arXiv subjects

Brian C. Williams

Publications and source records attributed to Brian C. Williams.

At least 19 recordsLinked to original sources

arXiv2026

Large Neighborhood Search for Multi-Agent Task Assignment and Path Finding with Precedence Constraints

Many multi-robot applications require tasks to be completed efficiently and in the correct order, so that downstream operations can proceed at the right time. Multi-agent path finding with precedence constraints (MAPF-PC) is a well-studied framework for computing collision-free plans that satisfy ordering relations when task sequences are fixed in advance. In many applications, however, solution quality depends not only on how agents move, but also on which agent performs which task. This motivates the lifted problem of task assignment and path finding with precedence constraints (TAPF-PC), which extends MAPF-PC by jointly optimizing assignment, precedence satisfaction, and routing cost. To address the resulting coupled TAPF-PC search space, we develop a large neighborhood search approach that starts from a feasible MAPF-PC seed and iteratively improves it through reassignment-based neighborhood repair, restoring feasibility within each selected neighborhood. Experiments across multiple benchmark families and scaling regimes show that the best-performing configuration improves 89.1% of instances over fixed-assignment seed solutions, demonstrating that large neighborhood search effectively captures the gains from flexible reassignment under precedence constraints.

cs.RO↗

arXiv2026

Risk-Bounded Multi-Agent Visual Navigation via Iterative Risk Allocation

Safe navigation is essential for autonomous systems operating in hazardous environments, especially when multiple agents must coordinate using only high-dimensional visual observations. While recent approaches successfully combine Goal-Conditioned RL (GCRL) for graph construction with Conflict-Based Search (CBS) for planning, they typically rely on deleting edges with high risk before running CBS to enforce safety. This binary strategy is overly conservative, precluding feasible missions that require traversing high-risk regions, even when the aggregate risk is acceptable. To address this, we introduce a framework for Risk-Bounded Multi-Agent Path Finding ($Δ$-MAPF), where agents share a user-specified global risk budget ($Δ$). Rather than permanently discarding edges, our framework dynamically distributes per-agent risk budgets ($δ_i$) during search via an Iterative Risk Allocation (IRA) layer that integrates with a standard CBS planner. We investigate two distribution strategies: a greedy surplus-deficit scheme for rapid feasibility repair, and a market-inspired mechanism that treats risk as a priced resource to guide improved allocation. The market-based mechanism yields a tunable trade-off wherein agents exploit available risk to secure shorter, more efficient paths, but revert to longer, safer detours under tighter budgets. Experiments in complex visual environments show that our dynamic allocation framework achieves higher success rates than baselines and effectively leverages the available safety budget to reduce travel time. Project website can be found at https://rb-visual-mapf-mers.csail.mit.edu

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arXiv2025

Diffusion-Guided Multi-Arm Motion Planning

Multi-arm motion planning is fundamental for enabling arms to complete complex long-horizon tasks in shared spaces efficiently but current methods struggle with scalability due to exponential state-space growth and reliance on large training datasets for learned models. Inspired by Multi-Agent Path Finding (MAPF), which decomposes planning into single-agent problems coupled with collision resolution, we propose a novel diffusion-guided multi-arm planner (DG-MAP) that enhances scalability of learning-based models while reducing their reliance on massive multi-arm datasets. Recognizing that collisions are primarily pairwise, we train two conditional diffusion models, one to generate feasible single-arm trajectories, and a second, to model the dual-arm dynamics required for effective pairwise collision resolution. By integrating these specialized generative models within a MAPF-inspired structured decomposition, our planner efficiently scales to larger number of arms. Evaluations against alternative learning-based methods across various team sizes demonstrate our method's effectiveness and practical applicability. Project website can be found at https://diff-mapf-mers.csail.mit.edu

