Inspection planning under execution uncertainty

Autonomous inspection tasks necessitate effective path-planning mechanisms to efficiently gather observations from points of interest (POI). However, localization errors commonly encountered in urban environments can introduce execution uncertainty, posing challenges to the successful completion of such tasks. To tackle these challenges, we present IRIS-under uncertainty (IRIS-U^2), an extension of the incremental random inspection-roadmap search (IRIS) algorithm, that addresses the offline planning problem via an A*-based approach, where the planning process occurs prior the online execution. The key insight behind IRIS-U^2 is transforming the computed localization uncertainty, obtained through Monte Carlo (MC) sampling, into a POI probability. IRIS-U^2 offers insights into the expected performance of the execution task by providing confidence intervals (CI) for the expected coverage, expected path length, and collision probability, which becomes progressively tighter as the number of MC samples increase. The efficacy of IRIS-U^2 is demonstrated through a case study focusing on structural inspections of bridges. Our approach exhibits improved expected coverage, reduced collision probability, and yields increasingly-precise CIs as the number of MC samples grows. Furthermore, we emphasize the potential advantages of computing bounded sub-optimal solutions to reduce computation time while still maintaining the same CI boundaries.

Terraforming -- Environment Manipulation during Disruptions for Multi-Agent Pickup and Delivery

In automated warehouses, teams of mobile robots fulfill the packaging process by transferring inventory pods to designated workstations while navigating narrow aisles formed by tightly packed pods. This problem is typically modeled as a Multi-Agent Pickup and Delivery (MAPD) problem, which is then solved by repeatedly planning collision-free paths for agents on a fixed graph, as in the Rolling-Horizon Collision Resolution (RHCR) algorithm. However, existing approaches make the limiting assumption that agents are only allowed to move pods that correspond to their current task, while considering the other pods as stationary obstacles (even though all pods are movable). This behavior can result in unnecessarily long paths which could otherwise be avoided by opening additional corridors via pod manipulation. To this end, we explore the implications of allowing agents the flexibility of dynamically relocating pods. We call this new problem Terraforming MAPD (tMAPD) and develop an RHCR-based approach to tackle it. As the extra flexibility of terraforming comes at a significant computational cost, we utilize this capability judiciously by identifying situations where it could make a significant impact on the solution quality. In particular, we invoke terraforming in response to disruptions that often occur in automated warehouses, e.g., when an item is dropped from a pod or when agents malfunction. Empirically, using our approach for tMAPD, where disruptions are modeled via a stochastic process, we improve throughput by over 10%, reduce the maximum service time (the difference between the drop-off time and the pickup time of a pod) by more than 50%, without drastically increasing the runtime, compared to the MAPD setting.

Robust-RRT: Probabilistically-Complete Motion Planning for Uncertain Nonlinear Systems

Robust motion planning entails computing a global motion plan that is safe under all possible uncertainty realizations, be it in the system dynamics, the robot's initial position, or with respect to external disturbances. Current approaches for robust motion planning either lack theoretical guarantees, or make restrictive assumptions on the system dynamics and uncertainty distributions. In this paper, we address these limitations by proposing the robust rapidly-exploring random-tree (Robust-RRT) algorithm, which integrates forward reachability analysis directly into sampling-based control trajectory synthesis. We prove that Robust-RRT is probabilistically complete (PC) for nonlinear Lipschitz continuous dynamical systems with bounded uncertainty. In other words, Robust-RRT eventually finds a robust motion plan that is feasible under all possible uncertainty realizations assuming such a plan exists. Our analysis applies even to unstable systems that admit only short-horizon feasible plans; this is because we explicitly consider the time evolution of reachable sets along control trajectories. Thanks to the explicit consideration of time dependency in our analysis, PC applies to unstabilizable systems. To the best of our knowledge, this is the most general PC proof for robust sampling-based motion planning, in terms of the types of uncertainties and dynamical systems it can handle. Considering that an exact computation of reachable sets can be computationally expensive for some dynamical systems, we incorporate sampling-based reachability analysis into Robust-RRT and demonstrate our robust planner on nonlinear, underactuated, and hybrid systems.

Multi-Agent Terraforming: Efficient Multi-Agent Path Finding via Environment Manipulation

Multi-agent pathfinding (MAPF) is concerned with planning collision-free paths for a team of agents from their start to goal locations in an environment cluttered with obstacles. Typical approaches for MAPF consider the locations of obstacles as being fixed, which limits their effectiveness in automated warehouses, where obstacles (representing pods or shelves) can be moved out of the way by agents (representing robots) to relieve bottlenecks and introduce shorter routes. In this work we initiate the study of MAPF with movable obstacles. In particular, we introduce a new extension of MAPF, which we call Terraforming MAPF (tMAPF), where some agents are responsible for moving obstacles to clear the way for other agents. Solving tMAPF is extremely challenging as it requires reasoning not only about collisions between agents, but also where and when obstacles should be moved. We present extensions of two state-of-the-art algorithms, CBS and PBS, in order to tackle tMAPF, and demonstrate that they can consistently outperform the best solution possible under a static-obstacle setting.

