Oren Salzman

Sidharth Talia, Oren Salzman, Siddhartha Srinivasa

We focus on the problem of efficient anytime kinodynamic planning for systems with complex dynamics in unstructured environments that make precomputing motion primitives infeasible. Directly applying A* to such problems is computationally infeasible due to the curse of dimensionality. Methods such as Hybrid A* addressed this burden by discretizing the state space, but in turn creating a coupling between tree discovery and the discretization resolution. The Incremental Generalized Hybrid A* (IGHA*) performs search over a hierarchy of resolutions in an anytime fashion to break this coupling, by freezing vertices to use in later search iterations rather than pruning them. However, the frozen vertices can hide solution-supporting vertices from the search at a particular iteration. While classical bidirectional search is motivated by the reduction of search depth, extending IGHA* into the bidirectional setting (termed Bi-IGHA*) obtains additional benefit by fundamentally mitigating the behaviour induced by frozen vertices hiding solutions. We show that Bi-IGHA* preserves IGHA*'s guarantees on monotonic cost improvement and termination. We empirically show that Bi-IGHA* substantially reduces expansions on R3, R4, and R6 planning problems, and achieves equivalent closed-loop performance with kinodynamic planning for high-speed off-road autonomy while requiring significantly fewer expansions. Website: https://personalrobotics.github.io/IGHAStar/biighastar.html

Doron Pinsky, Petr Váňa, Jan Faigl et al.

We consider the problem of finding collision-free paths for curvature-constrained systems in the presence of obstacles while minimizing execution time. Specifically, we focus on the setting where a planar system can travel at some range of speeds with unbounded acceleration. This setting can model many systems, such as fixed-wing drones. Unfortunately, planning for such systems might require evaluating many (local) time-optimal transitions connecting two close-by configurations, which is computationally expensive. Existing methods either pre-compute all such transitions in a preprocessing stage or use heuristics to speed up the search, thus foregoing any guarantees on solution quality. Our key insight is that computing all the time-optimal transitions is both~(i)~computationally expensive and~(ii)~unnecessary for many problem instances. We show that by finding bounded-suboptimal solutions (solutions whose cost is bounded by $1+\varepsilon$ times the cost of the optimal solution for any user-provided $\varepsilon$) and not time-optimal solutions, one can dramatically reduce the number of time-optimal transitions used. We demonstrate using empirical evaluation that our planning framework can reduce the runtime by several orders of magnitude compared to the state-of-the-art while still providing guarantees on the quality of the solution.

Adir Morgan, Kiril Solovey, Oren Salzman

Inspection planning is concerned with computing the shortest robot path to inspect a given set of points of interest (POIs) using the robot's sensors. This problem arises in a wide range of applications from manufacturing to medical robotics. To alleviate the problem's complexity, recent methods rely on sampling-based methods to obtain a more manageable (discrete) graph inspection planning (GIP) problem. Unfortunately, GIP still remains highly difficult to solve at scale as it requires simultaneously satisfying POI-coverage and path-connectivity constraints, giving rise to a challenging optimization problem, particularly at scales encountered in real-world scenarios. In this work, we present highly scalable Mixed Integer Linear Programming (MILP) solutions for GIP that significantly advance the state-of-the-art in both runtime and solution quality. Our key insight is a reformulation of the problem's core constraints as a network flow, which enables effective MILP models and a specialized Branch-and-Cut solver that exploits the combinatorial structure of flows. We evaluate our approach on medical and infrastructure benchmarks alongside large-scale synthetic instances. Across all scenarios, our method produces substantially tighter lower bounds than existing formulations, reducing optimality gaps by 30-50% on large instances. Furthermore, our solver demonstrates unprecedented scalability: it provides non-trivial solutions for problems with up to 15,000 vertices and thousands of POIs, where prior state-of-the-art methods typically exhaust memory or fail to provide any meaningful optimality guarantees.

Hadar Peer, Carlos Hernandez, Sven Koenig et al.

Empirical evaluation in multi-objective search (MOS) has historically suffered from fragmentation, relying on heterogeneous problem instances with incompatible objective definitions that make cross-study comparisons difficult. This standardization gap is further exacerbated by the realization that DIMACS road networks, a historical default benchmark for the field, exhibit highly correlated objectives that fail to capture diverse Pareto-front structures. To address this, we introduce the first comprehensive, standardized benchmark suite for exact and approximate MOS. Our suite spans four structurally diverse domains: real-world road networks, structured synthetic graphs, game-based grid environments, and high-dimensional robotic motion-planning roadmaps. By providing fixed graph instances, standardized start-goal queries, and both exact and approximate reference Pareto-optimal solution sets, this suite captures a full spectrum of objective interactions: from strongly correlated to strictly independent. Ultimately, this benchmark provides a common foundation to ensure future MOS evaluations are robust, reproducible, and structurally comprehensive.

David Vainshtein, Kiril Solovey, Oren Salzman

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.

Dan Elbaz, Gal Novik, Oren Salzman

Offline reinforcement-learning (RL) algorithms learn to make decisions using a given, fixed training dataset without online data collection. This problem setting is captivating because it holds the promise of utilizing previously collected datasets without any costly or risky interaction with the environment. However, this promise also bears the drawback of this setting as the restricted dataset induces uncertainty because the agent can encounter unfamiliar sequences of states and actions that the training data did not cover. To mitigate the destructive uncertainty effects, we need to balance the aspiration to take reward-maximizing actions with the incurred risk due to incorrect ones. In financial economics, modern portfolio theory (MPT) is a method that risk-averse investors can use to construct diversified portfolios that maximize their returns without unacceptable levels of risk. We propose integrating MPT into the agent's decision-making process, presenting a new simple-yet-highly-effective risk-aware planning algorithm for offline RL. Our algorithm allows us to systematically account for the \emph{estimated quality} of specific actions and their \emph{estimated risk} due to the uncertainty. We show that our approach can be coupled with the Transformer architecture to yield a state-of-the-art planner, which maximizes the return for offline RL tasks. Moreover, our algorithm reduces the variance of the results significantly compared to conventional Transformer decoding, which results in a much more stable algorithm -- a property that is essential for the offline RL setting, where real-world exploration and failures can be costly or dangerous.

