We consider some classical optimization problems in path planning and network transport, and we introduce new auction-based algorithms for their optimal and suboptimal solution. The algorithms are based on mathematical ideas that are related to competitive bidding by persons for objects and the attendant market equilibrium, which underlie auction processes. However, the starting point of our algorithms is different, namely weighted and unweighted path construction in directed graphs, rather than assignment of persons to objects. The new algorithms have several potential advantages over existing methods: they are empirically faster in some important contexts, such as max-flow, they are well-suited for on-line replanning, and they can be adapted to distributed asynchronous operation. Moreover, they allow arbitrary initial prices, without complementary slackness restrictions, and thus are better-suited to take advantage of reinforcement learning methods that use off-line training with data, as well as on-line training during real-time operation. The new algorithms may also find use in reinforcement learning contexts involving approximation, such as multistep lookahead and tree search schemes, and/or rollout algorithms.

We present a centralized algorithm for labeled, disk-shaped Multi-Robot Path Planning (MPP) in a continuous planar workspace with polygonal boundaries. Our method automatically transform the continuous problem into a discrete, graph-based variant termed the pebble motion problem, which can be solved efficiently. To construct the underlying pebble graph, we identify inscribed circles in the workspace via a medial axis transform and organize robots into layers within each inscribed circle. We show that our layered pebble-graph enables collision-free motions, allowing all graph-restricted MPP instances to be feasible. MPP instances with continuous start and goal positions can then be solved via local navigations that route robots from and to graph vertices. We tested our method on several environments with high robot-packing densities (up to $61.6\%$ of the workspace). For environments with narrow passages, such density violates the well-separated assumptions made by state-of-the-art MPP planners, while our method achieves an average success rate of $83\%$.

This paper introduces a novel motion planner, incrementally stochastic and accelerated gradient information mixed optimization (iSAGO), for robotic manipulators in a narrow workspace. Primarily, we propose the overall scheme of iSAGO informed by the mixed momenta for an efficient constrained optimization based on the penalty method. In the stochastic part, we generate the adaptive stochastic momenta via the random selection of sub-functionals based on the adaptive momentum (Adam) method to solve the body-obstacle stuck case. Due to the slow convergence of the stochastic part, we integrate the accelerated gradient descent (AGD) to improve the planning efficiency. Moreover, we adopt the Bayesian tree inference (BTI) to transform the whole trajectory optimization (SAGO) into an incremental sub-trajectory optimization (iSAGO), which improves the computation efficiency and success rate further. Finally, we tune the key parameters and benchmark iSAGO against the other 5 planners on LBR-iiwa in a bookshelf and AUBO-i5 on a storage shelf. The result shows the highest success rate and moderate solving efficiency of iSAGO.

The problem of path planning in unknown environments remains a challenging problem - as the environment is gradually observed during the navigation, the underlying planner has to update the environment representation and replan, promptly and constantly, to account for the new observations. In this paper, we present a visibility graph-based planning framework capable of dealing with navigation tasks in both known and unknown environments. The planner employs a polygonal representation of the environment and constructs the representation by extracting edge points around obstacles to form enclosed polygons. With that, the method dynamically updates a global visibility graph using a two-layered data structure, expanding the visibility edges along with the navigation and removing edges that become occluded by newly observed obstacles. When navigating in unknown environments, the method is attemptable in discovering a way to the goal by picking up the environment layout on the fly, updating the visibility graph, and fast re-planning corresponding to the newly observed environment. We evaluate the method in simulated and real-world settings. The method shows the capability to attempt and navigate through unknown environments, reducing the travel time by up to 12-47% from search-based methods: A*, D* Lite, and more than 24-35% than sampling-based methods: RRT*, BIT*, and SPARS.

To develop an automated workflow for rectal cancer three-dimensional conformal radiotherapy treatment planning that combines deep-learning(DL) aperture predictions and forward-planning algorithms. We designed an algorithm to automate the clinical workflow for planning with field-in-field. DL models were trained, validated, and tested on 555 patients to automatically generate aperture shapes for primary and boost fields. Network inputs were digitally reconstructed radiography, gross tumor volume(GTV), and nodal GTV. A physician scored each aperture for 20 patients on a 5-point scale(>3 acceptable). A planning algorithm was then developed to create a homogeneous dose using a combination of wedges and subfields. The algorithm iteratively identifies a hotspot volume, creates a subfield, and optimizes beam weight all without user intervention. The algorithm was tested on 20 patients using clinical apertures with different settings, and the resulting plans(4 plans/patient) were scored by a physician. The end-to-end workflow was tested and scored by a physician on 39 patients using DL-generated apertures and planning algorithms. The predicted apertures had Dice scores of 0.95, 0.94, and 0.90 for posterior-anterior, laterals, and boost fields, respectively. 100%, 95%, and 87.5% of the posterior-anterior, laterals, and boost apertures were scored as clinically acceptable, respectively. Wedged and non-wedged plans were clinically acceptable for 85% and 50% of patients, respectively. The final plans hotspot dose percentage was reduced from 121%($\pm$ 14%) to 109%($\pm$ 5%) of prescription dose. The integrated end-to-end workflow of automatically generated apertures and optimized field-in-field planning gave clinically acceptable plans for 38/39(97%) of patients. We have successfully automated the clinical workflow for generating radiotherapy plans for rectal cancer for our institution.