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arXiv2024

LaPlaSS: Latent Space Planning for Stochastic Systems

Autonomous mobile agents often operate in hazardous environments, necessitating an awareness of safety. These agents can have non-linear, stochastic dynamics that must be considered during planning to guarantee bounded risk. Most state of the art methods require closed-form dynamics to verify plan correctness and safety however modern robotic systems often have dynamics that are learned from data. Thus, there is a need to perform efficient trajectory planning with guarantees on risk for agents without known dynamics models. We propose a "generate-and-test" approach to risk-bounded planning in which a planner generates a candidate trajectory using an approximate linear dynamics model and a validator assesses the risk of the trajectory, computing additional safety constraints for the planner if the candidate does not satisfy the desired risk bound. To acquire the approximate model, we use a variational autoencoder to learn a latent linear dynamics model and encode the planning problem into the latent space to generate the candidate trajectory. The VAE also serves to sample trajectories around the candidate to use in the validator. We demonstrate that our algorithm, LaPlaSS, is able to generate trajectory plans with bounded risk for a real-world agent with learned dynamics and is an order of magnitude more efficient than the state of the art.

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arXiv2023

Adaptation and Communication in Human-Robot Teaming to Handle Discrepancies in Agents' Beliefs about Plans

When agents collaborate on a task, it is important that they have some shared mental model of the task routines -- the set of feasible plans towards achieving the goals. However, in reality, situations often arise that such a shared mental model cannot be guaranteed, such as in ad-hoc teams where agents may follow different conventions or when contingent constraints arise that only some agents are aware of. Previous work on human-robot teaming has assumed that the team has a set of shared routines, which breaks down in these situations. In this work, we leverage epistemic logic to enable agents to understand the discrepancy in each other's beliefs about feasible plans and dynamically plan their actions to adapt or communicate to resolve the discrepancy. We propose a formalism that extends conditional doxastic logic to describe knowledge bases in order to explicitly represent agents' nested beliefs on the feasible plans and state of execution. We provide an online execution algorithm based on Monte Carlo Tree Search for the agent to plan its action, including communication actions to explain the feasibility of plans, announce intent, and ask questions. Finally, we evaluate the success rate and scalability of the algorithm and show that our agent is better equipped to work in teams without the guarantee of a shared mental model.

cs.AI↗

arXiv2022

P4P: Conflict-Aware Motion Prediction for Planning in Autonomous Driving

Motion prediction is crucial in enabling safe motion planning for autonomous vehicles in interactive scenarios. It allows the planner to identify potential conflicts with other traffic agents and generate safe plans. Existing motion predictors often focus on reducing prediction errors, yet it remains an open question on how well they help identify the conflicts for the planner. In this paper, we evaluate state-of-the-art predictors through novel conflict-related metrics, such as the success rate of identifying conflicts. Surprisingly, the predictors suffer from a low success rate and thus lead to a large percentage of collisions when we test the prediction-planning system in an interactive simulator. To fill the gap, we propose a simple but effective alternative that combines a physics-based trajectory generator and a learning-based relation predictor to identify conflicts and infer conflict relations. We demonstrate that our predictor, P4P, achieves superior performance over existing learning-based predictors in realistic interactive driving scenarios from Waymo Open Motion Dataset.

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arXiv2022

InterSim: Interactive Traffic Simulation via Explicit Relation Modeling

Interactive traffic simulation is crucial to autonomous driving systems by enabling testing for planners in a more scalable and safe way compared to real-world road testing. Existing approaches learn an agent model from large-scale driving data to simulate realistic traffic scenarios, yet it remains an open question to produce consistent and diverse multi-agent interactive behaviors in crowded scenes. In this work, we present InterSim, an interactive traffic simulator for testing autonomous driving planners. Given a test plan trajectory from the ego agent, InterSim reasons about the interaction relations between the agents in the scene and generates realistic trajectories for each environment agent that are consistent with the relations. We train and validate our model on a large-scale interactive driving dataset. Experiment results show that InterSim achieves better simulation realism and reactivity in two simulation tasks compared to a state-of-the-art learning-based traffic simulator.