Hadar Peer, Eyal Weiss, Ron Alterovitz et al.

Multi-objective search (MOS) has become essential in robotics, as real-world robotic systems need to simultaneously balance multiple, often conflicting objectives. Recent works explore complex interactions between objectives, leading to problem formulations that do not allow the usage of out-of-the-box state-of-the-art MOS algorithms. In this paper, we suggest a generalized problem formulation that optimizes solution objectives via aggregation functions of hidden (search) objectives. We show that our formulation supports the application of standard MOS algorithms, necessitating only to properly extend several core operations to reflect the specific aggregation functions employed. We demonstrate our approach in several diverse robotics planning problems, spanning motion-planning for navigation, manipulation and planning fr medical systems under obstacle uncertainty as well as inspection planning, and route planning with different road types. We solve the problems using state-of-the-art MOS algorithms after properly extending their core operations, and provide empirical evidence that they outperform by orders of magnitude the vanilla versions of the algorithms applied to the same problems but without objective aggregation.

Yaron Halle, Ariel Felner, Sven Koenig et al.

The bi-objective shortest-path (BOSP) problem seeks to find paths between start and target vertices of a graph while optimizing two conflicting objective functions. We consider the BOSP problem in the presence of correlated objectives. Such correlations often occur in real-world settings such as road networks, where optimizing two positively correlated objectives, such as travel time and fuel consumption, is common. BOSP is generally computationally challenging as the size of the search space is exponential in the number of objective functions and the graph size. Bounded sub-optimal BOSP solvers such as A*pex alleviate this complexity by approximating the Pareto-optimal solution set rather than computing it exactly (given a user-provided approximation factor). As the correlation between objective functions increases, smaller approximation factors are sufficient for collapsing the entire Pareto-optimal set into a single solution. We leverage this insight to propose an efficient algorithm that reduces the search effort in the presence of correlated objectives. Our approach for computing approximations of the entire Pareto-optimal set is inspired by graph-clustering algorithms. It uses a preprocessing phase to identify correlated clusters within a graph and to generate a new graph representation. This allows a natural generalization of A*pex to run up to five times faster on DIMACS dataset instances, a standard benchmark in the field. To the best of our knowledge, this is the first algorithm proposed that efficiently and effectively exploits correlations in the context of bi-objective search while providing theoretical guarantees on solution quality.

Oren Salzman, Carlos Hernández Ulloa, Ariel Felner et al.

Multi-objective search (MOS) has emerged as a unifying framework for planning and decision-making problems where multiple, often conflicting, criteria must be balanced. While the problem has been studied for decades, recent years have seen renewed interest in the topic across AI applications such as robotics, transportation, and operations research, reflecting the reality that real-world systems rarely optimize a single measure. This paper surveys developments in MOS while highlighting cross-disciplinary opportunities, and outlines open challenges that define the emerging frontier of MOS

Dan Elbaz, Oren Salzman

Offline Reinforcement Learning (RL) algorithms learn a policy using a fixed training dataset, which is then deployed online to interact with the environment and make decisions. Transformers, a standard choice for modeling time-series data, are gaining popularity in offline RL. In this context, Beam Search (BS), an approximate inference algorithm, is the go-to decoding method. Offline RL eliminates the need for costly or risky online data collection. However, the restricted dataset induces uncertainty as the agent may encounter unfamiliar sequences of states and actions during execution that were not covered in the training data. In this context, BS lacks two important properties essential for offline RL: It does not account for the aforementioned uncertainty, and its greedy left-right search approach often results in sequences with minimal variations, failing to explore potentially better alternatives. To address these limitations, we propose Portfolio Beam Search (PBS), a simple-yet-effective alternative to BS that balances exploration and exploitation within a Transformer model during decoding. We draw inspiration from financial economics and apply these principles to develop an uncertainty-aware diversification mechanism, which we integrate into a sequential decoding algorithm at inference time. We empirically demonstrate the effectiveness of PBS on the D4RL locomotion benchmark, where it achieves higher returns and significantly reduces outcome variability.

David Vainshtein, Yaakov Sherma, Kiril Solovey et al.

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.

Dean Zadok, Oren Salzman, Alon Wolf et al.

A central challenge in building robotic prostheses is the creation of a sensor-based system able to read physiological signals from the lower limb and instruct a robotic hand to perform various tasks. Existing systems typically perform discrete gestures such as pointing or grasping, by employing electromyography (EMG) or ultrasound (US) technologies to analyze muscle states. While estimating finger gestures has been done in the past by detecting prominent gestures, we are interested in detection, or inference, done in the context of fine motions that evolve over time. Examples include motions occurring when performing fine and dexterous tasks such as keyboard typing or piano playing. We consider this task as an important step towards higher adoption rates of robotic prostheses among arm amputees, as it has the potential to dramatically increase functionality in performing daily tasks. To this end, we present an end-to-end robotic system, which can successfully infer fine finger motions. This is achieved by modeling the hand as a robotic manipulator and using it as an intermediate representation to encode muscles' dynamics from a sequence of US images. We evaluated our method by collecting data from a group of subjects and demonstrating how it can be used to replay music played or text typed. To the best of our knowledge, this is the first study demonstrating these downstream tasks within an end-to-end system.