This letter proposes traffic management for multiple automated mobile robots (AMRs) based on a layered cost map. Multiple AMRs communicate via a data distribution service (DDS), which is shared by topics in the same DDS domain. The cost of each layer is manipulated by topics. The traffic management server in the domain sends or receives topics to each of AMRs. Using the layered cost map, the new concept of prohibition filter, lane filter, fleet layer, and region filter are proposed and implemented. The prohibition filter can help a user set an area that would prohibit an AMR from trespassing. The lane filter can help set one-way directions based on an angle image. The fleet layer can help AMRs share their locations via the traffic management server. The region filter requests for or receives an exclusive area, which can be occupied by only one AMR, from the traffic management server. All the layers are experimentally validated with real-world AMRs. Each area can be configured with user-defined images or text-based parameter files.

We propose a novel approach for planning agents to compose abstract skills via observing and learning from historical interactions with the world. Our framework operates in a Markov state-space model via a set of actions under unknown pre-conditions. We formulate skills as high-level abstract policies that propose action plans based on the current state. Each policy learns new plans by observing the states' transitions while the agent interacts with the world. Such an approach automatically learns new plans to achieve specific intended effects, but the success of such plans is often dependent on the states in which they are applicable. Therefore, we formulate the evaluation of such plans as infinitely many multi-armed bandit problems, where we balance the allocation of resources on evaluating the success probability of existing arms and exploring new options. The result is a planner capable of automatically learning robust high-level skills under a noisy environment; such skills implicitly learn the action pre-condition without explicit knowledge. We show that this planning approach is experimentally very competitive in high-dimensional state space domains.

Autonomous agents operating in perceptually aliased environments should ideally be able to solve the data association problem. Yet, planning for future actions while considering this problem is not trivial. State of the art approaches therefore use multi-modal hypotheses to represent the states of the agent and of the environment. However, explicitly considering all possible data associations, the number of hypotheses grows exponentially with the planning horizon. As such, the corresponding Belief Space Planning problem quickly becomes unsolvable. Moreover, under hard computational budget constraints, some non-negligible hypotheses must eventually be pruned in both planning and inference. Nevertheless, the two processes are generally treated separately and the effect of budget constraints in one process over the other was barely studied. We present a computationally efficient method to solve the nonmyopic Belief Space Planning problem while reasoning about data association. Moreover, we rigorously analyze the effects of budget constraints in both inference and planning.

We investigate the problem of coordinating two robot arms to solve non-monotone tabletop multi-object rearrangement tasks. In a non-monotone rearrangement task, complex object-object dependencies exist that require moving some objects multiple times to solve an instance. In working with two arms in a large workspace, some objects must be handed off between the robots, which further complicates the planning process. For the challenging dual-arm tabletop rearrangement problem, we develop effective task planning algorithms for scheduling the pick-n-place sequence that can be properly distributed between the two arms. We show that, even without using a sophisticated motion planner, our method achieves significant time savings in comparison to greedy approaches and naive parallelization of single-robot plans.

We devise a 3D scene graph representation, contact graph+ (cg+), for efficient sequential task planning. Augmented with predicate-like attributes, this contact graph-based representation abstracts scene layouts with succinct geometric information and valid robot-scene interactions. Goal configurations, naturally specified on contact graphs, can be produced by a genetic algorithm with a stochastic optimization method. A task plan is then initialized by computing the Graph Editing Distance (GED) between the initial contact graphs and the goal configurations, which generates graph edit operations corresponding to possible robot actions. We finalize the task plan by imposing constraints to regulate the temporal feasibility of graph edit operations, ensuring valid task and motion correspondences. In a series of simulations and experiments, robots successfully complete complex sequential object rearrangement tasks that are difficult to specify using conventional planning language like Planning Domain Definition Language (PDDL), demonstrating the high feasibility and potential of robot sequential task planning on contact graph.