Brian C. Williams

Viraj Parimi, Brian C. Williams · mit

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.

Viraj Parimi, Brian C. Williams · mit

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

Viraj Parimi, Brian C. Williams · mit

Safe navigation is essential for autonomous systems operating in hazardous environments, especially when multiple agents must coordinate using just visual inputs over extended time horizons. Traditional planning methods excel at solving long-horizon tasks but rely on predefined distance metrics, while safe Reinforcement Learning (RL) can learn complex behaviors using high-dimensional inputs yet struggles with multi-agent, goal-conditioned scenarios. Recent work combined these paradigms by leveraging goal-conditioned RL (GCRL) to build an intermediate graph from replay buffer states, pruning unsafe edges, and using Conflict-Based Search (CBS) for multi-agent path planning. Although effective, this graph-pruning approach can be overly conservative, limiting mission efficiency by precluding missions that must traverse high-risk regions. To address this limitation, we propose RB-CBS, a novel extension to CBS that dynamically allocates and adjusts user-specified risk bound ($Δ$) across agents to flexibly trade off safety and speed. Our improved planner ensures that each agent receives a local risk budget ($δ$) enabling more efficient navigation while still respecting overall safety constraints. Experimental results demonstrate that this iterative risk-allocation framework yields superior performance in complex environments, allowing multiple agents to find collision-free paths within the user-specified $Δ$.

Marlyse Reeves, Brian C. Williams

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.

Xin Huang, Meng Feng, Ashkan Jasour et al.

Risk-bounded motion planning is an important yet difficult problem for safety-critical tasks. While existing mathematical programming methods offer theoretical guarantees in the context of constrained Markov decision processes, they either lack scalability in solving larger problems or produce conservative plans. Recent advances in deep reinforcement learning improve scalability by learning policy networks as function approximators. In this paper, we propose an extension of soft actor critic model to estimate the execution risk of a plan through a risk critic and produce risk-bounded policies efficiently by adding an extra risk term in the loss function of the policy network. We define the execution risk in an accurate form, as opposed to approximating it through a summation of immediate risks at each time step that leads to conservative plans. Our proposed model is conditioned on a continuous spectrum of risk bounds, allowing the user to adjust the risk-averse level of the agent on the fly. Through a set of experiments, we show the advantage of our model in terms of both computational time and plan quality, compared to a state-of-the-art mathematical programming baseline, and validate its performance in more complicated scenarios, including nonlinear dynamics and larger state space.

Ashkan Jasour, Allen Wang, Brian C. Williams

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.

Siyu Dai, Andreas Hofmann, Brian C. Williams

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.

Allen Wang, Ashkan Jasour, Brian Williams

Chance-constrained motion planning requires uncertainty in dynamics to be propagated into uncertainty in state. When nonlinear models are used, Gaussian assumptions on the state distribution do not necessarily apply since almost all random variables propagated through nonlinear dynamics results in non-Gaussian state distributions. To address this, recent works have developed moment-based approaches for enforcing chance-constraints on non-Gaussian state distributions. However, there still lacks fast and accurate moment propagation methods to determine the necessary statistical moments of these state distributions. To address this gap, we present a framework that, given a stochastic dynamical system, can algorithmically search for a new dynamical system in terms of moment state that can be used to propagate moments of disturbance random variables into moments of the state distribution. The key algorithm, TreeRing, can be applied to a large class of nonlinear systems which we refer to as trigonometric polynomial systems. As an example application, we present a distributionally robust RRT (DR-RRT) algorithm that propagates uncertainty through the nonlinear Dubin's car model without linearization.

Jingkai Chen, Cheng Fang, David Wang et al.

In planning and scheduling, solving problems with both state and temporal constraints is hard since these constraints may be highly coupled. Judicious orderings of events enable solvers to efficiently make decisions over sequences of actions to satisfy complex hybrid specifications. The ordering problem is thus fundamental to planning. Promising recent works have explored the ordering problem as search, incorporating a special tree structure for efficiency. However, such approaches only reason over partial order specifications. Having observed that an ordering is inconsistent with respect to underlying constraints, prior works do not exploit the tree structure to efficiently generate orderings that resolve the inconsistency. In this paper, we present Conflict-directed Incremental Total Ordering (CDITO), a conflict-directed search method to incrementally and systematically generate event total orders given ordering relations and conflicts returned by sub-solvers. Due to its ability to reason over conflicts, CDITO is much more efficient than Incremental Total Ordering. We demonstrate this by benchmarking on temporal network configuration problems that involve routing network flows and allocating bandwidth resources over time.

