and achieve a notable improvement. The costs of token lengths and runtime are thoroughly discussed for all the methods. We believe the problem of steering LLM code/text generation is critical for future research and has much space for further improvement. Project Page, Datasets, and Codes are available at https://yongchao98.github.io/CodeSteer/.

Rigid Body Path Planning using Mixed-Integer Linear Programming

Navigating rigid body objects through crowded environments can be challenging, especially when narrow passages are presented. Existing sampling-based planners and optimization-based methods like mixed integer linear programming (MILP) formulations, suffer from limited scalability with respect to either the size of the workspace or the number of obstacles. In order to address the scalability issue, we propose a three-stage algorithm that first generates a graph of convex polytopes in the workspace free of collision, then poses a large set of small MILPs to generate viable paths between polytopes, and finally queries a pair of start and end configurations for a feasible path online. The graph of convex polytopes serves as a decomposition of the free workspace and the number of decision variables in each MILP is limited by restricting the subproblem within two or three free polytopes rather than the entire free region. Our simulation results demonstrate shorter online computation time compared to baseline methods and scales better with the size of the environment and tunnel width than sampling-based planners in both 2D and 3D environments.

Optimization of Multi-Agent Flying Sidekick Traveling Salesman Problem over Road Networks

The mixed truck-drone delivery systems have attracted increasing attention for last-mile logistics, but real-world complexities demand a shift from single-agent, fully connected graph models to multi-agent systems operating on actual road networks. We introduce the multi-agent flying sidekick traveling salesman problem (MA-FSTSP) on road networks, extending the single truck-drone model to multiple trucks, each carrying multiple drones while considering full road networks for truck restrictions and flexible drone routes. We propose a mixed-integer linear programming model and an efficient three-phase heuristic algorithm for this NP-hard problem. Our approach decomposes MA-FSTSP into manageable subproblems of one truck with multiple drones. Then, it computes the routes for trucks without drones in subproblems, which are used in the final phase as heuristics to help optimize drone and truck routes simultaneously. Extensive numerical experiments on Manhattan and Boston road networks demonstrate our algorithm's superior effectiveness and efficiency, significantly outperforming both column generation and variable neighborhood search baselines in solution quality and computation time. Notably, our approach scales to more than 300 customers within a 5-minute time limit, showcasing its potential for large-scale, real-world logistics applications.

Scalable Surrogate Verification of Image-based Neural Network Control Systems using Composition and Unrolling

Verifying safety of neural network control systems that use images as input is a difficult problem because, from a given system state, there is no known way to mathematically model what images are possible in the real-world. We build on recent work that considers a surrogate verification approach, training a conditional generative adversarial network (cGAN) as an image generator in place of the real world. This enables set-based formal analysis of the closed-loop system, providing analysis beyond simulation and testing. While existing work is effective on small examples, excessive overapproximation both within a single control period and across multiple control periods limits its scalability. We propose approaches to overcome these two sources of error. First, we overcome one-step error by composing the system's dynamics along with the cGAN and neural network controller, without losing the dependencies between input states and the control outputs as in the monotonic analysis of the system dynamics. Second, we reduce multi-step error by repeating the single-step composition, essentially unrolling multiple steps of the control loop into a large neural network. We then leverage existing network verification tools to compute accurate reachable sets for multiple steps, avoiding the accumulation of abstraction error at each step. We demonstrate the effectiveness of our approach in terms of both accuracy and scalability using two case studies: an autonomous aircraft taxiing system and an advanced emergency braking system. On the aircraft taxiing system, the converged reachable set is 175% larger using the prior baseline method compared with our proposed approach. On the emergency braking system, with 24x the number of image output variables from the cGAN, the baseline method fails to prove any states are safe, whereas our improvements enable set-based safety analysis.

Large Language Models Can Plan Your Travels Rigorously with Formal Verification Tools

The recent advancements of Large Language Models (LLMs), with their abundant world knowledge and capabilities of tool-using and reasoning, fostered many LLM planning algorithms. However, LLMs have not shown to be able to accurately solve complex combinatorial optimization problems. In Xie et al. (2024), the authors proposed TravelPlanner, a U.S. domestic travel planning benchmark, and showed that LLMs themselves cannot make travel plans that satisfy user requirements with a best success rate of 0.6%. In this work, we propose a framework that enables LLMs to formally formulate and solve the travel planning problem as a satisfiability modulo theory (SMT) problem and use SMT solvers interactively and automatically solve the combinatorial search problem. The SMT solvers guarantee the satisfiable of input constraints and the LLMs can enable a language-based interaction with our framework. When the input constraints cannot be satisfiable, our LLM-based framework will interactively offer suggestions to users to modify their travel requirements via automatic reasoning using the SMT solvers. We evaluate our framework with TravelPlanner and achieve a success rate of 97%. We also create a separate dataset that contain international travel benchmarks and use both dataset to evaluate the effectiveness of our interactive planning framework when the initial user queries cannot be satisfied. Our framework could generate valid plans with an average success rate of 78.6% for our dataset and 85.0% for TravelPlanner according to diverse humans preferences.

Large Language Models to the Rescue: Deadlock Resolution in Multi-Robot Systems

Multi-agent robotic systems are prone to deadlocks in an obstacle environment where the system can get stuck away from its desired location under a smooth low-level control policy. Without an external intervention, often in terms of a high-level command, it is not possible to guarantee that just a low-level control policy can resolve such deadlocks. Utilizing the generalizability and low data requirements of large language models (LLMs), this paper explores the possibility of using LLMs for deadlock resolution. We propose a hierarchical control framework where an LLM resolves deadlocks by assigning a leader and direction for the leader to move along. A graph neural network (GNN) based low-level distributed control policy executes the assigned plan. We systematically study various prompting techniques to improve LLM's performance in resolving deadlocks. In particular, as part of prompt engineering, we provide in-context examples for LLMs. We conducted extensive experiments on various multi-robot environments with up to 15 agents and 40 obstacles. Our results demonstrate that LLM-based high-level planners are effective in resolving deadlocks in MRS.