Nitzan Madar, Kiril Solovey, Oren Salzman

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, as in the Rolling-Horizon Collision Resolution (RHCR) algorithm. Therefore, 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 an extension of Priority-Based Search (PBS), a state-of-the-art MAPF solver. The extension, which we call 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 instances up to 39% faster than RHCR, and has the potential to increase system throughput for given task streams by increasing the number of agents a planner can cope with for a given time budget.

Mengyu Fu, Kiril Solovey, Oren Salzman et al.

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.

Mengyu Fu, Oren Salzman, Ron Alterovitz

Medical steerable needles can move along 3D curvilinear trajectories to avoid anatomical obstacles and reach clinically significant targets inside the human body. Automating steerable needle procedures can enable physicians and patients to harness the full potential of steerable needles by maximally leveraging their steerability to safely and accurately reach targets for medical procedures such as biopsies and localized therapy delivery for cancer. For the automation of medical procedures to be clinically accepted, it is critical from a patient care, safety, and regulatory perspective to certify the correctness and effectiveness of the motion planning algorithms involved in procedure automation. In this paper, we take an important step toward creating a certifiable motion planner for steerable needles. We introduce the first motion planner for steerable needles that offers a guarantee, under clinically appropriate assumptions, that it will, in finite time, compute an exact, obstacle-avoiding motion plan to a specified target, or notify the user that no such plan exists. We present an efficient, resolution-complete motion planner for steerable needles based on a novel adaptation of multi-resolution planning. Compared to state-of-the-art steerable needle motion planners (none of which provide any completeness guarantees), we demonstrate that our new resolution-complete motion planner computes plans faster and with a higher success rate.

Nir Greshler, Ofir Gordon, Oren Salzman et al.

We introduce the Cooperative Multi-Agent Path Finding (Co-MAPF) problem, an extension to the classical MAPF problem, where cooperative behavior is incorporated. In this setting, a group of autonomous agents operate in a shared environment and have to complete cooperative tasks while avoiding collisions with the other agents in the group. This extension naturally models many real-world applications, where groups of agents are required to collaborate in order to complete a given task. To this end, we formalize the Co-MAPF problem and introduce Cooperative Conflict-Based Search (Co-CBS), a CBS-based algorithm for solving the problem optimally for a wide set of Co-MAPF problems. Co-CBS uses a cooperation-planning module integrated into CBS such that cooperation planning is decoupled from path planning. Finally, we present empirical results on several MAPF benchmarks demonstrating our algorithm's properties.

Ofir Gordon, Yuval Filmus, Oren Salzman

The problem of Multi-Agent Path Finding (MAPF) calls for finding a set of conflict-free paths for a fleet of agents operating in a given environment. Arguably, the state-of-the-art approach to computing optimal solutions is Conflict-Based Search (CBS). In this work we revisit the complexity analysis of CBS to provide tighter bounds on the algorithm's run-time in the worst-case. Our analysis paves the way to better pinpoint the parameters that govern (in the worst case) the algorithm's computational complexity. Our analysis is based on two complementary approaches: In the first approach we bound the run-time using the size of a Multi-valued Decision Diagram (MDD) -- a layered graph which compactly contains all possible single-agent paths between two given vertices for a specific path length. In the second approach we express the running time by a novel recurrence relation which bounds the algorithm's complexity. We use generating functions-based analysis in order to tightly bound the recurrence. Using these technique we provide several new upper-bounds on CBS's complexity. The results allow us to improve the existing bound on the running time of CBS for many cases. For example, on a set of common benchmarks we improve the upper-bound by a factor of at least $2^{10^{7}}$.

Mengyu Fu, Oren Salzman, Ron Alterovitz

The inspection-planning problem calls for computing motions for a robot that allow it to inspect a set of points of interest (POIs) while considering plan quality (e.g., plan length). This problem has applications across many domains where robots can help with inspection, including infrastructure maintenance, construction, and surgery. Incremental Random Inspection-roadmap Search (IRIS) is an asymptotically-optimal inspection planner that was shown to compute higher-quality inspection plans orders of magnitudes faster than the prior state-of-the-art method. In this paper, we significantly accelerate the performance of IRIS to broaden its applicability to more challenging real-world applications. A key computational challenge that IRIS faces is effectively searching roadmaps for inspection plans -- a procedure that dominates its running time. In this work, we show how to incorporate lazy edge-evaluation techniques into \iris's search algorithm and how to reuse search efforts when a roadmap undergoes local changes. These enhancements, which do not compromise IRIS's asymptotic optimality, enable us to compute inspection plans much faster than the original IRIS. We apply IRIS with the enhancements to simulated bridge inspection and surgical inspection tasks and show that our new algorithm for some scenarios can compute similar-quality inspection plans 570x faster than prior work.

Fahad Islam, Oren Salzman, Aditya Agarwal et al.

In warehouse and manufacturing environments, manipulation platforms are frequently deployed at conveyor belts to perform pick and place tasks. Because objects on the conveyor belts are moving, robots have limited time to pick them up. This brings the requirement for fast and reliable motion planners that could provide provable real-time planning guarantees, which the existing algorithms do not provide. Besides the planning efficiency, the success of manipulation tasks relies heavily on the accuracy of the perception system which is often noisy, especially if the target objects are perceived from a distance. For fast moving conveyor belts, the robot cannot wait for a perfect estimate before it starts executing its motion. In order to be able to reach the object in time, it must start moving early on (relying on the initial noisy estimates) and adjust its motion on-the-fly in response to the pose updates from perception. We propose a planning framework that meets these requirements by providing provable constant-time planning and replanning guarantees. To this end, we first introduce and formalize a new class of algorithms called Constant-Time Motion Planning algorithms (CTMP) that guarantee to plan in constant time and within a user-defined time bound. We then present our planning framework for grasping objects off a conveyor belt as an instance of the CTMP class of algorithms.

Michael Bentley, Caleb Rucker, Chakravarthy Reddy et al.