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arXiv2022

TIP: Task-Informed Motion Prediction for Intelligent Vehicles

When predicting trajectories of road agents, motion predictors usually approximate the future distribution by a limited number of samples. This constraint requires the predictors to generate samples that best support the task given task specifications. However, existing predictors are often optimized and evaluated via task-agnostic measures without accounting for the use of predictions in downstream tasks, and thus could result in sub-optimal task performance. In this paper, we propose a task-informed motion prediction model that better supports the tasks through its predictions, by jointly reasoning about prediction accuracy and the utility of the downstream tasks, which is commonly used to evaluate the task performance. The task utility function does not require the full task information, but rather a specification of the utility of the task, resulting in predictors that serve a wide range of downstream tasks. We demonstrate our approach on two use cases of common decision making tasks and their utility functions, in the context of autonomous driving and parallel autonomy. Experiment results show that our predictor produces accurate predictions that improve the task performance by a large margin in both tasks when compared to task-agnostic baselines on the Waymo Open Motion dataset.

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arXiv2022

Hierarchical Constrained Stochastic Shortest Path Planning via Cost Budget Allocation

Stochastic sequential decision making often requires hierarchical structure in the problem where each high-level action should be further planned with primitive states and actions. In addition, many real-world applications require a plan that satisfies constraints on the secondary costs such as risk measure or fuel consumption. In this paper, we propose a hierarchical constrained stochastic shortest path problem (HC-SSP) that meets those two crucial requirements in a single framework. Although HC-SSP provides a useful framework to model such planning requirements in many real-world applications, the resulting problem has high complexity and makes it difficult to find an optimal solution fast which prevents user from applying it to real-time and risk-sensitive applications. To address this problem, we present an algorithm that iteratively allocates cost budget to lower level planning problems based on branch-and-bound scheme to find a feasible solution fast and incrementally update the incumbent solution. We demonstrate the proposed algorithm in an evacuation scenario and prove the advantage over a state-of-the-art mathematical programming based approach.

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arXiv2022

M2I: From Factored Marginal Trajectory Prediction to Interactive Prediction

Predicting future motions of road participants is an important task for driving autonomously in urban scenes. Existing models excel at predicting marginal trajectories for single agents, yet it remains an open question to jointly predict scene compliant trajectories over multiple agents. The challenge is due to exponentially increasing prediction space as a function of the number of agents. In this work, we exploit the underlying relations between interacting agents and decouple the joint prediction problem into marginal prediction problems. Our proposed approach M2I first classifies interacting agents as pairs of influencers and reactors, and then leverages a marginal prediction model and a conditional prediction model to predict trajectories for the influencers and reactors, respectively. The predictions from interacting agents are combined and selected according to their joint likelihoods. Experiments show that our simple but effective approach achieves state-of-the-art performance on the Waymo Open Motion Dataset interactive prediction benchmark.

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arXiv2022

Cooperative Task and Motion Planning for Multi-Arm Assembly Systems

Multi-robot assembly systems are becoming increasingly appealing in manufacturing due to their ability to automatically, flexibly, and quickly construct desired structural designs. However, effectively planning for these systems in a manner that ensures each robot is simultaneously productive, and not idle, is challenging due to (1) the close proximity that the robots must operate in to manipulate the structure and (2) the inherent structural partial orderings on when each part can be installed. In this paper, we present a task and motion planning framework that jointly plans safe, low-makespan plans for a team of robots to assemble complex spatial structures. Our framework takes a hierarchical approach that, at the high level, uses Mixed-integer Linear Programs to compute an abstract plan comprised of an allocation of robots to tasks subject to precedence constraints and, at the low level, builds on a state-of-the-art algorithm for Multi-Agent Path Finding to plan collision-free robot motions that realize this abstract plan. Critical to our approach is the inclusion of certain collision constraints and movement durations during high-level planning, which better informs the search for abstract plans that are likely to be both feasible and low-makespan while keeping the search tractable. We demonstrate our planning system on several challenging assembly domains with several (sometimes heterogeneous) robots with grippers or suction plates for assembling structures with up to 23 objects involving Lego bricks, bars, plates, or irregularly shaped blocks.