Leveraging Experience in Lifelong Multi-Agent Pathfinding

In Lifelong Multi-Agent Path Finding (L-MAPF) a team of agents performs a stream of tasks consisting of multiple locations to be visited by the agents on a shared graph while avoiding collisions with one another. L-MAPF is typically tackled by partitioning it into multiple consecutive, and hence similar, "one-shot" MAPF queries with a single task assigned to each agent, as in the Rolling-Horizon Collision Resolution (RHCR) algorithm. Thus, a solution to one query informs the next query, which leads to similarity with respect to the agents' start and goal positions, and how collisions need to be resolved from one query to the next. Thus, experience from solving one MAPF query can potentially be used to speedup solving the next one. Despite this intuition, current L-MAPF planners solve consecutive MAPF queries from scratch. In this paper, we introduce a new RHCR-inspired approach called exRHCR, which exploits experience in its constituent MAPF queries. In particular, exRHCR employs a new extension of Priority-Based Search (PBS), a state-of-the-art MAPF solver. Our extension, called exPBS, allows to warm-start the search with the priorities between agents used by PBS in the previous MAPF instances. We demonstrate empirically that exRHCR solves L-MAPF up to 25% faster than RHCR, and allows to increase throughput for given task streams by as much as 3%-16% by increasing the number of agents we can cope with for a given time budget.

Coordinated Multi-Agent Pathfinding for Drones and Trucks over Road Networks

We address the problem of routing a team of drones and trucks over large-scale urban road networks. To conserve their limited flight energy, drones can use trucks as temporary modes of transit en route to their own destinations. Such coordination can yield significant savings in total vehicle distance traveled, i.e., truck travel distance and drone flight distance, compared to operating drones and trucks independently. But it comes at the potentially prohibitive computational cost of deciding which trucks and drones should coordinate and when and where it is most beneficial to do so. We tackle this fundamental trade-off by decoupling our overall intractable problem into tractable sub-problems that we solve stage-wise. The first stage solves only for trucks, by computing paths that make them more likely to be useful transit options for drones. The second stage solves only for drones, by routing them over a composite of the road network and the transit network defined by truck paths from the first stage. We design a comprehensive algorithmic framework that frames each stage as a multi-agent path-finding problem and implement two distinct methods for solving them. We evaluate our approach on extensive simulations with up to $100$ agents on the real-world Manhattan road network containing nearly $4500$ vertices and $10000$ edges. Our framework saves on more than $50\%$ of vehicle distance traveled compared to independently solving for trucks and drones, and computes solutions for all settings within $5$ minutes on commodity hardware.

Resolution-Optimal Motion Planning for Steerable Needles

Medical steerable needles can follow 3D curvilinear trajectories inside body tissue, enabling them to move around critical anatomical structures and precisely reach clinically significant targets in a minimally invasive way. Automating needle steering, with motion planning as a key component, has the potential to maximize the accuracy, precision, speed, and safety of steerable needle procedures. In this paper, we introduce the first resolution-optimal motion planner for steerable needles that offers excellent practical performance in terms of runtime while simultaneously providing strong theoretical guarantees on completeness and the global optimality of the motion plan in finite time. Compared to state-of-the-art steerable needle motion planners, simulation experiments on realistic scenarios of lung biopsy demonstrate that our proposed planner is faster in generating higher-quality plans while incorporating clinically relevant cost functions. This indicates that the theoretical guarantees of the proposed planner have a practical impact on the motion plan quality, which is valuable for computing motion plans that minimize patient trauma.

Near-Optimal Multi-Robot Motion Planning with Finite Sampling

An underlying structure in several sampling-based methods for continuous multi-robot motion planning (MRMP) is the tensor roadmap (TR), which emerges from combining multiple PRM graphs constructed for the individual robots via a tensor product. We study the conditions under which the TR encodes a near-optimal solution for MRMP---satisfying these conditions implies near optimality for a variety of popular planners, including dRRT*, and the discrete methods M* and CBS when applied to the continuous domain. We develop the first finite-sample analysis of this kind, which specifies the number of samples, their deterministic distribution, and magnitude of the connection radii that should be used by each individual PRM graph, to guarantee near-optimality using the TR. This significantly improves upon a previous asymptotic analysis, wherein the number of samples tends to infinity, and supports guaranteed high-quality solutions in practice, within bounded running time. To achieve our new result, we first develop a sampling scheme, which we call the staggered grid, for finite-sample motion planning for individual robots, which requires significantly less samples than previous work. We then extend it to the much more involved MRMP setting which requires to account for interactions among multiple robots. Finally, we report on a few experiments that serve as a verification of our theoretical findings and raise interesting questions for further investigation.

Fast Near-Optimal Heterogeneous Task Allocation via Flow Decomposition

Multi-robot systems are uniquely well-suited to performing complex tasks such as patrolling and tracking, information gathering, and pick-up and delivery problems, offering significantly higher performance than single-robot systems. A fundamental building block in most multi-robot systems is task allocation: assigning robots to tasks (e.g., patrolling an area, or servicing a transportation request) as they appear based on the robots' states to maximize reward. In many practical situations, the allocation must account for heterogeneous capabilities (e.g., availability of appropriate sensors or actuators) to ensure the feasibility of execution, and to promote a higher reward, over a long time horizon. To this end, we present the FlowDec algorithm for efficient heterogeneous task-allocation achieving an approximation factor of at least 1/2 of the optimal reward. Our approach decomposes the heterogeneous problem into several homogeneous subproblems that can be solved efficiently using min-cost flow. Through simulation experiments, we show that our algorithm is faster by several orders of magnitude than a MILP approach.

Complexity of Planning

This is a chapter in the Encyclopedia of Robotics. It is devoted to the study of complexity of complete (or exact) algorithms for robot motion planning. The term ``complete'' indicates that an approach is guaranteed to find the correct solution (a motion path or trajectory in our setting), or to report that none exists otherwise (in case that for instance, no feasible path exists). Complexity theory is a fundamental tool in computer science for analyzing the performance of algorithms, in terms of the amount of resources they require. (While complexity can express different quantities such as space and communication effort, our focus in this chapter is on time complexity.) Moreover, complexity theory helps to identify ``hard'' problems which require excessive amount of computation time to solve. In the context of motion planning, complexity theory can come in handy in various ways, some of which are illustrated here.