Steerable needles are capable of accurately targeting difficult-to-reach clinical sites in the body. By bending around sensitive anatomical structures, steerable needles have the potential to reduce the invasiveness of many medical procedures. However, inserting these needles with curved trajectories increases the risk of tissue damage due to perpendicular forces exerted on the surrounding tissue by the needle's shaft, potentially resulting in lateral shearing through tissue. Such forces can cause significant damage to surrounding tissue, negatively affecting patient outcomes. In this work, we derive a tissue and needle force model based on a Cosserat string formulation, which describes the normal forces and frictional forces along the shaft as a function of the planned needle path, friction model and parameters, and tip piercing force. We propose this new force model and associated cost function as a safer and more clinically relevant metric than those currently used in motion planning for steerable needles. We fit and validate our model through physical needle robot experiments in a gel phantom. We use this force model to define a bottleneck cost function for motion planning and evaluate it against the commonly used path-length cost function in hundreds of randomly generated 3-D environments. Plans generated with our force-based cost show a 62% reduction in the peak modeled tissue force with only a 0.07% increase in length on average compared to using the path-length cost in planning. Additionally, we demonstrate the ability to plan motions with our force-based cost function in a lung tumor biopsy scenario from a segmented computed tomography (CT) scan. By planning motions for the needle that aim to minimize the modeled needle-to-tissue force explicitly, our method plans needle paths that may reduce the risk of significant tissue damage while still reaching desired targets in the body.

Fahad Islam, Oren Salzman, Aditya Agarwal et al.

In warehouse and manufacturing environments, manipulation platforms are frequently deployed at conveyor belts to perform pick and place tasks. Because objects on the conveyor belts are moving, robots have limited time to pick them up. This brings the requirement for fast and reliable motion planners that could provide provable real-time planning guarantees, which the existing algorithms do not provide. Besides the planning efficiency, the success of manipulation tasks relies heavily on the accuracy of the perception system which is often noisy, especially if the target objects are perceived from a distance. For fast moving conveyor belts, the robot cannot wait for a perfect estimate before it starts executing its motion. In order to be able to reach the object in time it must start moving early on (relying on the initial noisy estimates) and adjust its motion on-the-fly in response to the pose updates from perception. We propose an approach that meets these requirements by providing provable constant-time planning and replanning guarantees. We present it, give its analytical properties and show experimental analysis in simulation and on a real robot.

Abhijeet Tallavajhula, Adrian Schoisengeier, Sung-Kyun Kim et al.

Simulators are an important tool in robotics that is used to develop robot software and generate synthetic data for machine learning algorithms. Faster simulation can result in better software validation and larger amounts of data. Previous efforts for speeding up simulators have been performed at the level of simulator building blocks, and robot systems. Our key insight, motivating this work, is that further speedups can be obtained at the level of the robot task. Building on the observation that not all parts of a scene need to be simulated in high fidelity at all times, our approach is to toggle between high- and low-fidelity states for scene objects in a task-informed manner. Our contribution is a framework for speeding up robot simulation by exploiting task knowledge. The framework is agnostic to the underlying simulator, and preserves simulation fidelity. As a case study, we consider a complex material-handling task. For the associated simulation, which contains many of the characteristics that make robot simulation slow, we achieve a speedup that can be up to three times faster than high fidelity without compromising on the quality of the results. We also demonstrate that faster simulation allows us to train better policies for performing the task at hand in a short period of time. A video summarizing our contributions can be found at https://youtu.be/PEzypDyqc3o .

Fahad Islam, Anirudh Vemula, Sung-Kyun Kim et al.

We consider the task of autonomously unloading boxes from trucks using an industrial manipulator robot. There are multiple challenges that arise: (1) real-time motion planning for a complex robotic system carrying two articulated mechanisms, an arm and a scooper, (2) decision-making in terms of what action to execute next given imperfect information about boxes such as their masses, (3) accounting for the sequential nature of the problem where current actions affect future state of the boxes, and (4) real-time execution that interleaves high-level decision-making with lower level motion planning. In this work, we propose a planning, learning, and reasoning framework to tackle these challenges, and describe its components including motion planning, belief space planning for offline learning, online decision-making based on offline learning, and an execution module to combine decision-making with motion planning. We analyze the performance of the framework on real-world scenarios. In particular, motion planning and execution modules are evaluated in simulation and on a real robot, while offline learning and online decision-making are evaluated in simulated real-world scenarios.

Tushar Kusnur, Shohin Mukherjee, Dhruv Mauria Saxena et al.

Planning for multi-robot coverage seeks to determine collision-free paths for a fleet of robots, enabling them to collectively observe points of interest in an environment. Persistent coverage is a variant of traditional coverage where coverage-levels in the environment decay over time. Thus, robots have to continuously revisit parts of the environment to maintain a desired coverage-level. Facilitating this in the real world demands we tackle numerous subproblems. While there exist standard solutions to these subproblems, there is no complete framework that addresses all of their individual challenges as a whole in a practical setting. We adapt and combine these solutions to present a planning framework for persistent coverage with multiple unmanned aerial vehicles (UAVs). Specifically, we run a continuous loop of goal assignment and globally deconflicting, kinodynamic path planning for multiple UAVs. We evaluate our framework in simulation as well as the real world. In particular, we demonstrate that (i) our framework exhibits graceful coverage given sufficient resources, we maintain persistent coverage; if resources are insufficient (e.g., having too few UAVs for a given size of the enviornment), coverage-levels decay slowly and (ii) planning with global deconfliction in our framework incurs a negligibly higher price compared to other weaker, more local collision-checking schemes. (Video: https://youtu.be/aqDs6Wymp5Q)

Mengyu Fu, Alan Kuntz, Oren Salzman et al.