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arXiv2021

HYPER: Learned Hybrid Trajectory Prediction via Factored Inference and Adaptive Sampling

Modeling multi-modal high-level intent is important for ensuring diversity in trajectory prediction. Existing approaches explore the discrete nature of human intent before predicting continuous trajectories, to improve accuracy and support explainability. However, these approaches often assume the intent to remain fixed over the prediction horizon, which is problematic in practice, especially over longer horizons. To overcome this limitation, we introduce HYPER, a general and expressive hybrid prediction framework that models evolving human intent. By modeling traffic agents as a hybrid discrete-continuous system, our approach is capable of predicting discrete intent changes over time. We learn the probabilistic hybrid model via a maximum likelihood estimation problem and leverage neural proposal distributions to sample adaptively from the exponentially growing discrete space. The overall approach affords a better trade-off between accuracy and coverage. We train and validate our model on the Argoverse dataset, and demonstrate its effectiveness through comprehensive ablation studies and comparisons with state-of-the-art models.

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arXiv2021

Fast nonlinear risk assessment for autonomous vehicles using learned conditional probabilistic models of agent futures

This paper presents fast non-sampling based methods to assess the risk for trajectories of autonomous vehicles when probabilistic predictions of other agents' futures are generated by deep neural networks (DNNs). The presented methods address a wide range of representations for uncertain predictions including both Gaussian and non-Gaussian mixture models to predict both agent positions and control inputs conditioned on the scene contexts. We show that the problem of risk assessment when Gaussian mixture models (GMMs) of agent positions are learned can be solved rapidly to arbitrary levels of accuracy with existing numerical methods. To address the problem of risk assessment for non-Gaussian mixture models of agent position, we propose finding upper bounds on risk using nonlinear Chebyshev's Inequality and sums-of-squares (SOS) programming; they are both of interest as the former is much faster while the latter can be arbitrarily tight. These approaches only require higher order statistical moments of agent positions to determine upper bounds on risk. To perform risk assessment when models are learned for agent control inputs as opposed to positions, we propagate the moments of uncertain control inputs through the nonlinear motion dynamics to obtain the exact moments of uncertain position over the planning horizon. To this end, we construct deterministic linear dynamical systems that govern the exact time evolution of the moments of uncertain position in the presence of uncertain control inputs. The presented methods are demonstrated on realistic predictions from DNNs trained on the Argoverse and CARLA datasets and are shown to be effective for rapidly assessing the probability of low probability events.

cs.LG↗

arXiv2021

Generalized Conflict-directed Search for Optimal Ordering Problems

Solving planning and scheduling problems for multiple tasks with highly coupled state and temporal constraints is notoriously challenging. An appealing approach to effectively decouple the problem is to judiciously order the events such that decisions can be made over sequences of tasks. As many problems encountered in practice are over-constrained, we must instead find relaxed solutions in which certain requirements are dropped. This motivates a formulation of optimality with respect to the costs of relaxing constraints and the problem of finding an optimal ordering under which this relaxing cost is minimum. In this paper, we present Generalized Conflict-directed Ordering (GCDO), a branch-and-bound ordering method that generates an optimal total order of events by leveraging the generalized conflicts of both inconsistency and suboptimality from sub-solvers for cost estimation and solution space pruning. Due to its ability to reason over generalized conflicts, GCDO is much more efficient in finding high-quality total orders than the previous conflict-directed approach CDITO. We demonstrate this by benchmarking on temporal network configuration problems, which involves managing networks over time and makes necessary tradeoffs between network flows against CDITO and Mixed Integer-Linear Programing (MILP). Our algorithm is able to solve two orders of magnitude more benchmark problems to optimality and twice the problems compared to CDITO and MILP within a runtime limit, respectively.