Ashkan Jasour, Andreas Hofmann, Brian C. Williams

In this paper, we address the risk estimation problem where one aims at estimating the probability of violation of safety constraints for a robot in the presence of bounded uncertainties with arbitrary probability distributions. In this problem, an unsafe set is described by level sets of polynomials that is, in general, a non-convex set. Uncertainty arises due to the probabilistic parameters of the unsafe set and probabilistic states of the robot. To solve this problem, we use a moment-based representation of probability distributions. We describe upper and lower bounds of the risk in terms of a linear weighted sum of the moments. Weights are coefficients of a univariate Chebyshev polynomial obtained by solving a sum-of-squares optimization problem in the offline step. Hence, given a finite number of moments of probability distributions, risk can be estimated in real-time. We demonstrate the performance of the provided approach by solving probabilistic collision checking problems where we aim to find the probability of collision of a robot with a non-convex obstacle in the presence of probabilistic uncertainties in the location of the robot and size, location, and geometry of the obstacle.

Benjamin J Ayton, Brian C Williams

Chance Constrained Markov Decision Processes maximize reward subject to a bounded probability of failure, and have been frequently applied for planning with potentially dangerous outcomes or unknown environments. Solution algorithms have required strong heuristics or have been limited to relatively small problems with up to millions of states, because the optimal action to take from a given state depends on the probability of failure in the rest of the policy, leading to a coupled problem that is difficult to solve. In this paper we examine a generalization of a CCMDP that trades off probability of failure against reward through a functional relationship. We derive a constraint that can be applied to each state history in a policy individually, and which guarantees that the chance constraint will be satisfied. The approach decouples states in the CCMDP, so that large problems can be solved efficiently. We then introduce Vulcan, which uses our constraint in order to apply Monte Carlo Tree Search to CCMDPs. Vulcan can be applied to problems where it is unfeasible to generate the entire state space, and policies must be returned in an anytime manner. We show that Vulcan and its variants run tens to hundreds of times faster than linear programming methods, and over ten times faster than heuristic based methods, all without the need for a heuristic, and returning solutions with a mean suboptimality on the order of a few percent. Finally, we use Vulcan to solve for a chance constrained policy in a CCMDP with over $10^{13}$ states in 3 minutes.

Masahiro Ono, Brian C. Williams, L. Blackmore

This paper presents a model-based planner called the Probabilistic Sulu Planner or the p-Sulu Planner, which controls stochastic systems in a goal directed manner within user-specified risk bounds. The objective of the p-Sulu Planner is to allow users to command continuous, stochastic systems, such as unmanned aerial and space vehicles, in a manner that is both intuitive and safe. To this end, we first develop a new plan representation called a chance-constrained qualitative state plan (CCQSP), through which users can specify the desired evolution of the plant state as well as the acceptable level of risk. An example of a CCQSP statement is go to A through B within 30 minutes, with less than 0.001% probability of failure." We then develop the p-Sulu Planner, which can tractably solve a CCQSP planning problem. In order to enable CCQSP planning, we develop the following two capabilities in this paper: 1) risk-sensitive planning with risk bounds, and 2) goal-directed planning in a continuous domain with temporal constraints. The first capability is to ensures that the probability of failure is bounded. The second capability is essential for the planner to solve problems with a continuous state space such as vehicle path planning. We demonstrate the capabilities of the p-Sulu Planner by simulations on two real-world scenarios: the path planning and scheduling of a personal aerial vehicle as well as the space rendezvous of an autonomous cargo spacecraft.

Patrick Raymond Conrad, Brian Williams

This work presents Drake, a dynamic executive for temporal plans with choice. Dynamic plan execution strategies allow an autonomous agent to react quickly to unfolding events, improving the robustness of the agent. Prior work developed methods for dynamically dispatching Simple Temporal Networks, and further research enriched the expressiveness of the plans executives could handle, including discrete choices, which are the focus of this work. However, in some approaches to date, these additional choices induce significant storage or latency requirements to make flexible execution possible. Drake is designed to leverage the low latency made possible by a preprocessing step called compilation, while avoiding high memory costs through a compact representation. We leverage the concepts of labels and environments, taken from prior work in Assumption-based Truth Maintenance Systems (ATMS), to concisely record the implications of the discrete choices, exploiting the structure of the plan to avoid redundant reasoning or storage. Our labeling and maintenance scheme, called the Labeled Value Set Maintenance System, is distinguished by its focus on properties fundamental to temporal problems, and, more generally, weighted graph algorithms. In particular, the maintenance system focuses on maintaining a minimal representation of non-dominated constraints. We benchmark Drakes performance on random structured problems, and find that Drake reduces the size of the compiled representation by a factor of over 500 for large problems, while incurring only a modest increase in run-time latency, compared to prior work in compiled executives for temporal plans with discrete choices.