Inspection planning, the task of planning motions that allow a robot to inspect a set of points of interest, has applications in domains such as industrial, field, and medical robotics. Inspection planning can be computationally challenging, as the search space over motion plans that inspect the points of interest grows exponentially with the number of inspected points. We propose a novel method, Incremental Random Inspection-roadmap Search (IRIS), that computes inspection plans whose length and set of inspected points asymptotically converge to those of an optimal inspection plan. IRIS incrementally densifies a motion planning roadmap using sampling-based algorithms, and performs efficient near-optimal graph search over the resulting roadmap as it is generated. We demonstrate IRIS's efficacy on a simulated planar 5DOF manipulator inspection task and on a medical endoscopic inspection task for a continuum parallel surgical robot in anatomy segmented from patient CT data. We show that IRIS computes higher-quality inspection paths orders of magnitudes faster than a prior state-of-the-art method.

Aditya Mandalika, Sanjiban Choudhury, Oren Salzman et al.

Lazy search algorithms can efficiently solve problems where edge evaluation is the bottleneck in computation, as is the case for robotic motion planning. The optimal algorithm in this class, LazySP, lazily restricts edge evaluation to only the shortest path. Doing so comes at the expense of search effort, i.e., LazySP must recompute the search tree every time an edge is found to be invalid. This becomes prohibitively expensive when dealing with large graphs or highly cluttered environments. Our key insight is the need to balance both edge evaluation and search effort to minimize the total planning time. Our contribution is two-fold. First, we propose a framework, Generalized Lazy Search (GLS), that seamlessly toggles between search and evaluation to prevent wasted efforts. We show that for a choice of toggle, GLS is provably more efficient than LazySP. Second, we leverage prior experience of edge probabilities to derive GLS policies that minimize expected planning time. We show that GLS equipped with such priors significantly outperforms competitive baselines for many simulated environments in R2, SE(2) and 7-DoF manipulation.

Fahad Islam, Oren Salzman, Maxim Likhachev

In many robotic manipulation scenarios, robots often have to perform highly-repetitive tasks in structured environments e.g. sorting mail in a mailroom or pick and place objects on a conveyor belt. In this work we are interested in settings where the tasks are similar, yet not identical (e.g., due to uncertain orientation of objects) and motion planning needs to be extremely fast. Preprocessing-based approaches prove to be very beneficial in these settings. They analyze the configuration-space offline to generate some auxiliary information which can then be used in the query phase to speedup planning times. Typically, the tighter the requirement is on query times the larger the memory footprint will be. In particular, for high-dimensional spaces, providing real-time planning capabilities is extremely challenging. While there are planners that guarantee real-time performance by limiting the planning horizon, we are not aware of general-purpose planners capable of doing it for indefinite horizon (i.e., planning to the goal). To this end, we propose a preprocessing-based method that provides provable bounds on the query time while incurring only a small amount of memory overhead in the query phase. We evaluate our method on a 7-DOF robot arm and show a speedup of over tenfold in query time when compared to the PRM algorithm.

Aditya Mandalika, Oren Salzman, Siddhartha Srinivasa

Motion-planning problems, such as manipulation in cluttered environments, often require a collision-free shortest path to be computed quickly given a roadmap graph. Typically, the computational cost of evaluating whether an edge of the roadmap graph is collision-free dominates the running time of search algorithms. Algorithms such as Lazy Weighted A* (LWA*) and LazySP have been proposed to reduce the number of edge evaluations by employing a lazy lookahead (one-step lookahead and infinite-step lookahead, respectively). However, this comes at the expense of additional graph operations: the larger the lookahead, the more the graph operations that are typically required. We propose Lazy Receding-Horizon A* (LRA*) to minimize the total planning time by balancing edge evaluations and graph operations. Endowed with a lazy lookahead, LRA* represents a family of lazy shortest-path graph-search algorithms that generalizes LWA* and LazySP. We analyze the theoretic properties of LRA* and demonstrate empirically that, in many cases, to minimize the total planning time, the algorithm requires an intermediate lazy lookahead. Namely, using an intermediate lazy lookahead, our algorithm outperforms both LWA* and LazySP. These experiments span simulated random worlds in $\mathbb{R}^2$ and $\mathbb{R}^4$, and manipulation problems using a 7-DOF manipulator.

Vinitha Ranganeni, Sahit Chintalapudi, Oren Salzman et al.

Planning the motion for humanoid robots is a computationally-complex task due to the high dimensionality of the system. Thus, a common approach is to first plan in the low-dimensional space induced by the robot's feet---a task referred to as footstep planning. This low-dimensional plan is then used to guide the full motion of the robot. One approach that has proven successful in footstep planning is using search-based planners such as A* and its many variants. To do so, these search-based planners have to be endowed with effective heuristics to efficiently guide them through the search space. However, designing effective heuristics is a time-consuming task that requires the user to have good domain knowledge. Thus, our goal is to be able to effectively plan the footstep motions taken by a humanoid robot while obviating the burden on the user to carefully design local-minima free heuristics. To this end, we propose to use user-defined homotopy classes in the workspace that are intuitive to define. These homotopy classes are used to automatically generate heuristic functions that efficiently guide the footstep planner. Additionally, we present an extension to homotopy classes such that they are applicable to complex multi-level environments. We compare our approach for footstep planning with a standard approach that uses a heuristic common to footstep planning. In simple scenarios, the performance of both algorithms is comparable. However, in more complex scenarios our approach allows for a speedup in planning of several orders of magnitude when compared to the standard approach.

Shushman Choudhury, Oren Salzman, Sanjiban Choudhury et al.