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arXiv2021

CARPAL: Confidence-Aware Intent Recognition for Parallel Autonomy

Predicting driver intentions is a difficult and crucial task for advanced driver assistance systems. Traditional confidence measures on predictions often ignore the way predicted trajectories affect downstream decisions for safe driving. In this paper, we propose a novel multi-task intent recognition neural network that predicts not only probabilistic driver trajectories, but also utility statistics associated with the predictions for a given downstream task. We establish a decision criterion for parallel autonomy that takes into account the role of driver trajectory prediction in real-time decision making by reasoning about estimated task-specific utility statistics. We further improve the robustness of our system by considering uncertainties in downstream planning tasks that may lead to unsafe decisions. We test our online system on a realistic urban driving dataset, and demonstrate its advantage in terms of recall and fall-out metrics compared to baseline methods, and demonstrate its effectiveness in intervention and warning use cases.

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arXiv2021

Moment-Based Exact Uncertainty Propagation Through Nonlinear Stochastic Autonomous Systems

In this paper, we address the problem of uncertainty propagation through nonlinear stochastic dynamical systems. More precisely, given a discrete-time continuous-state probabilistic nonlinear dynamical system, we aim at finding the sequence of the moments of the probability distributions of the system states up to any desired order over the given planning horizon. Moments of uncertain states can be used in estimation, planning, control, and safety analysis of stochastic dynamical systems. Existing approaches to address moment propagation problems provide approximate descriptions of the moments and are mainly limited to particular set of uncertainties, e.g., Gaussian disturbances. In this paper, to describe the moments of uncertain states, we introduce trigonometric and also mixed-trigonometric-polynomial moments. Such moments allow us to obtain closed deterministic dynamical systems that describe the exact time evolution of the moments of uncertain states of an important class of autonomous and robotic systems including underwater, ground, and aerial vehicles, robotic arms and walking robots. Such obtained deterministic dynamical systems can be used, in a receding horizon fashion, to propagate the uncertainties over the planning horizon in real-time. To illustrate the performance of the proposed method, we benchmark our method against existing approaches including linear, unscented transformation, and sampling based uncertainty propagation methods that are widely used in estimation, prediction, planning, and control problems.

eess.SY↗

arXiv2020

Fast-reactive probabilistic motion planning for high-dimensional robots

Many real-world robotic operations that involve high-dimensional humanoid robots require fast-reaction to plan disturbances and probabilistic guarantees over collision risks, whereas most probabilistic motion planning approaches developed for car-like robots can not be directly applied to high-dimensional robots. In this paper, we present probabilistic Chekov (p-Chekov), a fast-reactive motion planning system that can provide safety guarantees for high-dimensional robots suffering from process noises and observation noises. Leveraging recent advances in machine learning as well as our previous work in deterministic motion planning that integrated trajectory optimization into a sparse roadmap framework, p-Chekov demonstrates its superiority in terms of collision avoidance ability and planning speed in high-dimensional robotic motion planning tasks in complex environments without the convexification of obstacles. Comprehensive theoretical and empirical analysis provided in this paper shows that p-Chekov can effectively satisfy user-specified chance constraints over collision risk in practical robotic manipulation tasks.

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arXiv2020

Helpfulness as a Key Metric of Human-Robot Collaboration

As robotic teammates become more common in society, people will assess the robots' roles in their interactions along many dimensions. One such dimension is effectiveness: people will ask whether their robotic partners are trustworthy and effective collaborators. This begs a crucial question: how can we quantitatively measure the helpfulness of a robotic partner for a given task at hand? This paper seeks to answer this question with regards to the interactive robot's decision making. We describe a clear, concise, and task-oriented metric applicable to many different planning and execution paradigms. The proposed helpfulness metric is fundamental to assessing the benefit that a partner has on a team for a given task. In this paper, we define helpfulness, illustrate it on concrete examples from a variety of domains, discuss its properties and ramifications for planning interactions with humans, and present preliminary results.

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