We propose an algorithmic framework for efficient anytime motion planning on large dense geometric roadmaps, in domains where collision checks and therefore edge evaluations are computationally expensive. A large dense roadmap (graph) can typically ensure the existence of high quality solutions for most motion-planning problems, but the size of the roadmap, particularly in high-dimensional spaces, makes existing search-based planning algorithms computationally expensive. We deal with the challenges of expensive search and collision checking in two ways. First, we frame the problem of anytime motion planning on roadmaps as searching for the shortest path over a sequence of subgraphs of the entire roadmap graph, generated by some densification strategy. This lets us achieve bounded sub-optimality with bounded worst-case planning effort. Second, for searching each subgraph, we develop an anytime planning algorithm which uses a belief model to compute the collision probability of unknown configurations and searches for paths that are Pareto-optimal in path length and collision probability. This algorithm is efficient with respect to collision checks as it searches for successively shorter paths. We theoretically analyze both our ideas and evaluate them individually on high-dimensional motion-planning problems. Finally, we apply both of these ideas together in our algorithmic framework for anytime motion planning, and show that it outperforms BIT* on high-dimensional hypercube problems.

Rachel Holladay, Oren Salzman, Siddhartha Srinivasa

We present an anytime algorithm that generates a collision-free configuration-space path that closely follows a desired path in task space, according to the discrete Frechet distance. By leveraging tools from computational geometry, we approximate the search space using a cross-product graph. We use a variant of Dijkstra's graph-search algorithm to efficiently search for and iteratively improve the solution. We compare multiple proposed densification strategies and empirically show that our algorithm outperforms a set of state-of-the-art planners on a range of manipulation problems. Finally, we offer a proof sketch of the asymptotic optimality of our algorithm.

Daqing Yi, Rohan Thakker, Cole Gulino et al.

Asymptotically-optimal motion planners such as RRT* have been shown to incrementally approximate the shortest path between start and goal states. Once an initial solution is found, their performance can be dramatically improved by restricting subsequent samples to regions of the state space that can potentially improve the current solution. When the motion planning problem lies in a Euclidean space, this region $X_{inf}$, called the informed set, can be sampled directly. However, when planning with differential constraints in non-Euclidean state spaces, no analytic solutions exists to sampling $X_{inf}$ directly. State-of-the-art approaches to sampling $X_{inf}$ in such domains such as Hierarchical Rejection Sampling (HRS) may still be slow in high-dimensional state space. This may cause the planning algorithm to spend most of its time trying to produces samples in $X_{inf}$ rather than explore it. In this paper, we suggest an alternative approach to produce samples in the informed set $X_{inf}$ for a wide range of settings. Our main insight is to recast this problem as one of sampling uniformly within the sub-level-set of an implicit non-convex function. This recasting enables us to apply Monte Carlo sampling methods, used very effectively in the Machine Learning and Optimization communities, to solve our problem. We show for a wide range of scenarios that using our sampler can accelerate the convergence rate to high-quality solutions in high-dimensional problems.

Nika Haghtalab, Simon Mackenzie, Ariel D. Procaccia et al.

The Lazy Shortest Path (LazySP) class consists of motion-planning algorithms that only evaluate edges along shortest paths between the source and target. These algorithms were designed to minimize the number of edge evaluations in settings where edge evaluation dominates the running time of the algorithm; but how close to optimal are LazySP algorithms in terms of this objective? Our main result is an analytical upper bound, in a probabilistic model, on the number of edge evaluations required by LazySP algorithms; a matching lower bound shows that these algorithms are asymptotically optimal in the worst case.

Fahad Islam, Oren Salzman, Maxim Likhachev

We consider the problem of planning a collision-free path for a high-dimensional robot. Specifically, we suggest a planning framework where a motion-planning algorithm can obtain guidance from a user. In contrast to existing approaches that try to speed up planning by incorporating experiences or demonstrations ahead of planning, we suggest to seek user guidance only when the planner identifies that it ceases to make significant progress towards the goal. Guidance is provided in the form of an intermediate configuration $\hat{q}$, which is used to bias the planner to go through $\hat{q}$. We demonstrate our approach for the case where the planning algorithm is Multi-Heuristic A* (MHA*) and the robot is a 34-DOF humanoid. We show that our approach allows to compute highly-constrained paths with little domain knowledge. Without our approach, solving such problems requires carefully-crafting domain-dependent heuristics.

Pankaj K. Agarwal, Kyle Fox, Oren Salzman

We study a path-planning problem amid a set $\mathcal{O}$ of obstacles in $\mathbb{R}^2$, in which we wish to compute a short path between two points while also maintaining a high clearance from $\mathcal{O}$; the clearance of a point is its distance from a nearest obstacle in $\mathcal{O}$. Specifically, the problem asks for a path minimizing the reciprocal of the clearance integrated over the length of the path. We present the first polynomial-time approximation scheme for this problem. Let $n$ be the total number of obstacle vertices and let $\varepsilon \in (0,1]$. Our algorithm computes in time $O(\frac{n^2}{\varepsilon ^2} \log \frac{n}{\varepsilon})$ a path of total cost at most $(1+\varepsilon)$ times the cost of the optimal path.

Aviel Atias, Kiril Solovey, Oren Salzman et al.

We study the effectiveness of metrics for Multi-Robot Motion-Planning (MRMP) when using RRT-style sampling-based planners. These metrics play the crucial role of determining the nearest neighbors of configurations and in that they regulate the connectivity of the underlying roadmaps produced by the planners and other properties like the quality of solution paths. After screening over a dozen different metrics we focus on the five most promising ones- two more traditional metrics, and three novel ones which we propose here, adapted from the domain of shape-matching. In addition to the novel multi-robot metrics, a central contribution of this work are tools to analyze and predict the effectiveness of metrics in the MRMP context. We identify a suite of possible substructures in the configuration space, for which it is fairly easy (i) to define a so-called natural distance which allows us to predict the performance of a metric. This is done by comparing the distribution of its values for sampled pairs of configurations to the distribution induced by the natural distance; (ii) to define equivalence classes of configurations and test how well a metric covers the different classes. We provide experiments that attest to the ability of our tools to predict the effectiveness of metrics: those metrics that qualify in the analysis yield higher success rate of the planner with fewer vertices in the roadmap. We also show how combining several metrics together leads to better results (success rate and size of roadmap) than using a single metric.

Oren Salzman, Brian Hou, Siddhartha Srinivasa

We consider the motion-planning problem of planning a collision-free path of a robot in the presence of risk zones. The robot is allowed to travel in these zones but is penalized in a super-linear fashion for consecutive accumulative time spent there. We suggest a natural cost function that balances path length and risk-exposure time. Specifically, we consider the discrete setting where we are given a graph, or a roadmap, and we wish to compute the minimal-cost path under this cost function. Interestingly, paths defined using our cost function do not have an optimal substructure. Namely, subpaths of an optimal path are not necessarily optimal. Thus, the Bellman condition is not satisfied and standard graph-search algorithms such as Dijkstra cannot be used. We present a path-finding algorithm, which can be seen as a natural generalization of Dijkstra's algorithm. Our algorithm runs in $O\left((n_B\cdot n) \log( n_B\cdot n) + n_B\cdot m\right)$ time, where~$n$ and $m$ are the number of vertices and edges of the graph, respectively, and $n_B$ is the number of intersections between edges and the boundary of the risk zone. We present simulations on robotic platforms demonstrating both the natural paths produced by our cost function and the computational efficiency of our algorithm.

Shushman Choudhury, Oren Salzman, Sanjiban Choudhury et al.

We consider the problem of computing shortest paths in a dense motion-planning roadmap $\mathcal{G}$. We assume that~$n$, the number of vertices of $\mathcal{G}$, is very large. Thus, using any path-planning algorithm that directly searches $\mathcal{G}$, running in $O(V\textrm{log}V + E) \approx O(n^2)$ time, becomes unacceptably expensive. We are therefore interested in anytime search to obtain successively shorter feasible paths and converge to the shortest path in $\mathcal{G}$. Our key insight is to provide existing path-planning algorithms with a sequence of increasingly dense subgraphs of $\mathcal{G}$. We study the space of all ($r$-disk) subgraphs of $\mathcal{G}$. We then formulate and present two densification strategies for traversing this space which exhibit complementary properties with respect to problem difficulty. This inspires a third, hybrid strategy which has favourable properties regardless of problem difficulty. This general approach is then demonstrated and analyzed using the specific case where a low-dispersion deterministic sequence is used to generate the samples used for $\mathcal{G}$. Finally we empirically evaluate the performance of our strategies for random scenarios in $\mathbb{R}^{2}$ and $\mathbb{R}^{4}$ and on manipulation planning problems for a 7 DOF robot arm, and validate our analysis.

Michal Kleinbort, Oren Salzman, Dan Halperin

The complexity of nearest-neighbor search dominates the asymptotic running time of many sampling-based motion-planning algorithms. However, collision detection is often considered to be the computational bottleneck in practice. Examining various asymptotically optimal planning algorithms, we characterize settings, which we call NN-sensitive, in which the practical computational role of nearest-neighbor search is far from being negligible, i.e., the portion of running time taken up by nearest-neighbor search is comparable, or sometimes even greater than the portion of time taken up by collision detection. This reinforces and substantiates the claim that motion-planning algorithms could significantly benefit from efficient and possibly specifically-tailored nearest-neighbor data structures. The asymptotic (near) optimality of these algorithms relies on a prescribed connection radius, defining a ball around a configuration $q$, such that $q$ needs to be connected to all other configurations in that ball. To facilitate our study, we show how to adapt this radius to non-Euclidean spaces, which are prevalent in motion planning. This technical result is of independent interest, as it enables to compare the radial-connection approach with the common alternative, namely, connecting each configuration to its $k$ nearest neighbors ($k$-NN). Indeed, as we demonstrate, there are scenarios where using the radial connection scheme, a solution path of a specific cost is produced ten-fold (and more) faster than with $k$-NN.

Kiril Solovey, Oren Salzman, Dan Halperin

Roadmaps constructed by many sampling-based motion planners coincide, in the absence of obstacles, with standard models of random geometric graphs (RGGs). Those models have been studied for several decades and by now a rich body of literature exists analyzing various properties and types of RGGs. In their seminal work on optimal motion planning Karaman and Frazzoli (2011) conjectured that a sampling-based planner has a certain property if the underlying RGG has this property as well. In this paper we settle this conjecture and leverage it for the development of a general framework for the analysis of sampling-based planners. Our framework, which we call localization-tessellation, allows for easy transfer of arguments on RGGs from the free unit-hypercube to spaces punctured by obstacles, which are geometrically and topologically much more complex. We demonstrate its power by providing alternative and (arguably) simple proofs for probabilistic completeness and asymptotic (near-)optimality of probabilistic roadmaps (PRMs). Furthermore, we introduce several variants of PRMs, analyze them using our framework, and discuss the implications of the analysis.

Oren Salzman, Kiril Solovey, Dan Halperin

We study the problem of motion-planning for free-flying multi-link robots and develop a sampling-based algorithm that is specifically tailored for the task. Our work is based on the simple observation that the set of configurations for which the robot is self-collision free is independent of the obstacles or of the exact placement of the robot. This allows to eliminate the need to perform costly self-collision checks online when solving motion-planning problems, assuming some offline preprocessing. In particular, given a specific robot type our algorithm precomputes a tiling roadmap, which efficiently and implicitly encodes the self-collision free (sub-)space over the entire configuration space, where the latter can be infinite for that matter. To answer any query, in any given scenario, we traverse the tiling roadmap while only testing for collisions with obstacles. Our algorithm suggests more flexibility than the prevailing paradigm in which a precomputed roadmap depends both on the robot and on the scenario at hand. We show through various simulations the effectiveness of this approach on open and closed-chain multi-link robots, where in some settings our algorithm is more than fifty times faster than the state-of-the-art.

Michal Kleinbort, Oren Salzman, Dan Halperin

Sampling-based motion-planning algorithms typically rely on nearest-neighbor (NN) queries when constructing a roadmap. Recent results suggest that in various settings NN queries may be the computational bottleneck of such algorithms. Moreover, in several asymptotically-optimal algorithms these NN queries are of a specific form: Given a set of points and a radius r report all pairs of points whose distance is at most r. This calls for an application-specific NN data structure tailored to efficiently answering this type of queries. Randomly transformed grids (RTG) were recently proposed by Aiger et al. as a tool to answer such queries and have been shown to outperform common implementations of NN data structures in this context. In this work we employ RTG for sampling-based motion-planning algorithms and describe an efficient implementation of the approach. We show that for motion-planning, RTG allow for faster convergence to high-quality solutions when compared with existing NN data structures. Additionally, RTG enable significantly shorter construction times for batched-PRM variants; specifically, we demonstrate a speedup by a factor of two to three for some scenarios.

Oren Salzman, Dan Halperin

Many path-finding algorithms on graphs such as A* are sped up by using a heuristic function that gives lower bounds on the cost to reach the goal. Aiming to apply similar techniques to speed up sampling-based motion-planning algorithms, we use effective lower bounds on the cost between configurations to tightly estimate the cost-to-go. We then use these estimates in an anytime asymptotically-optimal algorithm which we call Motion Planning using Lower Bounds (MPLB). MPLB is based on the Fast Marching Trees (FMT*) algorithm recently presented by Janson and Pavone. An advantage of our approach is that in many cases (especially as the number of samples grows) the weight of collision detection in the computation is almost negligible with respect to nearest-neighbor calls. We prove that MPLB performs no more collision-detection calls than an anytime version of FMT*. Additionally, we demonstrate in simulations that for certain scenarios, the algorithmic tools presented here enable efficiently producing low-cost paths while spending only a small fraction of the running time on collision detection.

Oren Salzman, Dan Halperin

We present Lower Bound Tree-RRT (LBT-RRT), a single-query sampling-based algorithm that is asymptotically near-optimal. Namely, the solution extracted from LBT-RRT converges to a solution that is within an approximation factor of 1+epsilon of the optimal solution. Our algorithm allows for a continuous interpolation between the fast RRT algorithm and the asymptotically optimal RRT* and RRG algorithms. When the approximation factor is 1 (i.e., no approximation is allowed), LBT-RRT behaves like RRG. When the approximation factor is unbounded, LBT-RRT behaves like RRT. In between, LBT-RRT is shown to produce paths that have higher quality than RRT would produce and run faster than RRT* would run. This is done by maintaining a tree which is a sub-graph of the RRG roadmap and a second, auxiliary graph, which we call the lower-bound graph. The combination of the two roadmaps, which is faster to maintain than the roadmap maintained by RRT*, efficiently guarantees asymptotic near-optimality. We suggest to use LBT-RRT for high-quality, anytime motion planning. We demonstrate the performance of the algorithm for scenarios ranging from 3 to 12 degrees of freedom and show that even for small approximation factors, the algorithm produces high-quality solutions (comparable to RRG and RRT*) with little running-time overhead when compared to RRT.

Kiril Solovey, Oren Salzman, Dan Halperin

We present a sampling-based framework for multi-robot motion planning which combines an implicit representation of a roadmap with a novel approach for pathfinding in geometrically embedded graphs tailored for our setting. Our pathfinding algorithm, discrete-RRT (dRRT), is an adaptation of the celebrated RRT algorithm for the discrete case of a graph, and it enables a rapid exploration of the high-dimensional configuration space by carefully walking through an implicit representation of a tensor product of roadmaps for the individual robots. We demonstrate our approach experimentally on scenarios of up to 60 degrees of freedom where our algorithm is faster by a factor of at least ten when compared to existing algorithms that we are aware of.

Doron Shaharabani, Oren Salzman, Pankaj K. Agarwal et al.

We present Roadmap Sparsification by Edge Contraction (RSEC), a simple and effective algorithm for reducing the size of a motion-planning roadmap. The algorithm exhibits minimal effect on the quality of paths that can be extracted from the new roadmap. The primitive operation used by RSEC is edge contraction - the contraction of a roadmap edge to a single vertex and the connection of the new vertex to the neighboring vertices of the contracted edge. For certain scenarios, we compress more than 98% of the edges and vertices at the cost of degradation of average shortest path length by at most 2%.

Oren Salzman, Michael Hemmer, Dan Halperin

We extend our study of Motion Planning via Manifold Samples (MMS), a general algorithmic framework that combines geometric methods for the exact and complete analysis of low-dimensional configuration spaces with sampling-based approaches that are appropriate for higher dimensions. The framework explores the configuration space by taking samples that are entire low-dimensional manifolds of the configuration space capturing its connectivity much better than isolated point samples. The contributions of this paper are as follows: (i) We present a recursive application of MMS in a six-dimensional configuration space, enabling the coordination of two polygonal robots translating and rotating amidst polygonal obstacles. In the adduced experiments for the more demanding test cases MMS clearly outperforms PRM, with over 20-fold speedup in a coordination-tight setting. (ii) A probabilistic completeness proof for the most prevalent case, namely MMS with samples that are affine subspaces. (iii) A closer examination of the test cases reveals that MMS has, in comparison to standard sampling-based algorithms, a significant advantage in scenarios containing high-dimensional narrow passages. This provokes a novel characterization of narrow passages which attempts to capture their dimensionality, an attribute that had been (to a large extent) unattended in previous definitions.